Which are the roots of the quadratic function f(b) = b² - 75? Select two options.
Ob=5√3
Ob=-5√3
Ob=3√5
Ob=-3√5
Ob=25√3

Answer: A. g(x) = 4∛x

Step-by-step explanation:

First, g(x) passes through the origin (0,0)

g(0) = 0

A,g(x) = ∛x+4,  g(0) = 4 ≠ 0

B,g(x) =  ∛x+4,  g(0) = ∛4≠0

So exclude A and B

Second, as can be seen in the figure,

The g(x) image is the magnification of the f(x) image on the y value.

f(x) = ∛x

So, Select A. g(x) = 4∛x quadruple the y value.

The tax charged on Omari's monthly earning of Ksh 24,200 is Ksh 3,340.

To calculate the tax charged on Omari's monthly earning, we need to consider the tax brackets and rates applicable in the specific tax system or country. Since you haven't specified a particular tax system, I will provide a general explanation.

Assuming we have a simplified progressive tax system with three tax brackets:

For the first tax bracket, let's say income up to Ksh 10,000 is taxed at a rate of 10%.

For the second tax bracket, income between Ksh 10,001 and Ksh 20,000 is taxed at a rate of 15%.

For the third tax bracket, income above Ksh 20,000 is taxed at a rate of 20%.

To calculate the tax charged on Omari's monthly earning of Ksh 24,200, we can divide it into the respective tax brackets:

Ksh 10,000 falls in the first tax bracket. So, the tax for this portion is 10% of Ksh 10,000, which is Ksh 1,000.

Ksh 20,000 - Ksh 10,000 = Ksh 10,000 falls in the second tax bracket. The tax for this portion is 15% of Ksh 10,000, which is Ksh 1,500.

The remaining amount, Ksh 24,200 - Ksh 20,000 = Ksh 4,200, falls in the third tax bracket. The tax for this portion is 20% of Ksh 4,200, which is Ksh 840.

Now, we can sum up the taxes for each bracket:

Total Tax = Tax in the first bracket + Tax in the second bracket + Tax in the third bracket

Total Tax = Ksh 1,000 + Ksh 1,500 + Ksh 840

Total Tax = Ksh 3,340

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Answer:

[tex]{A = 20000(1 + \frac{0.0625}{4})^{4t}}[/tex]

Step-by-step explanation:

The question asks us to find an expression for compound interest for the given scenario.

To do this, we have to use the following formula for compound interest:

[tex]\boxed{A = P(1 + \frac{r}{n})^{nt}}[/tex]

where:

• A ⇒ final amount

• P ⇒ principal amount = $20,000

• r ⇒ interest rate (decimal) = [tex]\frac{6.25}{100}[/tex] = 0.0625

• n ⇒ number of times interest is compounded per year = 4

• t ⇒ time in years

Therefore, if we substitute the data above into the formula, we can find the required expression:

[tex]{A = 20000(1 + \frac{0.0625}{4})^{4t}}[/tex]

`Both Meg and Cassandra are incorrect in their assessments (option a).

Meg and Cassandra have both misunderstood the logical relationships between the statements. Let's analyze each statement and compare their claims:

Statement 1: "If she is stuck in traffic, then she is late."

Statement 2: "If she is late, then she is stuck in traffic."

Statement 3: "If she is not late, then she is not stuck in traffic."

Meg's claims: Meg states that Statement 3 is the inverse of Statement 2 and the contrapositive of Statement 1. However, this is incorrect. The inverse of Statement 2 would be "If she is not stuck in traffic, then she is not late," and the contrapositive of Statement 1 would be "If she is not late, then she is not stuck in traffic." So Meg's analysis is incorrect.

Cassandra's claims: Cassandra states that Statement 2 is the converse of Statement 1 and the inverse of Statement 3. However, this is also incorrect. The converse of Statement 1 would be "If she is late, then she is stuck in traffic," and the inverse of Statement 3 would be "If she is late, then she is stuck in traffic." So Cassandra's analysis is incorrect as well.

Therefore, both Meg and Cassandra are wrong in their assessments. The correct logical relationships are as follows:

- The contrapositive of Statement 1 is Statement 3.

- The converse of Statement 1 is Statement 2.

Hence, the correct answer is that both Meg and Cassandra are incorrect.

