the length of a rectangualr park is twice its width. the aprk is surrounded by a 3foot wide path. write a quadratic function to represent the total area of the park and its path

Answers

Answer 1

The quadratic function to represent the total area of the park and its path is given by: f(x) = 2x² + 18x + 36.

In this problem, we are given that the length of a rectangular park is twice its width, and it is surrounded by a 3-foot wide path.

We are required to write a quadratic function to represent the total area of the park and its path.

The rectangular park can be represented as follows:

Length = 2x (twice the width)

Width = x

Therefore, the total length of the park including the 3-foot wide path can be represented as (2x + 2*3),

and the total width of the park including the 3-foot wide path can be represented as (x + 2*3).

The area of the park is given by the product of its length and width.

Thus, the area of the park can be represented as follows: Area of the park = (2x + 6)(x + 6)

To represent this as a quadratic function,

we can simplify the above expression using the distributive property.

Area of the park = 2x² + 6x + 12x + 36 = 2x² + 18x + 36.

For similar question on quadratic function.

https://brainly.com/question/29293854

#SPJ11


Related Questions

Help meee plssssss!!!!!!11

Write an explicit formula that can be used to find the number of bacteria cells after each generation. Then use the formula to find how many cells there are after 10 generations.

Answers

Answer:

N = N0 x 2^n

Step-by-step explanation:

The formula for calculating the number of bacteria cells after n generations is N = N0 x 2^n, where N is the total number of cells after n generations, N0 is the initial number of cells, and 2^n represents the number of times the population doubles after n generations. Assuming an initial population of 100 cells, there will be approximately 102,400 cells after 10 generations.

Answer:

The explicit formula for the number of bacteria cells after each generation can be written as:

N = N0 * r^n

Where:

N is the number of bacteria cells after n generations

N0 is the initial number of bacteria cells (at n=0)

r is the growth rate (how many new cells are produced per existing cell)

Assuming that each bacteria cell doubles in number with each generation (i.e. r=2), the formula can be simplified to:

N = N0 * 2^n

To find the number of cells after 10 generations, we can substitute n=10 into the formula:

N = N0 * 2^10

Since we don't have a specific value for N0, we can't find the exact number of cells after 10 generations. However, we can make some assumptions. For example, if we assume that there are initially 100 bacteria cells (N0=100), we can calculate:

N = 100 * 2^10 = 102,400

So, if each bacteria cell doubles in number with each generation and there were initially 100 cells, there will be 102,400 cells after 10 generations.

please thank me by marking my answer as brainlest!

Water tank A has 220 gallons of water and is being drained at a constant rate of 5 gallons per minute.
• Water tank B has 180 gallons of water and is being drained at a constant rate of 3 gallons per minute.
Part A
How much time, in minutes, do water tank A and water tank B have to be drained in order for them to have the same amount of water?
PART B
Which water tank, A or B, will be completely drained first?
How much less time, in minutes, will it take this water tank to completely drain than the other water tank?

Answers

By answering the presented question, we may conclude that

a) both tanks will have the same amount of water after 20 minutes.

b) difference in time required to thoroughly drain them is: 60 - 44 = 16 minutes.

What is equation?

An equation in mathematics is a statement that states the equality of two expressions. An equation is made up of two sides that are separated by an algebraic equation (=). For example, the argument "2x + 3 = 9" asserts that the phrase "2x + 3" equals the number "9." The purpose of equation solving is to determine the value or values of the variable(s) that will allow the equation to be true. Equations can be simple or complicated, regular or nonlinear, and include one or more elements. The variable x is raised to the second power in the equation "x2 + 2x - 3 = 0." Lines are utilised in many different areas of mathematics, such as algebra, calculus, and geometry.

Part A:

Let's assume that after t minutes, the amount of water remaining in tank A is x gallons, and the amount of water remaining in tank B is also x gallons. We can write equations based on the given information:

Tank A: x = 220 - 5t

Tank B: x = 180 - 3t

To find the time when both tanks have the same amount of water, we can set these two equations equal to each other and solve for t:

220 - 5t = 180 - 3t

40 = 2t

t = 20

Therefore, both tanks will have the same amount of water after 20 minutes.

Part B:

To determine which tank will be completely drained first, we need to find the time it takes for each tank to be completely drained. For tank A, we can set x = 0 in the equation we found in part A:

0 = 220 - 5t

t = 44

So it will take 44 minutes for tank A to be completely drained.

For tank B, we can set x = 0 in the equation given in the problem:

0 = 180 - 3t

t = 60

So it will take 60 minutes for tank B to be completely drained.

Therefore, tank A will be completely drained first. The amount of time it takes for tank A to be completely drained is 44 minutes, and the amount of time it takes for tank B to be completely drained is 60 minutes. The difference in time is:

60 - 44 = 16 minutes.

The difference in time required to thoroughly drain them is: 60 - 44 = 16 minutes.

To know more about equation visit:

brainly.com/question/649785

#SPJ1

begging for help lol pleaseee

Answers

Step-by-step explanation:

Find the area of the yellow circle using pie times radius squared. Then find the area of the entire circle using the same formula then take the answer for the area of the entire circle - area of the yellow circle

Rita started the day with R apps. then she deleted 5 apps and still had twice the amount of Cora (36). write an equation that represents the number of apps both girls have

Answers

Answer:

Step-by-step explanation:lllllLet's start by using "R" to represent the number of apps that Rita started with, and "C" to represent the number of apps that Cora started with.

We know that Rita deleted 5 apps, so she would have (R-5) apps remaining. And we know that she still had twice the amount of Cora, which is 36.

So we can write the equation:

R-5 = 2C

And we also know that Cora had 36 apps, so we can substitute that value in for C:

R-5 = 2(36)

Simplifying the right side:

R-5 = 72

Finally, we can solve for R by adding 5 to both sides:

R = 77

So Rita started with 77 apps, and Cora started with 36 apps. We can check that Rita deleted 5 and had twice as many as Cora by plugging our values into the original equation:

77 - 5 = 72

2(36) = 72

Both sides are equal, so our solution is correct.

A. ASA
B. SAS
C. HL
D. none of the above

Answers

Therefore , the solution of the given problem of congruence comes out to be the response is option A. ASA.

Congruence: What is it?

Two angles are spoken to be congruent when their respective shapes have the same dimensions. Similar to that, if the sides of one form are now exactly the same length as the edges of another figure, the edges are congruent.

Here,

We can identify the sort of congruence between the two triangles based on the provided figure.

We can see that segment AC and segment DF are the only pair of congruent sides shared by the two rectangles.

Additionally, angle A and angle D as well as angle C and angle F are two sets of congruent angles.

In light of this,

we can use the Angle-Side-Angle (ASA)

congruence criterion, which says that two triangles are congruent if they have two pairs of congruent angles and a congruent side between them.

Therefore, the response is A. ASA.

To know more about congruence , visit:

https://brainly.com/question/7888063

#SPJ1

Which function results after applying the sequence of transformations to
f(x) = x5?
• stretch vertically by 3
• translate up 1 unit
• translate left 2 units

Answers

Answer:

[tex]3(x + 2)^5 + 1[/tex]

Step-by-step explanation:

we have,

[tex]y = x^5[/tex]

1. stretch vertically up by 3

[tex]y = 3x^5[/tex]

2. translate up 1 unit (Y = y + 1)

[tex]y = 3x^5 + 1[/tex]

3. translate left 2 units (X = x + 2)

[tex]y = 3(x + 2)^5 + 1[/tex]

Hopefully this answer helped you!!!

Find the distance traveled by a particle with position ( x, y ) as t varies in the given time interval. Compare with the length of the curve.
x=sin^2(theta) , y=cos^2(theta) 0

Answers

The distance traveled is equal to sin^2(θ), as seen before.

To find the distance traveled by a particle with position (x, y) as t varies in the given time interval, we need to first find the parametric equations for x and y in terms of t, and then compute the arc length of the curve.

Given x = sin^2(t) and y = cos^2(t), we first find the derivatives of x and y with respect to t:
dx/dt = 2 * sin(t) * cos(t)
dy/dt = -2 * sin(t) * cos(t)

Next, we compute the square root of the sum of the squares of the derivatives:
sqrt((dx/dt)^2 + (dy/dt)^2) = sqrt((2 * sin(t) * cos(t))^2 + (-2 * sin(t) * cos(t))^2) = sqrt(4 * sin^2(t) * cos^2(t) + 4 * sin^2(t) * cos^2(t)) = 2 * sin(t) * cos(t)

Now, we can find the distance traveled by integrating the above expression with respect to t over the given time interval (0, θ):

Distance traveled = ∫(2 * sin(t) * cos(t) dt) from 0 to θ

Using the substitution u = sin(t), du = cos(t) dt, we get:

Distance traveled = ∫(2 * u du) from 0 to sin(θ)

Now, integrating with respect to u, we get:

Distance traveled = u^2 | from 0 to sin(θ) = (sin^2(θ)) - (0^2) = sin^2(θ)

The length of the curve can be computed as the arc length:

Length of the curve = ∫(2 * sin(t) * cos(t) dt) from 0 to θ

As we computed earlier, the distance traveled is equal to sin^2(θ). Therefore, the distance traveled by the particle is the same as the length of the curve.

To know more about distance, visit:

https://brainly.com/question/29055485#

#SPJ11

A gamer is observing her score, y, as she plays a video game. She currently has 3,200 points and is gaining 200 points for every minute, x, she plays.

Which of the following equations can be used to describe this linear relationship?

A. y = 3,200x − 200
B.y = 3,200x + 200
C. y = 200x − 3,200
D. y = 200x + 3,200

Answers

Answer: d

Step-by-step explanation:

the slope is positive 200 because she is gaining 200 points for every minute which is x. 200x or 200 multiplied by x is her slope and her y intercept is 3200

solve for x and find it​

Answers

[tex]\frac{65x-14x+49-4}{14} = 36[/tex]The value of x is 9.

What is inquality?

Inequality refers to a situation where there is a significant difference in the distribution of resources, opportunities, and power among individuals or groups in a society. It is a complex social and economic phenomenon that can manifest in various forms such as income inequality, wealth inequality, gender inequality, racial inequality, educational inequality, and healthcare inequality, among others.

Given by the question.

[tex]\frac{9x+7}{2} - \frac{7x-x+2}{7} = 36[/tex]

[tex]\frac{63x+44-14x+2x+4}{14} = 36[/tex]

[tex]\frac{65x-14x+49-4}{14} = 36[/tex]

[tex]51x+45=504\\51x= 459\\x=9[/tex]

To learn more about inquality:

https://brainly.com/question/29072717

#SPJ1

what is the probability that in a particular crossing, there are total 10 pedestrian and they are all crossing from left to right?

Answers

The probability of having exactly 10 pedestrians crossing from left to right during a 2-minute period is extremely low, at approximately 0.00118%.

We can approach this problem by using the Poisson distribution, which describes the probability of a certain number of events occurring within a given time period, given a known rate of occurrence.

Let X be the number of pedestrians crossing from left to right during a 2-minute period. Since the arrival processes from the left and right sides are independent Poisson processes with rates λL and λR, respectively, we can model X as a Poisson random variable with rate λ = λL + λR = 6.

Therefore, the probability of having exactly k pedestrians crossing from left to right during a 2-minute period is given by the Poisson distribution:

P(X = k) = (e^(-λ) * λ^k) / k!

Now we want to find the probability that in a particular crossing, there are a total of 10 pedestrians crossing from left to right. Let Y be the total number of pedestrians crossing in both directions during a 2-minute period.

Since the arrival processes from the left and right sides are independent, we can model Y as a Poisson random variable with rate 2λ = 12.

Since we know that there are 10 pedestrians crossing from left to right, there must be a total of 10 pedestrians crossing in both directions. Therefore, we want to find the probability that out of the 10 pedestrians, exactly 10 of them are crossing from left to right.

We can use the binomial distribution to calculate this probability. Let Z be the number of pedestrians crossing from left to right out of the 10 pedestrians. Since each pedestrian has an independent probability of crossing from left to right of 1/2, we have:

P(Z = 10) = (10 choose 10) * (1/2)^10

= 1/1024

Therefore, the probability that in a particular crossing, there are a total of 10 pedestrians and they are all crossing from left to right is:

P(X = 10, Y = 10) = P(X = 10) * P(Z = 10)

= (e^(-6) * 6^10 / 10!) * (1/1024)

≈ 0.0000118

Writing this probability in percentage gives = 0.0000118 x 100% = 0.00118%

To learn more about probability click on,

https://brainly.com/question/14937880

#SPJ4

Complete question is:

Pedestrians approach a crossing from the left and right sides following independent Poisson processes with average arrival rates of λL = 5 and λR = 1 arrivals per minute. Each pedestrian then waits until a light is flashed, at which time all waiting pedestrians must cross to the opposite side (either from left to right or from right to left). Assume that the left and right arrival processes are independent, that the light flashes every T = 2 minutes, and that crossing takes zero time – it is instantaneous.

1. What is the probability that in a particular crossing, there are total 10 pedestrian and they are all crossing from left to right?

a random sample is normally distributed. if all values in the sample and all values in the population are multiplied by 2, what is the impact on cohen's d?

Answers

Multiplying values by 2 in a normally distributed random sample and population increases the effect size as measured by Cohen's d.

The impact of multiplying all values in a normally distributed random sample and population by 2 on Cohen's d is an increase in effect size. Cohen's d measures the degree of difference between two sets of scores, calculated by dividing the difference between the two means by the pooled standard deviation. Therefore, when values are multiplied by 2, the means increase, leading to an increase in effect size as measured by Cohen's d.

In addition, multiplying values by 2 also increases the magnitude of the standard deviation, which is a measure of spread. When the standard deviation is larger, it requires a larger mean difference for Cohen's d to register a significant effect. Therefore, by increasing the standard deviation, the effect size measure will increase.

To summarize, multiplying values by 2 in a normally distributed random sample and population increases the effect size as measured by Cohen's d. This is because multiplying values by 2 increases both the mean and the standard deviation, which results in a larger mean difference and a larger standard deviation, respectively. Consequently, the effect size measure increases.

See more about normally distributed at: https://brainly.com/question/2579706

#SPJ11

WHAT IS THE ANSWER
I NEED HELP ASAP

Answers

Answer: yes, yes, no

Explanation: In order for a figure to be a triangle, the two smallest sides must add up to be larger than the biggest side. The reason why the last one isn't a triangle is because 6+8 EQUALS 14 and is not greater than 14.

a 3 didget whole number thats divisBle by 6,9,4

Answers

gtrgrghtrhthjAnswer:

Step-by-step explanation:

g

Answer:

36

Step-by-step explanation:

4*9=36

9*4=36

6*5=36

ASAP

Ω = {whole numbers from 2 to 9} A = {even numbers} B = {prime numbers} List the elements in:
a. A’
b. A∩B
c. A∪B

Answers

Answer:

a. A' = {3, 5, 7, 9} (complement of A)

b. A∩B = {2} (intersection of A and B, which contains only the even prime number 2)

c. A∪B = {2, 4, 6, 8, 3, 5, 7} (union of A and B, which contains all even numbers and all prime numbers between 2 and 9)

I will give brainliest to whoever gets it right first along with 20 points. ONLY ANSWER IF YOU KNOW IT!!!!

Answers

Ms. Leon will have a total of $840 in her savings account by the end of 4 years.

To calculate the total amount that Ms. Leon will have in her account at the end of 4 years with simple interest, we can use the following formula:

A = P(1 + rt)

where:

A = the total amount in the account at the end of the time period

P = the principal amount (initial deposit)

r = the annual interest rate (as a decimal)

t = the time period (in years)

Putting in the given values, we get:

A = 750(1 + 0.03 × 4)

A = 750(1.12)

A = $840

Therefore, at the end of 4 years, Ms. Leon will have a total of $840 in her savings account.

To know more about the simple interest visit:

https://brainly.com/question/25845758?

#SPJ1

during a one-month promotional campaign, tiger films gave either a free dvd rental or a 12-serving box of microwave popcorn to new members. it cost the store $1 for each free rental and $2 for each box of popcorn. a total of 89 new members were signed up and the store's cost for the incentives was $135. how many of each incentive were given away?

Answers

By using system of equations, there are 43 free DVD rentals and 46 boxes of microwave popcorn were given away during the promotional campaign.

Let's use the following variables

x: the number of free DVD rentals given away

y: the number of boxes of microwave popcorn given away

We can set up a system of equations to represent the given information:

x + y = 89 (total number of new members signed up)

1x + 2y = 135 (total cost of the incentives)

We can solve for x or y in the first equation and substitute into the second equation

x = 89 - y

1(89 - y) + 2y = 135

89 - y + 2y = 135

y = 46

Substituting y = 46 into the first equation:

x + 46 = 89

x = 43

Therefore, 43 free DVD rentals and 46 boxes of microwave popcorn.

To know more about System of equations:

https://brainly.com/question/12895249

#SPJ4

If f(1) = 10, and f(n) = f(n-1) + 4, then find the value of
ƒ (4).

Answers

The value of f(4) using recursive formula f(1) = 10 and f(n) = f(n-1) + 4 for n ≥ 2  is 22

Finding the Value of f(4) Using Recursive Formula

Given that f(1) = 10 and f(n) = f(n-1) + 4 for n ≥ 2.

To find the value of f(4), we can use the recursive formula to work our way up from f(1) to f(4):

Using the above as a guide, we have the following:

f(2) = f(1) + 4 = 10 + 4 = 14

Next, we have

f(3) = f(2) + 4 = 14 + 4 = 18

Next, we have

f(4) = f(3) + 4 = 18 + 4 = 22

Therefore, the value of f(4) is 22.

