G(b) = 5b- 9 h(b) = (b - 1)^2 Evaluate. (hog)(-6) =

Answers

Answer 1

Given:

The two functions are:

[tex]g(b)=5b-9[/tex]

[tex]h(b)=(b-1)^2[/tex]

To find:

The value of [tex](h\circ g)(-6)[/tex].

Solution:

We have,

[tex]g(b)=5b-9[/tex]

[tex]h(b)=(b-1)^2[/tex]

We know that,

[tex](h\circ g)(b)=h(g(b))[/tex]

[tex](h\circ g)(b)=h(5b-9)[/tex]

[tex](h\circ g)(b)=[(5b-9)-1]^2[/tex]

[tex](h\circ g)(b)=[5b-10]^2[/tex]

Putting [tex]b=-6[/tex], we get

[tex](h\circ g)(-6)=[5(-6)-10]^2[/tex]

[tex](h\circ g)(-6)=[-39-10]^2[/tex]

[tex](h\circ g)(-6)=[-49]^2[/tex]

[tex](h\circ g)(-6)=2401[/tex]

Therefore, the value of [tex](h\circ g)(-6)[/tex] is 2401.


Related Questions

The cost of a small salad at the deli was marked up 30% after a recent drought destroyed most of the lettuce crop. Determine the new cost if the price prior to the drought was $1.80. Then find the sales tax of the new price if the tax rate is 6%.

Answers

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

What is the area of the base?

Answers

Answer:

20

Step-by-step explanation:

The area can be calculated by Length times width. The length is 10 and the width is 2 so 10 x 2 = 20

Cheers

Answer:

I believe it is 20

Step-by-step explanation:

10 x 2 = 20

Simplify completely the quantity 5 times x to the third power plus 10 times x to the 2nd power plus 15 times x all over 5 times x

Answers

Answer:

x²+2x+3

Step-by-step explanation:

We are to simplify the expression;

5x³+10x²+15x/5x

Factor out 5x from the numerator

= 5x(x²+2x+3)/5x

5x will cancel out both at the top and bottom to have;

x²+2x+3

Factorize

x²+2x+3

Hence the simplified form is x²+2x+3

Three friends are sharing 4 cups of lemonade. If they share the lemonade equally, how many cups will each friend get?

Answers

Answer:

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

Step-by-step explanation:

1.3 bc you divide 4 by 3

please help me if you do not know do not answerr​

Answers

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

A rocket is launched from a tower. The height of the rocket, y in feet, is
related to the time after launch, x in seconds, by the given equation. Using
this equation, find the maximum height reached by the rocket, to the nearest
tenth of a foot.
y = -16x2 + 212x + 139

Answers

Answer:

y = 841.25 feet

Step-by-step explanation:

Given that,

The height of the rocket, y in feet, is  related to the time after launch, x in seconds, by the given equation as follows:

[tex]y = -16x^2 + 212x + 139[/tex] ....(1)

We need to find the maximum height reached by the rocket.

For maximum height, put dy/dx = 0

So,

[tex]\dfrac{d(-16x^2 + 212x + 139)}{dx}=0\\\\-32x+212=0\\\\x=\dfrac{212}{32}\\\\x=6.625\ s[/tex]

Pu x = 6.625 in equation (1).

[tex]y = -16(6.625)^2 + 212(6.625) + 139\\\\y=841.25\ feet[/tex]

So, the maximum height reached by the rocket is equal to 841.25 feet.

A cube is 0.5 cm on all sides, what is the surface area of the prism?

Answers

Answer:

[tex]0.5^{3}[/tex]=0.125

Step-by-step explanation:

.5*.5*.5

The probability that is will rain today is 65%, and the probability that it will rain tomorrow is 25%.

The probability that it will rain both days is 35%.

What is the probability that is will rain today or tomorrow?

Answers

Answer:

65%

Step-by-step explanation:

I need to know the vertex of this parabola can someone help me ASAP

Answers

The vertex is located at (-1,-9)

help fast pls .. Find the equation for g(x) by substituting the known point (1, 4) and solving for k.

Answers

Answer:

6=k×2

k=3

g(x)=k f(x)

g(x)=3 |x|

Amanda, Boris, and Jose sent a total of 124 text messages during the weekend. Amanda sent 8 fewer messages than Jose
Boris sent 4 times as many messages as Jose. How many messages did they each send?

Answers

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.

hello please help thanks

Answers

Answer:

D

Step-by-step explanation:

it states that the snikholes are from underneath when the soil it lose

A company that recently changed it slogan is hosting an optional big company picnic.Some members of the marketing team are eating together at the picnic and sharing their thoughts on the new slogan. they find that 80% of them like the new slogan. for which population is 80% a legitimate estimate of the percent of employees who like the new slogan?

Answers

Answer:

Only those members of the marketing team eating together at the picnic

Step-by-step explanation:

The members of the marketing team eating together at the picnic weren't randomly selected from a larger population. They may not be representative of employees (marketing team or not) beyond their group.

