How do you describe the transformation of a function?

Answer:

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

Step-by-step explanation:

Given

[tex](h,k) = (-3,-2)[/tex] --- vertex

[tex](x,y) = (-5,6)[/tex] --- point

Required

Determine the equation

The general form is:

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

First, we solve for a:

Substitute [tex](h,k) = (-3,-2)[/tex] and [tex](x,y) = (-5,6)[/tex] in [tex]y = a(x - h)^2 + k[/tex]

[tex]6 = a(-5 - (-3))^2 - 2[/tex]

[tex]6 = a(-2)^2 - 2[/tex]

[tex]6 = 4a - 2[/tex]

Solve for a

[tex]4a = 6 + 2[/tex]

[tex]4a = 8[/tex]

[tex]a = 2[/tex]

So:

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

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

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

Answer:

x = 26.5

y = 12.0

z = 13.4

Step-by-step explanation:

✔️To find x, apply the leg rule, which is:

Hypotenuse/leg = leg/part

Hypotenuse = 30

Leg = x

Part = 30 - 6 = 24

Plug in the values into the equation

30/x = x/24

Cross multiply

x² = 30*24

x² = 720

x = √720

x = 26.5 (nearest tenth)

✔️Apply the triangle altitude theorem to find y:

Based on the theorem, h = √(ab)

Where,

a = 6

b = 30 - 6 = 24

h = y

Plug in the values

y = √(6*24)

y = √144

y = 12

✔️Apply the leg rule, Hypotenuse/leg = leg/part to find z:

Hypotenuse = 30

Leg = z

Part = 6

Plug in the values into the equation

30/z = z/6

Cross multiply

z² = 30*6

z² = 180

z = √180

z = 13.4 (nearest tenth)

Answer:

x = 25°

Step-by-step explanation:

the angle adjacent to the 130 angle is 50 degrees

x = 180-(105+50)

x = 180-155

x = 25

Answer:

65%

Step-by-step explanation:

Answer:

Step-by-step explanation:

Part A

If the gardener increases the number of dahlia plants by buying the new bulbs,

Let the equation representing year (x) and number of bulbs purchased (y) is,

y = mx + b

Here, m = Number of plants purchased each year

b = Initial numbers of plants

For x = 0, and y = 6,

6 = m(0) + b

b = 6

For x = 1, y = 56,

56 = m(1) + 6

m = 50

Therefore, equation for this method of increasing the numbers of plants will be,

y = 50x+ 6

Let the equation for the second method of increasing the number of plants is represented by the equation,

y = a(b)ˣ

From the data given in the table,

For x = 0, y = 6

6 = a(b)⁰

a = 6

For x = 1, y = 12

12 = 6(b)¹

b = 2

Therefore, equation representing the second method (By diving the existing bulbs) will be,

y = 6(2)ˣ

Part B

By substituting the value of x = 10 years,

Method - 1

y = 50(10) + 6

y = 506 plants

Method - 2

y  = 6(2)¹⁰

y = 6144 plants

Part C

After 5 years number of plants by method - 1,

y = 50(5) + 6

  = 256

After 5 years number of plants by method - 2,

y = 6(2)⁵

y = 192

Similarly, After 10 years number of plants by method - 1,

y = 50(10) + 6

  = 506

By method - 2,

y = 6(2)¹⁰

y = 6144

Since, number of plants after 5 years are less by the second method as compared to method 1

But after 10 years second method results the number of plants more than method-1,

Therefore, gardener should adopt method 2 for increasing the numbers of plants.  

Functions are used to represent tables and equations.

(a) The equation of the functions

The function of "Buy New Bulbs" is a linear function with an initial value of 6, and a rate of 50 (i.e. 56 - 6)

So, the equation is:

[tex]y = 6 + 50x[/tex]

The function of "Divide Existing Bulbs" is an exponential function with an initial value of 6, and a rate of 2 (i.e. 12/6)

So, the equation is:

[tex]y = 6(2)^x[/tex]

Hence, the equations of the functions are [tex]y = 6 + 50x[/tex] and [tex]y = 6(2)^x[/tex]

The expected number of bulbs in 10 years

This means that x = 10.

So, we have:

[tex]y = 6 + 50x =6 + 50*10 = 506[/tex]

[tex]y = 6(2)^x =6 *2^{10} = 6144[/tex]

Hence, the expected number of bulbs in 10 years for both functions are 506 and 6144, respectively

Compare the expected number of bulbs in 5 and 10 years

When x = 5.

We have:

[tex]y = 6 + 50x =6 + 50*5 = 256[/tex]

[tex]y = 6(2)^x =6 *2^5 = 192[/tex]

When x = 15

We have:

[tex]y = 6 + 50x =6 + 50*15 = 756[/tex]

[tex]y = 6(2)^x =6 *2^{15} = 196608[/tex]

By comparison;

In 5 years, the expected number of bulbs for the function of "Buy New Bulbs" is greater than the function of "Divide Existing Bulbs", however the expected number of bulbs for the function of "Buy New Bulbs" is less than the function of "Divide Existing Bulbs" in 15 years

Read more about functions at:

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Answer:

6=k×2

k=3

g(x)=k f(x)

g(x)=3 |x|

Answer:

3/12 - 8/12= 5/12

10/12 - 5/12= 5/12

Answer:

13

Step-by-step explanation:

11+x=y

yx8=z

z/2=96

96x2=192

192/8=24

24-11=13

x=13

Answer:

Amanda= 14

Boris = 88

Jose= 22

Step-by-step explanation:

Amanda= jose-8

Boris = 4×jose

Jose= Jose

total all = 124

(jose-8)+(jose×4)+(jose)= 124

so we substitute jose with X .

(X-8)+(4X)+(X)=124

6X-8= 124.

6X=124+8

X=132/6

X= 22.

so that total jose is 22, minus 8 we get Amanda, times 4 we get Boris.

Answer:

3/35, 12/35, 16/35, 4/35

Step-by-step explanation:

The box has a total of 35 squares.

The pink fills 3 squares so the pink section is: 3/35

The dark blue section covers 12 squares

So 12/35 is another fraction.

The light blue area covers 16 squares so another fraction is 16/35

The white covers 4 squares

So the last possible fraction is 4/35.

Answer:

25%

Step-by-step explanation:

Step 1: Add all the possible choices up

8 + 5 + 7 = 20

Step 2: Note that your finding the probability for creme filled ones

Step 3: Make it a fraction

5 creme filles ones out of 20

5/20

Step 4: Simplify

1/4

Step 5: Convert into a decimal (if you don't already know it)

1 ÷ 4 =

.25

Step 6: Multiply by 100 to find percentage

.25 × 100 = 25%

Answer:

Quadratic

Step-by-step explanation:

Example of linear is 2x + 3

Example of quadratic is x² + 2x + 3

Example of cubic is x³ + 2x² + 3x + 4

Example of quartic is x⁴ + 2x³ + 3x² + 4x + 5

Answer:

A. x¹/²

B. x¹/³

C. x¹/⁷

D. x⁵/²

E. x¹¹/³

F. 1 / x¹/⁴

G. 1 / x²/³

H. 1 / x⁹/²

Step-by-step explanation:

A. √x

Recall

√M = M¹/²

Therefore,

√x = x¹/²

B. ³√x

Recall

ⁿ√M = M¹/ⁿ

Therefore,

³√x = x¹/³

C. ⁷√x

Recall

ⁿ√M = M¹/ⁿ

Therefore,

⁷√x = x¹/⁷

D. √x⁵

Recall

√Mⁿ = Mⁿ/²

Therefore,

√x⁵ = x⁵/²

E. ³√x¹¹

Recall

ⁿ√Mᵃ = Mᵃ/ⁿ

Therefore,

³√x¹¹ = x¹¹/³

F. 1 / ⁴√x

Recall

ⁿ√M = M¹/ⁿ

Therefore,

1 / ⁴√x = 1 / x¹/⁴

G. 1 / ³√x²

Recall

ⁿ√Mᵃ = Mᵃ/ⁿ

Therefore,

1 / ³√x² = 1 / x²/³

H. 1 / √x⁹

Recall

√Mⁿ = Mⁿ/²

Therefore,

1 / √x⁹ = 1 / x⁹/²

Answer:

D

Step-by-step explanation:

the figure is in the origin therefore no reflection will affect the shape

Answer:

170.67 cm^3

Step-by-step explanation:

The volume is given by ...

 V = 1/3s²h

We are given that 4s=32, so s=8. We are also given that h=8. (All linear dimensions are in centimeters.) Then the volume is ...

 V = (1/3)(8²)(8) = 512/3 = 170.67 . . . . cm³

Answer:

170.67 cm^3

Step-by-step explanation:

took the test

Answer:

b

Step-by-step explanation:

the answer when not rounded is 43.

Answer: it’s D

Step-by-step explanation:

The domain and the range of an exponential parent function mean that the domain is all real numbers and the range signifies positive real numbers y > 0.

The simplest parent function of an exponential function takes the form:

[tex]\mathbf{f(x) = p^x}[/tex], where p refers to the base.

So, if we have a number such that x = 3 and the base is 2

Therefore, we can conclude that the domain of an exponential parent function is all real numbers, and the range is positive real numbers (y > 0).

Learn more about exponential functions here;

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Answer:

The new cost is $ 2.34 and sales tax is .14.  Total cost is $2.48

Step-by-step explanation:

1.80 x 1.3 = 2.34

2.34 x .06 = .14

Add the two together for the total

Answer:

3/4 of a cup or .75 of a cup

Step-by-step explanation:

Answer:

the first one

Step-by-step explanation:

just trust me

Answer:

k = 0.5

Step-by-step explanation:

Given a varies directly with x² then the equation relating them is

a = kx² ( k is the constant of variation )

To find k use the condition a = 8 when x = 4 , then

8 = k × 4² = 16k ( divide both sides by 16 )

0.5 = k

Answer:

$13,325

Step-by-step explanation:

Answer:

The first answer is 31.5.

The second is 21.

Step-by-step explanation:

Answer:

7/1; 4/2=2;8/1

7 is rational number because 7/1 = 7

8 = 4 x 2 = 4/1 x 2/1 and both rational.

Step-by-step explanation:

Multiply by any number/ same with both

7/1×6=42/6

8/1×6=48/6

So,

43/6,44/6,45/6 Answer

hope it helps

Answer:

Solve for  x  in the first equation.

Subtract  8 y  from both sides of the equation.

2 x = 6 − 8 y

5 x + 20 y = 15

Divide each term by  2  and simplify.

Divide each term in  

2 x /2 =  6/2  − 8 y/2  

5 x + 20 y = 15

Cancel the common factor of  2 .

Cancel the common factor.

2 x /2  =  6 /2  + (− 8 y)/ 2

Step-by-step explanation:

I don't have room to put the rest. So go to math-way

Answer:

A

Step-by-step explanation:

Because the lengths are way off for A.

2cm, 8cm, 8cm