Answer:
The standard form of the parabola is
y = 2 x² + 4 x + 3
Step-by-step explanation:
Step(i):-
The standard form of the parabola
y = a x² + b x + c ...(i)
The equation for the parabola is passing through the point (2 , 19 )
19 = 4a + 2b +c ...(ii)
The equation for the parabola is passing through the point (6 , 99 )
99 = 36a + 6b +c ...(iii)
The equation for the parabola is passing through the point (-1,1) )
1 = a - b + c ...(iv)
step(ii):-
subtracting (ii) and (iii) , we get
8a + b = 20 ...(a)
Subtracting (iii) and (iv) , we get
5a + b = 14 ...(b)
solving (a) and (b) , we get
subtracting (a) and (b) , we get
8a + b-( 5a + b ) = 20 - 14
3 a = 6
a = 2
substitute a=2 in equation (a) , we get
8a + b = 20
8(2) + b = 20
b =20 -16
b = 4
Substitute a= 2 ,b = 4 in equation (ii) , we get
19 = 4a + 2b +c
19 = 8 + 8 + C
c = 19 -16 = 3
Final answer:-
The standard form of the parabola is
y = 2 x² + 4 x + 3
Which of the following statements best describes the relationship between the point (5,-20) and the system of
inequalities below?
Answer: The point (5,-20) only satisfies the second inequality statement in the system of inequalities shown.
Step-by-step explanation:
It isn't super clear exactly what you're asking, but the first thing we can do is see if the point (5, -20) satisfies the system of equations.
So, we start by plugging in -20 for y and 5 for x.
y > -2x-3
-20 > (-2)(5) - 3
-20 > -10-3
-20 > -13. - we can see that the coordinates DO NOT satisfy the first inequality, now we can try the second equation.
y ≤ 3x + 2
-20 ≤ 3(5) + 2
-20 ≤ 15 +2
-20 ≤ 17 - this inequality is true because -20 is indeed less than 17.
Natalia solved the problem 74.4/12=6.2. complete the model with partial products check Natalia's work using multiplication
Answer:
Natalia's work is wrong.
Step-by-step explanation:
Natalia divided a decimal number by an entire number. Since division is a operation derived from multiplication, the best approach to check if work was good is multiplying the given result by denomination, that is:
1) [tex]x = 6.2\times 12[/tex] Given.
2) [tex]x = \left(6+0.2\right)\times 12[/tex] Definition of addition.
3) [tex]x = 6\times 12 + 0.2\times 12[/tex] Distributive property.
4) [tex]x = 72 + \frac{2}{10}\times 12[/tex] Definitions of multiplication and decimal number.
5) [tex]x = 72 +[2\cdot (10)^{-1}]\cdot 12[/tex] Definition of division/Associative property.
6) [tex]x = 72 + [2\cdot 12]\cdot (10)^{-1}[/tex] Associative property.
7) [tex]x = 72 + 24\cdot 10^{-1}[/tex] Definition of multiplication.
8) [tex]x = 72 + \frac{24}{10}[/tex] Definition of divsion.
9) [tex]x = 72 + 2.4[/tex] Defintion of decimal number.
10) [tex]x = 74.4[/tex] Definition of addition/Result
Natalia's work is wrong.
In the triangle Tan A =
Answer:
Tan=(Opposite/Adjacent)
Step-by-step explanation:
Sin=(Opposite/Hypotnous)
Cos=(Adjacent/Hypotnouss)
Tan=(Opposite/Adjacent)
HELP ASAP ILL GIVE BRAINLIST
Answer:
(C) A diation followed by reflection
Step-by-step explanation:
if you dialate a shape then that shape can not be congruent to the previous one because it is not the same size, so it is similar but not congurent
If the sides of a square measure 9 3units, then find the length of the diagonal.
A rectangular living room has an area of 425 ft.² the width of the room is 17 feet
Please help how to solve
Multiply the following binomials. Write in descending order of degree.
What is the coefficient of the third term?
(3x + 2)(7x - 8)
Answer:
Step-by-step explanation:
if you multiply the polynomials
(3x+2)(7x-8)=21x^2-24x+14x-16=21x^2-10x-16
coefficient of the third term -16
(3x + 2)(7x - 8)
21x^2 - 24x + 14x -16
21x^2 -10x - 16
The power descending order is 2, 1 and 0.
You see, -16 = -16x^0. As you know, x^0 = 1.
So, the coefficient of the third terms is -16.
Use the distributive property to evaluate the following expression: 9 x (4 + 9) . Show your work in your answer.
