Let f(x) = 3x2 – x 2 and g(x) = 5x2 – 1. Find f(g(x)). Show each step of your work.

Answers

Answer 1

Answer: easy, sub g(x) for x in f(x)

f(g(x))=3(g(x))^2-(g(x))^2

g(x)=5x^2-1
f(g(x))=3(5x^2-1)^2-(5x^2-1)^2=
3(25x^4-10x^2+1)-(25x^4-10x^2)=
2(25x^4-10x^2+1)=
50x^4-20x^2+2

f(g(x))=50x^4-20x^2+2

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Part A: Describe the difference in combining functions and composing functions.
Part B: Give a real-world example of combining functions.
Part C: Give a real-world example of composing functions.

Answers

Part A:

A combined function is defined by combining with existing functions using addition, subtraction, multiplication or division.

A composite function is created by plugging one function into another.

Part B:

The class is selling sweaters an. the cost of each sweater is 8 dollars. There is a fee to create the design. The class plans to sell the sweaters for 12 dollars.

Part C:

Amy works at a baked goods store. She receivers a weekly salary of 350 dollars and is payed 3 percent commission on weekly sales over 1,500 dollars.

oof that took a while lol

Darnell's car used 8 gallons of gasoline to travel 340 miles. after a mechanic worked on the car, it used 7 gallons of gasoline to travel 350 miles. If the price of the gasoline was approximately $4.00 per gallon, how much lest to the nearst cent per mile, did it cost to run the car after the mechanic worked on it?

Answers

so, after the mechanic worked on it, it only does 7 gallons for 350miles, how many gallons will it be at that rate, for 340 miles then?

$\bf \begin{array}{ccll}gallons&miles\n\text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\n7&350\nx&340\end{array}\implies \cfrac{7}{x}=\cfrac{350}{340}\implies \cfrac{7\cdot 340}{350}=x\implies 6.8=x$

well, each gallon is 4 bucks, for 6.8 gallons that'd be 6.8*4.

we already know that before the mechanic worked on it, it was doing 8gallons for the same 340 miles, and at 4 bucks a gallon that'd be 8*4.

how much is her savings?

$\bf \stackrel{\stackrel{\textit{gallons cost}}{\textit{before being fixed}}}{(8\cdot 4)}\qquad -\qquad \stackrel{\stackrel{\textit{gallons cost}}{\textit{after it was fixed}}}{(6.8\cdot 4)}$

Solve each equation by finding all roots x^4-16=0

Answers

${ x }^( 4 )-16=0\n \n { x }^( 4 )=16\n \n x=\pm \sqrt [ 4 ]{ 16 } \n \n \therefore \quad x=\pm 2$

add both sides by 16
so you'll have x^4 =16
take the 4th root of both sides and you'll get x= 2

The radius of Venus is 3760.4 miles. What is the approximate volume of Venus?

Answers

Venus is a planet, hence is spherical shaped.

Formula for Volume of a Sphere: 4/3πr^2

Apply this formula
4/3π(3760.4)^2=59232040.95 miles^3

Which of the number(s) below are potential roots of the function?p(x) = x4 + 22x2 – 16x – 12

Answers

$Potential\ roots\ of\ the\ function:\n\np(x)=x^4+22x^2-16x-12\ are:\n\n\{\pm1;\pm2;\pm3;\pm4;\pm6;\pm12\}$

Answer:

6,1,3

Step-by-step explanation:

Three times a number increases by 15 is equal to 30

Answers

Answer: The number is 5.

Step-by-step explanation:

First, let d be our number.

Since we know that d is our number, we rewrite the expression this way:

3 times d incresed by 15 is 30.

3 times d is 3d; 3d increased by 15 => 3d + 15. This equals 30:

3d + 15 = 30

To solve for d, subtract 15 from both sides:

3d = 15

Next, divide both sides by 3:

d = 5

Using the equation 3x+15=30 x being the number we are trying to find out we replace x with 5 as 3*5 is 15+15 = 30

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