Only members of the marketing team eating together depicts a 80 percent legitimate estimate of the percent of employees who like the new slogan.

What is an Estimate?

This can be defined as the approximate calculation of a set of data or values.

The members of the marketing team eating together will represent 80 percent legitimate estimate because they weren't randomly selected from a larger population.

Read more about Estimates here https://brainly.com/question/24592593

Failing please please

Answers

Answer:

A = 102m squared (Brainiest?)

Equation = b x h / 2

Step-by-step explanation:

A = (12 x 17) / 2

A = 204 / 2

A = 102m squared

A gardener can increase the number of dahlia plants in an annual garden by either buying new bulbs each year or dividing the existing to create new plants. The table below shows the expected number of bulbs for each method.
Need Part A-C

Answers

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:

https://brainly.com/question/15602982

Find the slope between the two points:
(3,-2) and (-5, 2)

Answers

Answer:

the slope is -2

Step-by-step explanation:

Answer is is (5,-2) sowwy if I’m wrong

What value of b will make the equation a true statement? Explain how you arrived at your solution. (−34 + 43)+ b = 0

Answers

Answer:

b = -9

Step-by-step explanation:

Given the equation (−34 + 43)+ b = 0

We are to find the value of b

First solve for the value in parenthesis

(−34 + 43)+ b = 0

9+b = 0

Subtract 9  from both sides

9+b-9 = 0 - 9

b+0 = -9

b = -9

Hence the value of b will make the equation a true statement is -9

Hey! Please answer this fast, it’s due soon. It’s fractions

Answers

Answer:

3/12 - 8/12= 5/12

10/12 - 5/12= 5/12

Subtracting fractions with unlike denominators

Answers

Answer:

Answer is 9/8

Step-by-step explanation:

18/8-9/8=9/8

Answer:

9/8

Step-by-step explanation:

9/4 - 9/8

9/4 x 2 = 18/8 to match denominators

18/8 - 9/8

= 9/8

Find the second base of a trapezoid with an area of 96 inches, a height of 8 inches, and a 1st base measuring 11 inches.

Answers

Answer:

13

Step-by-step explanation:

11+x=y

yx8=z

z/2=96

96x2=192

192/8=24

24-11=13

x=13

Which of these does NOT represent the distance a car travels when going 55 miles per hour?

Answers

Answer:

the first one

Step-by-step explanation:

just trust me

Use the graph of the function f(x) = (x + 1)² + 2. Identify the vertex and
the axis of symmetry.

Answers

1. Vertex: f(x)=x^2+2x+3
=> a=1 b=2
=> x=-2/2*1 => x=-2/2
=> x=-1
=> (-1,2)

2. Axis of symmetry: x=-1

SOMEONE PLEASEEEE HELPPPP!?!!?!?!!?!?!

Answers

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.

What are the domain and
range
of an exponential parent function?
A. The domain is positive real numbers (x > 0), and the range is all
real numbers.
B. The domain is all real numbers, and the range is nonnegative real
numbers (y≥ 0).
C. The domain is nonnegative real numbers (x≥ 0), and the range is
all real numbers.
D. The domain is all real numbers, and the range is positive real
numbers (y > 0).

Answers

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.

What is an exponential parent function?

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

f(3) = 2³f(3) = 6

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;

https://brainly.com/question/2456547

#SPJ5

This table shows how the cost of Dana’s birthday party depends on the number of guests. What is the price per guest?

Answers

Answer:

it would be 60

Step-by-step explanation

4*5= 20

8*5=40

12*5=  60

We multiply by 5 because if we divide 20/4=5, 40/8=5, 60/12=5.

Re-write the quadratic function below in Standard Form
y= -9(x - 1)2 – 6

Answers

18x+y=12 hope this helpssssss

A store gives reward points for every dollar
spent. The number of reward points varies
directly with the total amount spent.
Sofia spends $300 and receives 15 reward
points.
Juan spends $900. He receives reward points
at the same rate as Sofia.
How many more reward points will Juan
receive than Sofia?




Please help me I give u 14 points please only correct answers ,!!!

Answers

Answer- 30

Explanation:
This is a picture I found of the ansewer hope this helped

an average speed of 57 km/h and the remaining 55 km at an average speed of 110 km/h. Find the average speed of the car for its entire journey.

Answers

Answer:

83.5km/h

Step-by-step explanation:

To find average you have to add up all the numbers in a given set then divide it by the amount of numbers in that set

A parabola has a vertex (-3, -2) and contains the point (-5, 6). Write the equation for this parabola in vertex form.

Answers

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]

Gllberto invests $10,000 in a savings account that pays 4.75% simple interest. If Gilberto
makes no withdrawals or deposits to the account, how much will be in the account after 7
years?

Answers

Answer:

$13,325

Step-by-step explanation:

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