Answer:
9x + 81
Step-by-step explanation:
Given that P(x)=x^5-8x^3-x^2+2, what is the remainder when it is divided by x-5?
Answer:
2102
Step-by-step explanation:
The polynomial function P(x)=x^5-8x^3-x^2+2, if it is divided by x-5, first we need to get x from the divisor as shown
since d(x) = x-5
x-5 = 0
x = 5
Substitute x = 5 into the expression to get the remainder
P(x)=x^5-8x^3-x^2+2
P(5)=(5)^5-8(5)^3-(5)^2+2
P(5) = 3125-1000-25+2
p(5) = 2100+2
P(5) = 2102
Hence the remainder is 2102
graph the image of this figure after a dilation with a scale factor of 2 centered at the origin use the polygon tool to graph the dilated figure ! Please help 100 pts and brainliest
Answer:
For this answer, I will label the points. Starting at the top left, then top right, then bottom left and bottom right let the points be A, B, C, D.
The new coordinates will be
A(-4,10)
B(4,10)
C(-4,4)
D(4,4)
Step-by-step explanation:
The question is asking for a dilation which is a transformation that makes an image proportionately smaller or larger by a scale factor. The scale factor is how much smaller or larger the shape will be, if the scale factor is between 0 and 1 then it will shrink, if it is greater than one then the image will stretch (be larger). In this case, the scale factor is 2, therefore the image will stretch. Since the center of dilation is the origin, to find the new coordinates simply multiply each x and y value by the scale factor. So A's original coordinates (-2,5) become (-4,10) and so forth. Therefore the equation for this dilation is (x, y) → (2x,2y).
Answer:
See below
Step-by-step explanation:
Points given on the graph:
(-2, 2), (-2, 5), (2, 5), (2, 2)Dilation by a scale factor of 2 will result in coordinates doubled for each point:
(x, y) → (2x, 2y)And the new points will be:
(-2, 2) → (-4, 4)(-2, 5) → (-4, 10)(2, 2) → (4, 4)(2, 5) → (4, 10)See attached for the graph
4. 3b - 27
HELP ASAP
Answer:
3(b-9)
Step-by-step explanation:
The GCF (greatest common factor) is 3. All you have to do is divide both the numbers by 3. You should get 3(b-9). I hope this helps! ;)
An object is launched on the moon at 16 feet per second (f/s) from a 1152-foot tall tower. The equation for the object's height s at time t seconds after launch is
s(t) = -16t^2 + 16t + 1152, where s is in feet. When does the object strike the moon’s surface and why?
Answer:
0.5seconds later
Step-by-step explanation:
Given the height modeled by the equation:
s(t) = -16t^2 + 16t + 1152
The velocity of the object at the moon surface is zero
ds(t)/dt = 0
ds(t)/dt = -32t + 16
0 = -32t + 16
32 t = 16
t = 16/32
t = 1/2
t = 0.5seconds
Hence the object strikes the moon surface 0.5seconds later
Figure ABCD is a kite. Find the
value of x.
Answer:
x=20
Step-by-step explanation:
(triangle angles must add up to 180º)
2x+10+2x+90=180
4x+100=180
4x=80
x=20
Hey can anyone help me out please
If u steal point i report
Answer:
The first option
Step-by-step explanation:
Jocelyn estimates that a piece of wood measures 5.5 cm. If it actually measures 5.62 cm, what is the percent error of Jocelyn's estimate?
O 2.13%
O 2.18%
O 12%
O 46.83%
Kiran's family has completed 40% of a trip. They have traveled 80 miles. How far will the total trip be?
Answer:200
Step-by-step explanation:
The two numbers that multiply together to equal -15 and add together to equal -2 are
Answer:
-5, 3
Step-by-step explanation:
If x=-1, what is n (x)?
n(x)=-3x+7
Answer:
Step-by-step explanation:
x = -1
n(x = -1) = -3(x) + 7
n(x = -1) = -3(-1) + 7
-3 x -1 = 3
n(x = -1) = 3 + 7
n(x = -1) = 10
I hope this is correct! And I hope this helps :)
One of the Starbucks managers strongly believes that the primary functions are to make valued or desired rewards available in the
workplace and clarify for the subordinate the kinds of behavior that will lead to goal accomplishment and valued
rewards Accordingli he is referring to - motivational theory, which is part of the --- motivational perspective/theories
A Substitute, Content
(B) Substitute, Process
Expectancy. Content
D) Expectancy, Process
Answer:
eyeyywhwywhwhehehhehehehehhehe the answer is a
If u steal point i report
Answer:
C = y=4x
Step-by-step explanation:
That answer because if you were to multiply on the way it will have the same graph
Answer:
The third option
Step-by-step explanation:
the last of my points i really enjoyed being here just the stress of it goodbye fellow brainlest
Answer:
Bye
Step-by-step explanation:
Answer:
thx
Step-by-step explanation:
pls mark brainliest :D
Suppose y varies directly with x. When
X is 2, y is 10. What is y when x is 4?
The profits of mr cash’s company is represented by the equation p(t)=-3t^2+18t-4, where p(t) is the amount of profit in hundreds of thousands of dollars and t is the number of years of operation. he realizes his company is on the down turn and wishes to sell before he ends up in debt. In what year of operation does Mr. Cash’s business show maximum profit? What is the maximum profit? What time will it be too late to sell business? show work
Answer:
$2300000- max profit5.77 years into operation - zero profit timeStep-by-step explanation:
Given function:
p(t)= -3t^2 + 18t - 4It is a quadratic function with general form of y = ax^2 + bx + c
It opens down if a < 0 and gets maximum value at vertex which is determined at x = -b/2a
For the given function vertex is:
t = -18/-3*2 = 3Maximum value of p is:
p(3) = -3*3^2 + 18*3 - 4 = -27 + 54 - 4 = 23 ($2300000)The time when profit is zero:
-3t^2 + 18t - 4 = 03t^2 - 18t + 4 = 0t = (18 ± √18² - 4*3*4)/2*3 = (18 ± √276)/6 = (18 ± 16.61)/6t = (18 - 16.61)/6 = 0.23 this is the time when company has just started to make profit, it is not applicable as is the past timet = (18 + 16.61)/6 = 5.77 years into operation, after this time there will be no profitWhich of the following is the best definition of a statistical population?
a. The distribution of all possible values that can be assumed by some statistic, computed from samples of different sizes randomly drawn from different populations.
b. Distribution of some characteristic based on individual observations – for each individual unit we measure the characteristic and then look at the distribution of all of these values.
c. The distribution of all possible values that can be assumed by some statistic, computed from samples of the same size randomly drawn from the same population.
d. The distribution of all possible values that can be assumed by some parameter, computed from a single sample randomly drawn from some population.
c. The distribution of all possible values that can be assumed by some statistic, computed from samples of the same size randomly drawn from the same population.
c. The distribution of all possible values that can be assumed by some statistic, computed from samples of the same size randomly drawn from the same population.
What is the statistical population?A population is the group of people from which a statistical sample is taken in statistics. Therefore, a population is any collection of people who have something in common. A statistically significant portion of a population, rather than the full population, may also be referred to as a sample.
When surveying a big number of people, it is just impracticable to examine everyone who fits the description you are looking at using a population parameter. It is often easier to study a smaller sample of participants, but by applying inferential statistics, it is possible to get a good approximation of the population parameter.
thus, statistical population is the distribution of all of the statistics calculated from all possible samples of the same size.
Therefore, The statistical population, which is calculated from samples of the same size randomly selected from the same population, is the distribution of all potential values that can be assumed by a statistic.
Learn more about statistical population here:
https://brainly.com/question/8222250
#SPJ5
1,If 1 − x, x + 3 and 2x + 1 are consecutive terms of an A.P, then find the common
difference.
Step-by-step explanation:
Since they are consecutive terms in an AP,
(1 - x) + (2x + 1) = 2(x + 3).
=> x + 2 = 2x + 6
=> x = -4.
Therefore the terms are 5, -1 and -7.
=> Common difference = -6.
what should i eat for lunch and also what is 25 to the power of 6 ? ill give brainly if u awnser both
Answer:a samichhh and 244,140,625
Step-by-step explanation:
What is the width of Averi's area model? (See picture)
Answer:
Width = x² + 5x - 4
Step-by-step explanation:
By the definition of an area model,
Area = Width × greatest common factor
Since, Area = 4x² + 20x - 16
And greatest common factor = 4
4x² + 20x - 16 = 4(Width)
By dividing both the sides of the equation by 4,
[tex]\frac{4x^2+20x-16}{4}=\frac{4(\text{Width})}{4}[/tex]
x² + 5x - 4 = Width
Therefore, width = (x² + 5x - 4) will be he answer.
2 + 5 please help I am really struggling
Answer:
the answer is 7 the problem is an easy one
Step-by-step explanation: