1) Consider the quadratic function: f (x) = (x + 3)2 – 2 and a function, g(x), which is created by translating
f (x) three units to the right, two units up, and reflected vertically over the x-axis. Complete the following tasks:
a) 15 points: Graph f (x) on the axes below and label it. Graph g(x) on the axes below and label it.
10 points: Write the vertex form equation for g(x) below.

The Exponential model is y = 0.74 (1.79)ˣ

We have,

(10, 160) and (11, 250)

Using the Exponential model

y = abˣ

where a is the initial amount and be is the constant.

Now, the value of b is

= 250/ 140

= 1.79

Now, y = abˣ

140 = a (1.79)⁹

a = 0.74

So, the Exponential model is y = 0.74 (1.79)ˣ

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Answer:21y -78

Step-by-step explanation: Distribute the 7 to 3y and -10 to get 21y and -70.

Then combine like terms so the equation would be 21y -78

Step-by-step explanation:

-8+7(3y-10)

-8+21y-70

21y-70+8

21y-78

Last step because there is no more like terms to combine

Hope this helps

Answer:

THE ANSWER OF 7×4=28 !!!!!!!

If three squares are placed to form a right triangle as shown. The statement that must be true is: C .The difference of the areas of the smaller squares is always equal to the area of the largest square.

Let's use the letters a, b, and c to denote the side lengths of the squares, with c standing for the hypotenuse of the right triangle. Assuming that an is the shortest side length to preserve generality a2 is the area of the smallest square. The largest square has a surface area of c2 whereas the medium square has a surface area of b2.

The Pythagorean theorem demonstrates that a + b equals c. If we rewrite this equation, we obtain:

c^2 - b^2 = a^2

c^2 - a^2 = b^2

This means that the size of the largest square is equal to the difference between the areas of the two smaller squares, which is either a2 or b2.

Therefore the correct option is C.

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The solution of the given system of equations is (-3, 4).

Given two linear equations.

2x - 3y = -18

3x + y = -5

Multiplying the first equation by 3 and the second equation by 2,

6x - 9y = -54

6x + 2y = -10

Subtracting the equations,

-11y = -44

y = 4

Substituting,

x = -3

The graph of the system of equations is given below.

Hence the solution is (-3, 4).

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Triangles PQR and LMK are not similar. Thus none.

Two or more triangles are said to be similar if on comparing their corresponding properties, some common relations holds. One important relation is the scale factor that relates one triangle with the other.

In the diagram given, we have;

scale factor = LK/ PR

                   = 18/ 10

scale factor = 1.8

But this scale factor can not be used to determine the side LM correctly.

That is,

LM ≠ 1.8*8

LM ≠ 14.4

since LM = 13

Therefore, it can be deduced that triangles PQR and LMK are not similar. Thus none.

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Answer: B: cone with a height of 4 units and a radius of 3 units

Step-by-step explanation:

Surface Area: 9pi + 15pi = 24pi square units

Volume: 9pi x 4 x 1/3 = 12pi cubic units

Answer: [tex]8(\sqrt{x} -10)[/tex]

Step-by-step explanation:

[tex]8\sqrt{x} - 80[/tex]

[tex]8(\sqrt{x} -10)[/tex]

The function that represents in the table is y = 0.5(2^x)

Option C is the correct answer.

We have,

Looking at the table,

We can observe that as the value of x increases, the value of f(x) doubles.

This doubling of f(x) indicates that the base of the exponential function is 2.

Also, when x = 0, the value of f(x) is 0.5, which means that the y-intercept of the exponential function is 0.5.

Thus,

The function can be represented as y = 0.5(2^x).

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It takes A. 5 months to pay off (Mini) the highest interest card.

To determine the number of months it takes to pay off the credit card debt, we shall calculate the monthly payment to pay off the highest interest card first.

First, calculate interest accrued on each card per month:

Murk: (5.6/100)/12 * $675.49 = $2.98 per month

Mini: (9.85/100)/12 * $902.43 = $7.42 per month

Next, we determine the order in which to pay off the cards, which is highest interest card first, we can allocate the entire $375 to Mini and leave a minimum for interest accrued on Murk.

This should be a percentage of the balance.

Assuming it's 2% of the balance, which is $13.51.

So, in month 1, we will pay:

Mini: $375

Murk: $13.51

Leaving these balances:

Murk: $675.49 + $2.98 - $13.51 = $664.96

Mini: $902.43 - $375 + $7.42 = $534.85

In month 2:

Mini: $534.85 + $7.42 = $542.27

Murk: $13.51 + $2.98 = $16.49

Balances:

Murk: $664.96 + $2.98 - $16.49 = $651.45

Mini: $542.27 - $375 + $7.42 = $174.69

month 3:

Mini: $174.69 + $7.42 = $182.11

Murk: $13.51 + $2.98 = $16.49

Balances:

Murk: $651.45 + $2.98 - $16.49 = $638.94

Mini: $182.11 - $174.69 + $5.52 = $12.94

month4:

Mini: $12.94 + $7.42 = $20.36

Murk: $13.51 + $2.98 = $16.49

Balances:

Murk: $638.94 + $2.98 - $16.49 = $625.43

Mini: $20.36 - $12.94 + $0.54 = $8.96

month 5:

Mini: $8.96 + $7.42 = $16.38

Murk: $13.51 + $2.98 = $16.49

Balances:

Murk: $625.43 + $2.98 - $16.49 = $612.92

Mini: $16.38 - $8.96 = $7.42

So, Mini's balance is paid off here.

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Note:

And we can allocate the entire $375 budget to Murk.

This means we will pay off Murk in month 6:

Murk: $612.92 + $2.98 + $375 - $13.51 = $977.39

The y-intercept of the line of best fit is: y = 20

The formula for equation of a line of best fit is:

y = mx + c

where:

m is slope

c is y-intercept

Now, the y-intercept is simply defined as the point where the line crosses the y-axis.

In this case, the line crosses the y-axis at y = 20.

Thus, we can conclude that it is the y-intercept

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Note that where the above is given, the Standard Error is: 0.0322; while

The Value of the two-sample z-statistics p1-p2 = 6.048

To get the standard error, we can say

SE = √((p1  x  (1-p1)/ n1) + (p2  x (1-p2)/n2) )

Substituting....

SE = √((0.7122  x (1-0.7122)/403) + (0.4594  x (1-0.4594)/468))

SE = 0.03223785349

SE ≈ 0.0322

2) For the two-sample z-statistic formula:

z = (p1 - p2) / SE

Substituting values    ..........

z = (0.7122 - 0.4594) / 0.042

z = 6.048

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The value of the composite function t(s (2)) is 8

From the question, we have the following parameters that can be used in our computation:

s(x) = -x + 5

t(x) = 2x + 2

The composite function t(s(x)) is calculated as

t(s(x)) = 2s(x) + 2

Substitute the known values in the above equation, so, we have the following representation

t(s(x)) = 2(-x + 5) + 2

Again, substitute the known values in the above equation, so, we have the following representation

t(s(2)) = 2(-2 + 5) + 2

Evaluate

t(s(2)) = 8

Hence, the value of t(s(2)) is 8

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The value of u -v is 6i - 10j.

We have,

u = 4i-3j, and v= -2i+ 7j.

So, u - v

= (4i - 3j) - (-2i + 7j)

= 4i - 3j + 2i - 7j

= (4i + 2i) + (-3j - 7j)

= 6i - 10j

Thus, the resultant vector is 6i - 10j.

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Expression for -16x squared +36 in factored form is [tex]-4(2x - 3)(2x + 3).[/tex]

The given equation is [tex]-16x^{2} +36[/tex]

simplifying the equation,

[tex]-16x^2 + 36 = 4(-4x^2 + 9)[/tex]

[tex]=-4x^2 + 9\\ = -(2x)^2 + 3^2 \\= -(2x - 3)(2x + 3)[/tex]

when compared together,

[tex]-16x^2 + 36 = 4(-4x^2 + 9) = 4(-(2x - 3)(2x + 3)) = -4(2x - 3)(2x + 3)[/tex]

The expression for the equation in factored form is -4(2x - 3)(2x + 3).

The question is incomplete. complete question will be "which of these expression is equivalent to [tex]-16x^{2} +36[/tex] in factored form?

options- 4(x+2)(3-2x) , -4(2x - 3)(2x + 3) or (4x+2x)(9x-2x)"

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Answer:

144

Step-by-step explanation:A first add 98 + 46 keyword Sum for interior angles

Answer:

  cylinder

Step-by-step explanation:

You want to know which of two popcorn containers is a better value:

The volume formulas for the two shapes are ...

  V = 1/3πr²h . . . . . cone

  V = r²h . . . . . . . . . cylinder

For r = d/2, the ratio of these two volumes is ...

  [tex]\dfrac{V_{con}}{V_{cyl}}=\dfrac{\dfrac{1}{3}\pi\left(\dfrac{d_{con}}{2}\right)^2h_{con}}{\pi\left(\dfrac{d_{cyl}}{2}\right)^2h_{cyl}}=\dfrac{d_{con}^2\cdot h_{con}}{3\cdot d_{cyl}^2\cdot h_{cyl}}=\dfrac{12^2\cdot19}{3\cdot 8^2\cdot 15}=\dfrac{2736}{2880}=0.95[/tex]

The cone has less volume and costs more, so the cylindrical container is the better value.

The equation for the gradient on the curve C is y = x³ - 2x² + 5x - 3

Given data ,

Let the gradient of every point on the curve C is given by the equation dy/dx = 3x² - 4x + k

Now , we can integrate this equation with respect to x to obtain the equation for C

∫(dy/dx)dx = ∫(3x² - 4x + k)dx

Integrating the right-hand side with respect to x, we get:

∫(3x² - 4x + k)dx = x^3 - 2x^2 + kx + C1

where C1 is the constant of integration

Now, on simplifying the points P(0, -3) and Q(2, 7) that lie on C to find the values of C1 and k

For point P(0, -3)

when x = 0, y = -3

Plugging these values into the equation x³ - 2x² + kx + C1 = y, we get:

0³ - 2(0)² + k(0) + C1 = -3

C1 = -3

For point Q(2, 7):

when x = 2, y = 7

Plugging these values into the equation x³ - 2x² + kx + C1 = y, we get:

2³ - 2(2)² + k(2) - 3 = 7

k = 5

On substituting the values of C1 and k back into the equation , we get

y = x³ - 2x² + 5x - 3

Hence , the equation is y = x³ - 2x² + 5x - 3

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Answer:

The given equation is:

det [a 10 e b d 0] = [2 10 3 6 -1 0]

The determinant of a 3x3 matrix is calculated as follows:

|a b c|

|d e f| = a(ei - fh) - b(di - fg) + c(dh - eg)

Applying this formula to the given matrix, we get:

det [a 10 e b d 0] = a(d0 - b-1) - 10(ed - b0) + e(10*-1 - d*3)

= ab + 10b - 10ed - 3e

Substituting the given values, we get:

ab + 10b - 10ed - 3e = 2(6-0) - 10(3-(-1)) + 3(10-(-1))

ab + 10b - 10ed - 3e = 12 + 40 + 33

ab + 10b - 10ed - 3e = 85

We can simplify this equation by factoring out b and e:

b(a + 10) - e(10d + 3) = 85 - 10b

We can solve for a, d, and e by setting up a system of equations using the given values of the determinant:

ab + 10b - 10ed - 3e = 85

From this equation, we can solve for b:

b(a + 10) - e(10d + 3) = 85 - 10b

Substituting the value of b from the determinant equation, we get:

(a+10)(-1) - e(10d+3) = -8.5

Simplifying, we get:

-a - 10e - 3.3d = -8.5 ...(1)

Also, from the determinant equation, we have:

6a + 10d + 3e = 29

Solving for e in terms of a and d, we get:

e = (29 - 6a - 10d)/3 ...(2)

Substituting equation (2) into equation (1), we get:

-a - 10[(29 - 6a - 10d)/3] - 3.3d = -8.5

Simplifying and multiplying both sides by -3, we get:

3a + 20d - 29e = 25.5

Substituting equation (2) into this equation, we get:

3a + 20d - 29[(29 - 6a - 10d)/3] = 25.5

Simplifying, we get:

a + 6d - 29 = 1.5

a + 6d = 30.5

We have two equations in two variables:

-a - 10e - 3.3d = -8.5

a + 6d = 30.5

Solving for a and d using any method (substitution, elimination, etc.), we get:

a = 7

d = 4

Substituting these values into equation (2), we get:

e = (29 - 6a - 10d)/3 = (29 - 6(7) - 10(4))/3 = -3

Therefore, a = 7, d = 4, and e = -3.

Step-by-step explanation:

The time taken to reach a population of 500 is gotten from  500=50e^0.55t

Exponential growth is a process that increases quantity over time as in the bacterial culture here.

We know that from the question, we have;

P(t)=Poe^rt

P(t) = population at time t

Po= Initial population

r = growth rate

t = time taken

Then we have that;

150 = 50e^2r

3=e^2r

ln3 = 2r

r = ln3/2

r = 0.55

If the rate of growth is 0.55, then to reach a population  of 500;

500=50e^0.55t

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The equation x² + y - 36 = 0 is symmetry about the y - axis.

We have to given that;

The equation of graph is,

⇒ x² + y - 36 = 0

Now, We get;

⇒ x² + y - 36 = 0

⇒ y = - x² + 36

By plotting the equation in graph we get;

The equation x² + y - 36 = 0 is symmetry about the y - axis.

Thus, The equation x² + y - 36 = 0 is symmetry about the y - axis.

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The number of ways in which a committee of four Democrats and three Republicans be formed from a group of ten Democrats and eleven Republicans is 34650 ways.

We have,

By choosing some items from a set and creating subsets, permutation and combination are two approaches to represent a group of objects. It outlines the numerous configurations for a particular set of data. Permutations are the selection of data or objects from a set, whereas combinations are the order in which they are represented. Both ideas are critical to mathematics.

Here, the differences between permutation and combination are described in detail.

The number of ways in which we can select a committee of 4 democrats from ten democrats is:

P = 10C 4 = 10! / (4)! (10 - 4)!

P = 210

The number of ways in which we can select a committee of 3 Republicans from 11 Republicans is:

P = 11C 3 = 11! / 3! (11 - 3)!

P = 165

The number of ways in which a committee of four Democrats and three Republicans be formed from a group of ten Democrats and eleven Republicans is:

P = (210) (165) = 34650

The number of ways in which a committee of four Democrats and three Republicans be formed from a group of ten Democrats and eleven Republicans is 34650 ways.

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32% of the students surveyed preferred grilled cheese, so in a group of 3500 students, about 1120 students will prefer grilled cheese.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

The total number of people surveyed is given as follows:

80 + 40 + 50 + 20 + 60 = 250.

80 students preferred grilled cheese sandwich, hence the percentage is obtained as follows:

p = 80/250 x 100%

p = 32%.

Hence the expected amount of 3500 students is given as follows:

0.32 x 3500 = 1120 students.

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Answer:

A. V = 81π(7.25) = 1,844.90 cubic inches

V = 81(3.14)(7.25) = 1,843.97 cubic inches

B. Let p be the number of cans of paint.

1,843.97p = 10,000, so p = 5.42

Jessie will need 6 cans of paint.

C. Area of each storage area = π(9.5^2) = 283.53 square inches. Using 3.14 for π, this area is (3.14)(9.5^2) = 283.385 square inches. The base area of each paint can is 81π = 254.46 square inches (254.34 square inches if we use 3.14 for π). Jessie can't use the carrier because the area of each storage area exceeds the base area of each paint can.

Answer:

The amount of money spent on tickets and snacks will be $39 and $20. And the total amount is $59.

Step-by-step explanation:

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

Ellie is going to see a movie and is taking her 2 kids. Each movie ticket costs $13 and there are an assortment of snacks available to purchase for $5 each.

The amount of tickets is given as,

Ticket's amount = 3 x $13

Ticket's amount = $39

Then the amount spent on snacks is given as,

Snack's amount = 4 x $5

Snack's amount = $20

Then the total amount is given as,

Total amount = $39 + $20

Total amount = $59

The amount of money spent on tickets and snacks will be $39 and $20. And the total amount is $59.

Answer:

Step-by-step explanation:

i think that you times the numbers

"Data are collected about a population," is not a characteristic of both experiments and surveys. Option A

A survey is a technique for gathering data about a study variable from the respondents of the population. An experiment is a technique used in science to isolate the problem being examined and test a theory.

Options B, C, and D are characteristics obtained in the case of the  experiments and surveys. In both types of research, subjects may be randomly selected (option B), the data collected may be studied for patterns (option C).

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Answer:

D

Step-by-step explanation:

The Percentages are as follows

History: 80%

English: 82%

Reading: 84%

Math: 85%

Science: 86%