Read more about sequence at

https://brainly.com/question/29431864

#SPJ1

how do these histograms demonstrate what the central limit theorem says about the sampling distribution model for sample means.

Answers

The histograms demonstrate that as sample size increases, the distribution of sample means becomes more normal, which is in line with the central limit theorem.

Histograms can be used to graphically represent a probability distribution, which is a measure of how likely it is that a random variable will take on a particular value.

The central limit theorem states that as the sample size increases, the sampling distribution of the mean approaches a normal distribution, regardless of the shape of the population distribution.

The histograms demonstrate this by showing the distribution of sample means for different sample sizes. As the sample size increases, the shape of the histogram becomes more normal, with a narrower and taller distribution.

Therefore, this demonstrates that the central limit theorem holds true, as the distribution of sample means becomes more normal as sample size increases, regardless of the shape of the population distribution.

To know more about population distribution refer here:

https://brainly.com/question/1539005?

#SPJ11

What is the standard form of the equation of the circle with the center and a radius of square 2 divided by 4

Answers

The standard form of the equation of the circle with center and radius of square 2 divided by 4 is (x - 1/2)² + (y + 1/2)² = 1/8.

The standard form of the equation of a circle is (x - h)² + (y - k)² = r², where (h, k) is the center of the circle and r is the radius.

To use this formula, we first need to find the values of h, k, and r for the given circle with center and radius of square 2 divided by 4.

We know that the center of the circle is (h, k) = (2/4, -2/4) = (1/2, -1/2).

This means that h = 1/2 and k = -1/2.

The radius of the circle is r = square 2 divided by 4.

We can write this as r² = (square 2 divided by 4)² = 2/16 = 1/8.

Now we can substitute these values into the standard form equation to get:

(x - 1/2)² + (y + 1/2)² = 1/8

So the standard form of the equation of the circle with center and radius of square 2 divided by 4 is (x - 1/2)² + (y + 1/2)² = 1/8.

for such more question on standard form

https://brainly.com/question/19169731

#SPJ11

130.25.122.63mario's pizzeria bakes olive pieces in the outer crust of its 20-inch (diameter) pizza. there is at least one olive piece per inch of crust. how many olive pieces will you get in one slice of pizza? assume the pizza is cut into eight slices.

Answers

By using circumference of circle, we find that In one slice of pizza you will get about 8 olive pieces from Mario's Pizzeria.

The circumference of circle of a 20-inch diameter pizza can be calculated as follows:

Circumference = π × diameter

Circumference = 3.14 × 20

Circumference = 62.8 inches

If there is at least one olive piece per inch of crust, then there will be 62.8 olive pieces on the outer crust of the entire pizza.

If the pizza is cut into eight slices, each slice will have 1/8th of the total circumference of the pizza. Therefore, each slice will have:

62.8 inches ÷ 8 slices = 7.85 inches of outer crust

Since there is at least one olive piece per inch of crust, each slice will have approximately 8 olive pieces on the outer crust.

Therefore, you can expect to get about 8 olive pieces in one slice of pizza from Mario's Pizzeria.

To know more about circumference of circle:

https://brainly.com/question/26605972

#SPJ4

suppose the average price for new cars has a mean of $30,100, a standard deviation of $5,600 and is normally distributed. based on this information, what interval of prices would we expect at least 95% of new car prices to fall within?

Answers

New car prices to fall within is $18,300 - $41,900

Interval of prices would we expect at least 95% of new car prices to fall within Suppose that the average price for new cars has a mean of $30,100, a standard deviation of $5,600 and is normally distributed. Based on this information, the interval of prices that we would expect at least 95% of new car prices to fall within is $18,300 - $41,900.How to solve the problem? We know that the average price of new cars is $30,100 and the standard deviation is $5,600. The normal distribution has 95% of the data points within two standard deviations of the mean. Therefore, the interval of prices that we would expect at least 95% of new car prices to fall within is given by:Lower limit: $30,100 - 2 × $5,600 = $18,300Upper limit: $30,100 + 2 × $5,600 = $41,900Thus, the interval of prices that we would expect at least 95% of new car prices to fall within is $18,300 - $41,900.

Learn more about Standard deviation

brainly.com/question/23907081

#SPJ11

a high school baseball player has a 0.253 batting average. in one game, he gets 8 at bats. what is the probability he will get at least 6 hits in the game?

Answers

The probability of a high school baseball player getting at least 6 hits in one game, given a 0.253 batting average, when he gets 8 at-bats, is 0.0197 or approximately 2%.


Given, the high school baseball player's batting average is 0.253, which means in 100 times he hits the ball, he will make 25.3 hits on average. We need to find the probability of getting at least 6 hits in a game when he gets 8 at-bats.

We will calculate the probability using the Binomial Probability formula. Here, the number of trials is 8, and the probability of success is 0.253. We need to find the probability of getting at least 6 hits.

P(X≥6) = 1 - P(X<6)

P(X<6) = ∑P(X=i), i=0 to 5

We can use the Binomial Probability Table to find these probabilities or use the Binomial Probability formula.

P(X<6) = P(X=0) + P(X=1) + P(X=2) + P(X=3) + P(X=4) + P(X=5)

= C(8,0) (0.253)^0 (1 - 0.253)^8 + C(8,1) (0.253)^1 (1 - 0.253)^7 + C(8,2) (0.253)^2 (1 - 0.253)^6 + C(8,3) (0.253)^3 (1 - 0.253)^5 + C(8,4) (0.253)^4 (1 - 0.253)^4 + C(8,5) (0.253)^5 (1 - 0.253)^3

≈ 0.9799

Therefore, P(X≥6) = 1 - 0.9799

= 0.0201 or approximately 2%.

Hence, approximately 0.0197 or 1.97% is the probability of a high school baseball player, who has a batting average of 0.253, obtaining at least 6 hits when given 8 at-bats during a single game.

To know more about probability refer here:

https://brainly.com/question/1596693#

#SPJ11

Triangle ABC has vertices at A(−4, 3), B(0, 5), and C(−2, 0). Determine the coordinates of the vertices for the image if the preimage is translated 4 units down.

A′(−4, −1), B′(0, 1), C′(−2, −4)
A′(−4, 7), B′(0, 9), C′(−2, 4)
A′(0, 3), B′(4, 4), C′(3, 0)
A′(−8, 7), B′(−4, 9), C′(−6, 4)

Answers

The coordinates of the vertices for the image if the preimage is translated 4 units down are A′(-4, -1), B′(0, 1), C′(-2, -4).

What is meant by preimage?

In geometry, a preimage is the original figure or shape before any transformation is applied. It is the initial configuration of the object that is being transformed. For example, if we have a square and we rotate it by 90 degrees, the original square is the preimage and the resulting figure after the rotation is the image.

To translate the preimage 4 units down, we need to subtract 4 from the y-coordinates of all vertices. Therefore, the coordinates of the image vertices are:

A′(-4, 3-4) = (-4, -1)

B′(0, 5-4) = (0, 1)

C′(-2, 0-4) = (-2, -4)

Therefore, the vertices of the image triangle are A′(-4, -1), B′(0, 1), and C′(-2, -4).

So, the correct option is: A′(-4, -1), B′(0, 1), C′(-2, -4).

To learn more about preimage visit:

https://brainly.com/question/30093252

#SPJ1

The graph of a quadratic function with vertex (-3, - 1)
Find the range and the domain.

Answers

Therefore  the range of the quadratic function with vertex (-3, -1) is y ≥ -1 and the domain is all real number and the Domain is real numbers .

How to the range ?

A quadratic function's vertex form is given by:

[tex]y = a(x - h)^2 + k[/tex]

where (h, k) is the parabola's vertex. In this instance, we have:

[tex]h = -3, k = -1[/tex]

So the quadratic function's equation is:

[tex]y = a(x + 3)^2 - 1[/tex]

To determine the function's range, we must first determine the minimum value of y. Because the squared term's coefficient is positive, the parabola opens upwards and the vertex is a minimum point. As a result, the range is:

Range: y ≥ -1

To determine the function's domain, we must first determine the set of all x-values for which the function is defined. Due to the fact that a quadratic function is defined for all real numbers, the domain is:

Domain: All real numbers

So the domain of the quadratic function with vertex (-3, -1) is all real numbers, and its range is y -1.

To know more about quadratic function visit:-

https://brainly.com/question/29775037

#SPJ9

Given f(x)=5x+7 and g(x)=2x+2, find g(g(1-3w))

Enter as the final value or expression without parentheses

Answers

As a result, the final number or expression is g(g(1-3w)) ≈ -12w + 10 (without parenthesis).

Which of these are they known as?

When adding extraneous information or perhaps an afterthought to a sentence, parentheses, a pair or punctuation marks, are most frequently utilized. Two curving vertical lines can be seen in parentheses: ( ).

We must first evaluate g(1-3w) and then re-insert that result into g(x) in order to determine g(g(1-3w)).

We must first determine g(1-3w):

Substitute x with 1-3w to get g(x) ≈ 2x + 2 and g(1-3w) ≈ 2(1-3w) + 2.

g(1-3w) ≈ 2 - 6w + 2  (distribute the 2)

g(1-3w) ≈ -6w + 4 (combine similar terms) (combine like terms)

We can again again enter the result of g(1-3w) into g(x):

If you substitute g(1-3w) for x, then g(x) ≈ 2x + 2 g(g(1-3w)) ≈ 2(-6w Plus 4) + 2

g(g(1-3w)) ≈ -12w + 8 + 2 (allocate the 2) (distribute the 2)

g(g(1-3w)) ≈ -12w + 10 (combine comparable terms) (combine like terms)

To know more about parentheses visit:

https://brainly.com/question/28146414

#SPJ1

Find the x-intercept of 3 tan(3x) over the interval (pi/6,3pi/6)
Express your answer in terms of pi.

Answers

The x-intercepts of the function 3 tan(3x) over the interval (π/6, 3π/6) are:

x = π/3 and x = 2π/3

What is function ?

A function is a mathematical object that takes one or more inputs, called the arguments or variables, and produces a unique output. The output is determined by a set of rules that specify how the function operates on the inputs. In other words, a function is a relationship between inputs and outputs.

Functions are typically denoted by a symbol or a name, such as f(x) or g(t). The input is usually represented by a variable, such as x or t, while the output is represented by the function value, such as f(x) or g(t).

Functions are used extensively in mathematics, science, engineering, and many other fields. They provide a way to model and analyze real-world phenomena, and they are essential tools for solving many problems in these fields. Examples of functions include polynomial functions, exponential functions, trigonometric functions, and logarithmic functions.

To find the x-intercept of the function 3 tan(3x) over the given interval, we need to find the values of x where the function equals zero.

Let's first simplify the function:

3 tan(3x) = 0

tan(3x) = 0

We know that tan(π/2) is undefined and that tan(π) = 0. Since the period of the tangent function is π, we can say that:

tan(3x) = 0 --> 3x = nπ for n ∈ ℤ

Now we solve for x:

3x = nπ

x = nπ/3

Since the interval is (π/6, 3π/6), we need to find the values of x that satisfy:

π/6 < x < 3π/6

π/6 < nπ/3 < 3π/6

1/2 < n < 3/2

So the values of x that satisfy the given condition are:

x = π/3 and x = 2π/3

Therefore, the x-intercepts of the function 3 tan(3x) over the interval (π/6, 3π/6) are:

x = π/3 and x = 2π/3

Expressed in terms of π, the x-intercepts are:

π/3π and 2π/3π, which simplify to:

x = 1/3 and x = 2/3.

To know more about Trigonometry visit :-

https://brainly.com/question/13729598

#SPJ1

Ms. Sanchez is planning two projects for her student’s final assignment. Each student will have an equal chance of selecting Project A or Project B. Ms. Sanchez flips a coin to represent each student’s choice, with heads representing Project A and tails representing Project B. After 110 trials, there are 58 heads and 52 tails. To the nearest percent, what is the experimental probability of Project A?

Answers

Answer:

Step-by-step explanation:

Ms. Sanchez is planning two projects for her student’s final assignment. Each student will have an equal chance of selecting Project A or Project B. Ms. Sanchez flips a coin to represent each student’s choice, with heads representing Project A and tails representing Project B. After 110 trials, there are 58 heads and 52 tails.

To the nearest percent, what is the experimental probability of Project B?

The experimental probability of Project A is 0.53.

What is Probability?

A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1.

As per the given data:

We are given that there are two projects, Project A and Project B.

A student has to choose one out of the two projects and, the student's choice is represented by the flip of a coin where heads representing Project A and tails representing Project B.

Head's = Project A

Tail's = Project B

Total number of trials = 110

Number of heads in the trials = 58 heads

Number of tails in the trials = 52 tails

For finding out the experimental probability of Project A:

= Number of favorable outcomes / Total number of trials

Number of favorable outcomes = Number of heads

= Number of heads / Total number of trials

= 58 / 110

= 0.53 (approx)

The experimental probability of Project A is 0.53.

Hence, The experimental probability of Project A is 0.53.

To learn more on Probability, click:

brainly.com/question/30034780

#SPJ2

a counseling service records the number of calls to their hotline for the last year. what is the forecast for august if the forecast for june was 164 and the service uses exponential smoothing with an alpha of 0.7?

Answers

Forecast for August with an alpha of 0.7 and forecast of June 164 are to be calculated using exponential smoothing.

Exponential smoothing is a forecasting method that uses a weighted average of past time-series values to forecast future values. In a time-series, data values are obtained over time, such as over months or years, and then plotted in sequence.

The weights decrease exponentially as the observations get older. The EWMA formula used in exponential smoothing is as follows:

St=α × Yt-1+(1-α) × St-1

where,St is the smoothed statistic for the current period tYt is the original observation for the current period tSt-1 is the smoothed statistic for the previous period t-1α is the smoothing parameter 0≤α≤1, and usually close to 0.1.The smoothed statistic is also called the exponentially weighted moving average (EWMA).Calculating the forecast for August with alpha=0.7 and forecast of June 164 as follows:

St=α × Yt-1+(1-α) × St-1St =0.7 × 164+(1-0.7) × 164St=164

for such more question on exponential smoothing

https://brainly.com/question/15061467

#SPJ11

Divide. Write the answer in simplest form.

6 and 3/5÷ 3/4

Answers

Answer:

44/5

Step-by-step explanation:

6 3/5 ÷ 3/4

6 3/5 = 33/5

33/5 ÷ 3/4 = 33/5 × 4/3 = 132/15 = 44/5

So, the answer is 44/5

Answer:

Step-by-step explanation:

1) Write the equation

[tex]\frac{3}{5}[/tex] ÷ [tex]\frac{3}{4}[/tex] = ?

2) Multiply by the reciprocal of [tex]\frac{3}{4}[/tex]

[tex]\frac{3}{5}[/tex] × [tex]\frac{4}{3}[/tex] =?

3) Cancel out the GCF 3

[tex]\frac{1}{5}[/tex] × 4 =?

4) Solve

[tex]\frac{4}{5}[/tex] or 0.8

Mitchell orders a plain turkey sandwich and a drink for lunch. The drink is $2.95
. Instead he is served the super sandwich with lettuce, tomato, and mayonnaise. The restaurant manager takes 15%
off the price of the sandwich.

Write an equation to determine the original price of Mitchell’s sandwich, x
, if his new bill is $8.86
.

Enter the correct equation in the box.

Answers

Answer:

7$

Step-by-step explanation:

Other Questions
Plot a point that best represents the value of square root 215 on the number line determine the value of the enthalpy change for the following reaction using the information below H2O(l) to H2O (g) Ch4(g)+2o2 to co2+2h2o(l) Ch4+2o2 to co2 +2h2o(g) which of the following statements is true of operations management (om)? a. the application of the concepts and methods of om is limited to the technology industry. b. om is the only function by which managers can directly affect the value provided to all stakeholders. c. the activities involved in om focus on creating value solely for external customers. Where can freshwater aquatic life zones NOT be found?O mangrove communitiesstreamsinland wetlandslakes2 points Find the value of x. there are 3 soccer games in a month, and 8 are played at night. the season is 4 months. how many games are the season? an investor purchases a zero coupon bond with 22 years to maturity at a price of $311.99. the bond has a par value of $1,000. what is the implicit interest for the first year? assume semiannual compounding. species diversity, genetic diversity and habitat diversity are interlinked. explain the link between the different types of diversity __________ has the second largest population in the world and is a major source of technological and scientific brainpower. during which stage of team development is high performance not a top priority and attention is devoted to wrapping up the project? What value is reflected in both the photograph and the poster? a school-age child is seen in the family clinic. the parents ask the nurse if their child should start taking growth hormones to help the child grow because the parents are short. what is the best response by the nurse? failure to perform an action that a reasonable person would have performed in a similar situation is A tsunami brings a bunch of new sand onto a beach in a coastal region and newsand dunes develop. This region will undergosuccessionto become a climax community which 2 reports could be used to verify that the retirement contributions were accurately remitted for the most recent payroll period? What describes the primary purpose of the House and the Senate opinion del diario de ana frank the biggest reason for performing drug tests is to a. increase company profits. b. increase customer confidence. c. protect lives. d. protect assets if individuals lack the enzyme that converts phosphoenolpyruvate to pyruvate, what would you expect to happen to the concentration of 2-phosphoglycerate as an immediate consequence? Life decision pls help so heres my problem when I look at the screen for a long time my eye gets like red like strings going to my eye and this happens both two my left and right eye from both sides and one eye is blurry and other is not when I look from fat and something when I look its blurry from far with both eyes?