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Answer:

$248.00

Step-by-step explanation:

Hours worked on Friday:  6 hr and 30 min = 6.5 hr

Money earned on Friday:  $15.5/hr x 6.5 hr = $100.75

Hours worked on Saturday:  6.5 hr - 1.167 hr = 5.33   *10 min = 10/60 = 0.1667 hr

Money earned on Saturday:  $15.50 x 5.33 hr = $82.67

Hours worked on Monday:  4.167 hr

Money earned on Monday:  $15.50/hr x 4.167 hr = $64.58

Total money made:  100.75 + 82.67 + 64.58 = $248.00

Answer:

m = -3

Step-by-step explanation:

The slope-intercept form is y = mx + b

m = the slope

b = y-intercept

The equation is  y = -3x + 2

m = -3

So, the slope of the line is -3

Answer:

The slope is -3

Step-by-step explanation:

You were given the easiest form of linear equation, the slope-intercept form, because these are the ones that directly tell you the slope and       the y-intercept.

y=mx+b, Where m is the slope and b is the y-intercept.

Step-by-step explanation:

Parallel to the x-axis means it is just a horizontal line with the value being the y-coordinate of the point:

y = -2

Answer:

y=-2

and m=0 must be your answer

Step-by-step explanation:

as line is parallel to x axis its slope will be zero as it does not have any definite x coordinate

so

equation of line is y-y'=m(x-x')

so m=0 m is slope

y'=-2 and x'=4

so by substituting the values

y+2=0

so y=-2

and m=0 is your answer

The length of BD is 22.

In the given scenario, let's consider the following information.

AD = 8

AE = 6

EC is 12 more than BD.

To find the length of BD, we can utilize the Intercepted Arcs Theorem, which states that when two secants intersect outside a circle, the measure of an intercepted arc formed by those secants is equal to half the difference of the measures of the intercepted angles.

From the given information, we know that AD = 8 and AE = 6.

Since these are the lengths of the secants, we can use them to calculate the intercepted arcs.

First, let's find the intercepted arc corresponding to AD:

Intercepted Arc ADB = 2 [tex]\times[/tex] AD = 2 [tex]\times[/tex] 8 = 16

Similarly, we can find the intercepted arc corresponding to AE:

Intercepted Arc AEC = 2 [tex]\times[/tex] AE = 2 [tex]\times[/tex] 6 = 12

Now, we know that EC is 12 more than BD.

Let's assume the length of BD as x.

BD + 12 = EC

Now, let's consider the intercepted arcs theorem:

Intercepted Arc ADB - Intercepted Arc AEC = Intercepted Angle B - Intercepted Angle C

16 - 12 = Angle B - Angle C

4 = Angle B - Angle C.

Since Angle B and Angle C are vertical angles, they are congruent:

Angle B = Angle C.

Therefore, we can say:

4 = Angle B - Angle B

4 = 0

However, we have reached an inconsistency here.

The equation does not hold true, indicating that the given information is not consistent or there may be an error in the problem statement.

As a result, we cannot determine the length of BD based on the given information.

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Answer: The correct ratio to represent the ratio of paperback books to hardcover books is 5:3.

The speed of the boat in still water is 3 times the speed of the river current.

To find the speed of the boat in still water, we can use the concept of relative motion and the given information about the boat's speed while traveling upstream and downstream.

Let's assume the speed of the boat in still water is "v" km/h, and the speed of the river current is "c" km/h.

When the boat is traveling upstream, it moves against the current, so its effective speed is reduced.

The boat's speed relative to the ground is given by (v - c) km/h.

Similarly, when the boat is traveling downstream, it moves with the current, so its effective speed is increased.

The boat's speed relative to the ground is given by (v + c) km/h.

According to the problem, the boat can travel 40 km upstream in the same time it would take to travel 80 km downstream.

Since time is constant in both cases, we can set up the following equation:

40/(v - c) = 80/(v + c)

To solve this equation, we can cross-multiply and simplify:

40(v + c) = 80(v - c)

40v + 40c = 80v - 80c

40c + 80c = 80v - 40v

120c = 40v

Dividing both sides by 40, we get:

3c = v.

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Answer:

Step-by-step explanation:

To find the value of x, we can use the Angle Bisector Theorem, which states that in a triangle, a line segment that bisects an angle divides the opposite side into segments that are proportional to the other two sides.

In this case, segment AD bisects angle A, so we can set up the following proportion:

BD/DC = AB/AC

Plugging in the given values, we have:

14/DC = 28/25

To solve for DC (segment CD), we can cross-multiply:

28 * DC = 14 * 25

Simplifying further:

DC = (14 * 25) / 28

DC ≈ 12.5

Therefore, the length of segment CD is approximately 12.5.

The degree of f(x) is 5, and the leading coefficient is negative. There are 3 distinct real zeros and 2 relative maximum values.

From the graph of a function, the zeros of the function are the x-intercepts, that is, the values of x for which the graph crosses or touches the x-axis.

The function in this problem has three distinct zeros, given as follows:

Hence the degree of the function is given as follows:

2 x 2 + 1 = 5.

The leading coefficient is negative, as the function has an odd degree, but increases to left and decreases to right.

The relative maximums of the functions are the points where the function makes a downward turn, changing from increasing to decreasing, hence there are two points.

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Answer:B

Step-by-step explanation:

Answer: 98 This statement is true

Step-by-step explanation:

100-11=89

89-12=77

77+21=98

┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈

✦ The number is - 5

┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈

[tex]\begin{gathered} \; \sf{\color{pink}{Let \; the \; other \; number \; be \; (x)::}} \\ \end{gathered}[/tex]

Atq,,

[tex]\begin{gathered} \; \color{skyblue} :\dashrightarrow \: \tt{3 \times \bigg \lgroup \: x + ( - 7) \bigg \rgroup = - 36} \\ \\ \end{gathered}[/tex]

[tex]\begin{gathered} \; \color{skyblue} :\dashrightarrow \: \tt{3 \times \bigg \lgroup \: x - 7 \bigg \rgroup = - 36} \\ \\ \end{gathered}[/tex]

[tex]\begin{gathered} \; \color{skyblue} :\dashrightarrow \: \tt{3x - 21 = - 36} \\ \\ \end{gathered}[/tex]

[tex]\begin{gathered} \; \color{skyblue} :\dashrightarrow \: \tt{3x = - 36 + 21} \\ \\ \end{gathered}[/tex]

[tex]\begin{gathered} \; \color{skyblue} :\dashrightarrow \: \tt{3x = - 15} \\ \\ \end{gathered}[/tex]

[tex]\begin{gathered} \; \color{skyblue} :\dashrightarrow \: \tt{x = \dfrac{\cancel{ - 15}}{\cancel{ \: 3}}} \qquad \bigg \lgroup \sf{Cancelling \: by \: 3} \bigg \rgroup \\ \\ \end{gathered}[/tex]

[tex]\begin{gathered} \; \color{pink} :\dashrightarrow \underline{\color{pink}\boxed{\colorbox{black}{x = - 5}}} \: \pmb{\bigstar} \\ \\ \end{gathered}[/tex]

The answer is:

Work/explanation:

The product means we multiply two numbers.

Here, we multiply 3 and a number increased by -7; let that number be z.

So we have

[tex]\sf{3(z+(-7)}[/tex]

simplify:

[tex]\sf{3(z-7)}[/tex]

This equals -36

[tex]\sf{3(z-7)=-36}[/tex]

[tex]\hspace{300}\above2[/tex]

[tex]\frak{solving~for~z}[/tex]

Distribute

[tex]\sf{3z-21=-36}[/tex]

Add 21 on each side

[tex]\sf{3z=-36+21}[/tex]

[tex]\sf{3z=-15}[/tex]

Divide each side by 3

[tex]\boxed{\boxed{\sf{z=-5}}}[/tex]

Starting with an initial population of 3.3 million yeast cells and a constant relative growth rate of 0.4465 per hour, the population size reaches approximately 5.892 million cells after 4 hours.

To calculate the population size after 4 hours, we can use the formula for exponential growth:

Population size = Initial population * [tex](1 + growth rate)^t^i^m^e[/tex]

Given that the initial population is 3.3 million cells and the relative growth rate is 0.4465 per hour, we can plug in these values into the formula:

Population size = 3.3 million *[tex](1 + 0.4465)^4[/tex]

Calculating the exponent first:

[tex](1 + 0.4465)^4 = 1.4465^4[/tex] ≈ 1.7879

Now, we can substitute this value back into the formula:

Population size = 3.3 million * 1.7879

Calculating the population size:

Population size = 5.892 million

Therefore, the population size after 4 hours is approximately 5.892 million cells.

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The z-score for Brazil is given as follows:

Z = 0.87.

The z-score formula is defined as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

In which:

The parameters for this problem are given as follows:

[tex]X = 6.24, \mu = 4.8, \sigma = 1.66[/tex]

Hence the z-score for Brazil is given as follows:

Z = (6.24 - 4.8)/1.66

Z = 0.87.

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The best measure of center of the data is (a) mean; because the data are close together

From the question, we have the dataset of 10 values

In the given dataset, we can see that there are no outliers present in the dataset

By definition, outliers are extreme values.

Since there are no outliers, it means that the mean is the best measure of center

This is because the mean is affected by the presence of outliers and since no outlier is present, we use the mean

From the list of options, we have the mean value to be 42.536

Hence, the true statement is (a)

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The probability that a randomly student at the university has a commuting time between ​​​​ 55 and 70 mins is about 0.56. Given information:The commuting time (the average number of hours spent commuting each week) for students at a particular university is normally distributed with a mean of 63 mins and standard deviation of 9.61.

Find: We are to determine the probability that a randomly student at the university has a commuting time between ​​​​ 55 and 70 mins.

Here,μ = 63 min σ = 9.61 min. We have to find the probability of a random student has commuting time between 55 and 70 min. That is P(55 ≤ X ≤ 70).First, we need to convert the given range to Standard Normal Distribution form.i.e., z-score for X = 55 and X = 70.Z-score formula:z = (X - μ) / σFor X = 55z = (55 - 63) / 9.61z = -0.83For X = 70z = (70 - 63) / 9.61z = 0.73. We need to find the probability of a random student has a z-score between -0.83 and 0.73.P(-0.83 < z < 0.73)

Using standard normal table or calculator, we can find the probability P(-0.83 < z < 0.73) = P(z < 0.73) - P(z < -0.83)= 0.7665 - 0.2033≈ 0.56

Thus, the probability that a randomly student at the university has a commuting time between ​​​​ 55 and 70 mins is about 0.56.

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The net area of the curve represented by f(x) = ex - e on the interval [0, 2] is e2 - 1.

To find the net area of the curve represented by the function f(x) = ex - e on the interval [0, 2], we need to calculate the definite integral of the function over that interval. The net area can be determined by taking the absolute value of the integral.

The integral of f(x) = ex - e with respect to x can be computed as follows:

∫[0, 2] (ex - e) dx

Using the power rule of integration, the antiderivative of ex is ex, and the antiderivative of e is ex. Thus, the integral becomes:

∫[0, 2] (ex - e) dx = ∫[0, 2] ex dx - ∫[0, 2] e dx

Integrating each term separately:

= [ex] evaluated from 0 to 2 - [ex] evaluated from 0 to 2

= (e2 - e0) - (e0 - e0)

= e2 - 1

The net area of the curve represented by f(x) = ex - e on the interval [0, 2] is e2 - 1.

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The volume of revolution generated by revolving the region about the x-axis is -512π.

To find the volume of revolution using the washer method, we need to integrate the area of the cross-sections formed by rotating the region bounded by the graphs of y = 8√x, y = 16, and the y-axis about the x-axis.

Let's start by setting up the integral. We will integrate with respect to x since the region is bounded by the x-axis.

The lower limit of integration (x) is 0, and the upper limit is found by setting y = 8√x equal to y = 16 and solving for x:

8√x = 16

√x = 2

x = 4

So the integral setup is:

V = ∫[0, 4] π(R^2 - r^2) dx

To find the outer radius (R), we consider the distance between the curve y = 8√x and the x-axis. Since we are revolving around the x-axis, R is simply y = 8√x.

The inner radius (r) is the distance between the line y = 16 and the x-axis, which is simply 16.

Now we can set up the integral:

V = ∫[0, 4] π((8√x)^2 - 16^2) dx

= ∫[0, 4] π(64x - 256) dx

Integrating:

V = π(32x^2 - 256x) |[0, 4]

= π[(32(4)^2 - 256(4)) - (32(0)^2 - 256(0))]

= π[512 - 1024 - 0]

= -512π

The volume of revolution generated by revolving the region about the x-axis is -512π.

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Answer:

The correct answer is D. The graph of f(x) = 3(4)² - 5 + 3 is a transformation of the parent function. The parent function is y = x², which is a simple quadratic function.

In the given equation, the number 4 inside the parentheses represents a horizontal compression or shrink of the graph. The factor of 3 outside the parentheses represents a vertical stretch or expansion. The constant term -5 represents a vertical translation down by 5 units, and the constant term 3 represents a vertical translation up by 3 units.

Therefore, the graph of f(x) = 3(4)² - 5 + 3 is a compressed version of the parent function y = x², shifted down by 5 units and then shifted up by 3 units.

Answer:

BC = 24 (D)

Step-by-step explanation:

Special Right Triangles (30-60-90 triangle)

Answer:

Step-by-step explanation:

To find the number of antiviral proteins injected into the person, we can set up a proportion:

2 mL contains 2.3 × 10^3 antiviral proteins

x mL contains how many antiviral proteins?

The proportion can be written as:

2 mL / 2.3 × 10^3 = x mL / (unknown number of antiviral proteins)

We can solve this proportion by cross-multiplication:

2 mL * (unknown number of antiviral proteins) = 2.3 × 10^3 antiviral proteins * x mL

x = (2.3 × 10^3 antiviral proteins * x mL) / 2 mL

Simplifying, we get:

x = 1.15 × 10^3 * x mL

Therefore, the number of antiviral proteins injected into the person is 1.15 × 10^3.

The total number of cells in the person's body is approximately 1 × 10^14. If 8% of the person's cells are infected with the virus, we can calculate the percentage of cells that can be affected by the medication:

Percentage of cells affected = (Number of infected cells / Total number of cells) * 100

Number of infected cells = 8% of 1 × 10^14 cells

Number of infected cells = (8/100) * 1 × 10^14

Number of infected cells = 8 × 10^12

Percentage of cells affected = (8 × 10^12 / 1 × 10^14) * 100

Percentage of cells affected = 8 × 10^-2 * 100

Percentage of cells affected = 8%

Therefore, the administered medication can affect 8% of the person's cells.

To find the amount of medication needed to have 1 antiviral protein for every infected cell, we can set up a proportion:

2.3 × 10^3 antiviral proteins in 2 mL

1 antiviral protein in x mL

The proportion can be written as:

2.3 × 10^3 antiviral proteins / 2 mL = 1 antiviral protein / x mL

We can solve this proportion by cross-multiplication:

(2.3 × 10^3 antiviral proteins) * x mL = 2 mL * 1 antiviral protein

x = (2 mL * 1 antiviral protein) / (2.3 × 10^3 antiviral proteins)

Simplifying, we get:

x = 0.8696 mL

Therefore, to have 1 antiviral protein for every infected cell, approximately 0.8696 mL of medication needs to be administered. This is equivalent to 0.0008696 liters.

Answer:

Step-by-step explanation:

(x^3 - 10x + K)/(X+3) = 6 GIVEN

for different values of x there are many possible values of k some i will show

when we substitute x=1

we get k=33

at x=2

weget k=42

so many values are possible for k

because there is no intervel in question which restrics us from taking different values of x or k so you take any value of x you will get different values of k

The answer is:

↬ f(x + 2) = 2x + 11

Work/explanation:

To evaluate the function, plug in x + 2 for x:

[tex]\boxed{\large\begin{gathered}\sf{f(x)=2x+7}\\\\\bf{distribute}\\sf{f(x+2)=2(x+2)+7}\\\\\bf{simplify}\\\sf{f(x+2)=2x+4+7}\\\\\sf{f(x+2)=2x+11}\end{gathered}}[/tex]

Answer:

D.

Step-by-step explanation:

To find the number of customers Sam's Swimming Pool Cleaning has, we need to calculate the total revenue generated by the business and divide it by the weekly charge per customer.

Total revenue = 52 x $25 x number of customers

We know that the annual gross profit is $88,400. So, we can set up an equation to find the number of customers:

$88,400 = 52 x $25 x number of customers - $48,000

$88,400 + $48,000 = 52 x $25 x number of customers

$136,400 = $1,300 x number of customers

Number of customers = $136,400/$1,300

Number of customers = 105

Therefore, Sam's Swimming Pool Cleaning has 105 customers. The correct answer is D.

Sam’s Swimming Pool Cleaning have 105 customers.

An expression in math is a sentence with a minimum of two numbers or variables and at least one math operation. This math operation can be addition, subtraction, multiplication, or division. The structure of an expression is:

To get how many customers Sam has, write an equation that will relate to the gross profit. Let n be the customers. Since for 52 weeks, Sam charges $25 per week per person, multiply n by the number of weeks and the charge. The equation is written as $88,400 = 52 weeks x $25 per week x n persons. Divide $88,400 by the product of 52 weeks and the $25 charge. The answer will be 105.

Therefore, Sam’s Swimming Pool Cleaning have 105 customers.

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The total amount to pay would be 8800 Ethiopian Birr.

To find the amount to pay including VAT, we need to know the applicable VAT rate. VAT, or Value Added Tax, is a consumption tax added to the value of goods and services. The VAT rate can vary from country to country or even within different regions.

Assuming a VAT rate of 10%, we can calculate the VAT amount by multiplying the net value of the shoes by the VAT rate. In this case, the net value of the shoes is 8000 Ethiopian Birr. Therefore, the VAT amount would be 8000 * 0.10 = 800 Ethiopian Birr.

To find the total amount to pay including VAT, we add the VAT amount to the net value of the shoes. Thus, the total amount to pay would be 8000 + 800 = 8800 Ethiopian Birr.

It's important to note that the VAT rate and regulations can vary, so it's always advisable to check the specific VAT rate applicable in a given country or region. Additionally, different goods and services may have different VAT rates or exemptions, so it's crucial to consider the specific rules governing the shoe industry in the relevant jurisdiction.

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