The expression 3 + 2(x - 5)2
models the height of a ball after X seconds. The constant in the simplified form of the expression represents the initial height, in feet, of the ball. What is the initial height of the ball?
A. -30 feet
B. -5 feet
C. 3 feet
D. 53 feet​

Answer:

A (g(x) = }(x-2)5.1).

Step-by-step explanation:

The function which results after the sequence of transformations given is B. g(x) = 1/2 (x + 2)⁵ - 1.

Translation of functions is defined as the when each point in the original graph is moved by a fixed units in the same direction.

There are horizontal translation and vertical translation of functions.

Given function is,

f(x) = x⁵

When a function is compressed vertically, then new function formed will be of the form, k f(x), where k is the factor that is compressed.

After compress vertically by 1/2,

f(x) changes to 1/2 f(x) = 1/2 x⁵

After the horizontal translation of 2 units to the left,

1/2 f(x) changes to 1/2 f(x + 2) = 1/2 (x + 2)⁵.

After vertical translation of 1 unit to the down,

1/2 f(x + 2) changes to 1/2 f(x + 2) - 1 = 1/2 (x + 2)⁵ - 1

Hence the correct option is B . g(x) = 1/2 (x + 2)⁵ - 1.

Learn more about Transformations of Functions here :

https://brainly.com/question/13810353

#SPJ7

Answer:

1.the square pan is larger by 12 inches

40 cm^2

Step-by-step explanation:

The difference in size can be determined by calculating the difference between the perimeter of the square pan and the circumference of a circle

perimeter of a square = 4 x length

14 x 4 = 56 inches

Circumference of a circle = πD = (22/7) x 14 = 44 inches

Difference in size = 56 - 44 = 12 inches

Area of a rectangle = length x width

10 x 4 - 40 cm^2

Answer:

10m+10

Step-by-step explanation:

5x2=10

5x2m=10m

10m+10

9514 1404 393

Answer:

  32 yd²

Step-by-step explanation:

Use the area formula with the given dimensions.

  A = 1/2(b1 +b2)h . . . . . base lengths b1, b2; height h

  A = 1/2(2 +6)8 = 1/2(8)(8) = 32 . . . . square yards

The area of the trapezoid is 32 square yards.

Answer:

11 students brought both a pen and a pencil

Step-by-step explanation:

59 students brought a pen or pencil or both

48 + 22 = 70

70-59 = 11

11 students brought both a pen and a pencil

Answer:

No

Step-by-step explanation:

70 is divisible by 5. 5 is not an even number.

Answer:

No

Step-by-step explanation:

The factors of 70 are 1, 2, 5,7,10, 14, 35, and 70. the even numbers are 2, 10,14, and 70. but there are odd numbers, like 1, 5, 7, and 35. And since we know there are odd factors, the answer is No. 70 has even AND odd factors.

Answer:

C) Yes, it’s a reflection over line f.

Step-by-step explanation:

It’s a reflection over line f.

The answer is D

If this helped a brainliest would be appreciated!

Answer:

32600

Step-by-step explanation:

Answer:

11,15,7

Step-by-step explanation:

11+15+7=33 33/3=11 the mean

then 15-7=8 the range

Answer:

-11 :)

Step-by-step explanation:

Answer: 0

Step-by-step explanation:

Answer:

Two figures are similar if the figures have the same shape but different sizes.

Then if we have two figures X and X'

Such that one dimension of X is D, the correspondent dimension on X' will be:

D' = k*D

Such that k is the scale factor that relates the figures.

1:k

Because all the dimensions will be rescaled by the same scale factor k, we can conclude that any surface on X will be related to the same surface in X' by:

S' = k^2*S

then the ratio of the surfaces is:

1:k^2

While the relation between the volumes will be:

V' = k^3*V

Here the ratio is:

1:k^3

Ok, in this case we have two cylinders

We know that the ratio between the base area ( a surface) is:

9:25

a) We want to find the ratio: curved surface area of A : curved surface area of B

Because again we have a surface area, the ratio should be exactly the same as before, 9:25

b) height of A : height of B

In this case, we have a single dimension.

Because in the rescaling of a surface we need to use k^2, then we can conclude that the ratios:

9:25

is related to k^2

Then the ratio, in this case, is given by applying the square root to both sides of the previous ratio, so we get:

√9:√25

3:5

This is the ratio of the heights.

Also from this we could get the value of k, that is the right value when we leave the left value equal to 1, we can get that if we divide both sides by 3.

(3/3):(5/3)

1:(5/3)

Then:

k = 5/3

Answer:

[tex]d=1.61\times 10^{10}\ miles[/tex]

Step-by-step explanation:

Given that,

The speed of light, v = 300,000,000

eWe need to find the distance light travel in 1 day. We know that,

1 day = 86400 seconds

Distance = speed × time

So,

[tex]d=3\times 10^8\times 86400[/tex]

[tex]d=2.592\times 10^{13}\ m[/tex]

or

[tex]d=0.001610\times 10^{13}\\\\d=1.61\times 10^{-3}\times 10^{13}\\\\d=1.61\times 10^{10}\ miles[/tex]

So, the required distance is equal to [tex]1.61\times 10^{10}\ miles[/tex].

Answer:

Step-by-step explanation:

When you are taking off percentages from numbers, you first want to make the percent a number. This step is super simple. Just divide the 18 by 100

This gets you 0.18

Now multiply

84 * 0.18 = 15.12

So 15.12 is the discount

Then take 84 and subtract 15.12

84 - 15.12 = 68.88

So 68.88 is the sell price

Answer:

[tex] \frac{x - 1}{2x} [/tex]

Step-by-step explanation:

This is a correct answer.

Answer: 10:8

Step-by-step explanation:

There are 10 hamsters and 8 cats

Since hamsters is first in the ratio, you put the 10 and then the 8

10:8

Hope this helps!

Answer:

the last option 10:8....

Answer:

[tex]\boxed{ \displaystyle y = 7\sin\left(\frac{2}{9}x-\frac{1}{4}\right)}[/tex]

Step-by-step explanation:

we want to figure out the equation of a sine function that has the following characteristics.

the standard form of sine function is given by

[tex] \displaystyle y = a\sin(bx-c)+d[/tex]

where:

Finding a and phase shift:

a and c is simply given which is

finding b:

using the equation we acquire:

[tex]\dfrac{2\pi}{b}=9\pi[/tex]

solving the equation for b,we obtain:

b=2/9

finding d:

Since d Isn't mentioned, we would assume it 0

finding the equation:

substitute what we got:

[tex]\boxed{ \displaystyle y = 7\sin\left(\frac{2}{9}x-\frac{1}{4}\right)}[/tex]

and we're done!

Answer:

B

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

He already has 150 cards and he is buying 15 cards EACH WEEK. W represents the amount of weeks and since 15W +150 needs to be greater than 500 we need to use this lil guy (>)

Answer:

Your answer is 12

Because the three numbers 24,36,72 are the factors of 12

If you are helped with my answer pls tag me brianliest

THANK YOU....

Answer:

Pls add the image

Step-by-step explanation:

Answer:

f(x) = (x - 3)^2 + 34

Step-by-step explanation:

Answer:

15.)  104 ... I hope angles are not drawn to scale

16.)  144

17.)  37

Step-by-step explanation:

15.)

3x + 10 = 4x -12

22 = x

so 3x +10 = 76

180 - 76 = t = 104

16.)

2(21) + 36 + 90 + bcd + a = 360

a = 90 - 21 = 69

360 - (2(21) + 36 + 90 + 69) = bcd

bcd = 360 - 237 = 123

angle acd = 21 + bcd = 21 + 123 = 144

17.)

(5x - 7) + 90 + (3x + 1) = 180

8x -6 = 90

8x = 96

x = 12

so 5x - 7 = 53

90 - 53 = angle lmn = 37

Answer:

Alli khanaw .................

Answer:

8x^36

Step-by-step explanation:

first term (a) = [tex]8x^{8}[/tex]

Second term (t2)= [tex]8x^{12}[/tex]

common ratio (r)

= [tex]\frac{8x^{12} }{8x^{8} }[/tex]

= [tex]x^{4}[/tex]

now the 8th term of the G.S is

t8 = [tex]ar^{n-1}[/tex]

  = [tex]8x^8 * (x^4)^8^-^1[/tex]

  = [tex]8x^8 * (x^4)^7\\[/tex]

  = [tex]8x^8 *x^2^8\\= 8x^3^6[/tex]

hope it will help

Step-by-step explanation:

That 'd be the square root of 300, which is equivalent to 10sqrt(3).

Answer:

C) 2/7, 1/2, 5/6, 4/2

Step-by-step explanation:

Answer: 8

Step-by-step explanation: