For the functions f(x) = 2x − 6 and g(x) = 5x + 1, which composition produces the greatest output? A. Both compositions produce the same output B. Neither composition produces an output. C. f(g(x)) produces the greatest output. D. g(f(x)) produces the greatest output.

Answers

Answer 1
Answer: f(g(x)) = 2(5x+1)-6 = 10x+2-6 = 10x-4

g(f(x)) = 5(2x-6)+1 = 10x-30+1 = 10-29

10x-4>10-29 because from f(g(x)) you subtract less quantity. 
The answer to your question is C. I hope that this is the answer that you were looking for and it has helped you.
Answer 2
Answer:

Answer:

-24

Step-by-step explanation:


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Vertex (0,0) focus (0,-1)A) y=1/4 x^2
B) y=-1/4x^2
C) y=1/16x^2
D) y=-1/16x^2

Answers

Answer:B

Step-by-step explanation:

Write an expression that represents the height of a tree that begins at 2 feet and increases by 4 feet per year. Let y represent the number of years. PLEASE HELP ME

Answers

Answer:
2+4y

Explanation:
The height of the tree increases by 4 feet per year, so we know to multiply 4 by the number of years to find its height. The initial height of the tree is 2, so we add 2 to 4y.

Example: The height of the tree in 6 years
2+4y
2+4*6
=2+24
=26

I hope this helps!

Answer:

2+4y

Step-by-step explanation:

Which of the following points lie in the solution set to the following system of inequalities?y < −3x + 3
y < x + 2
(1, −5)
(1, 5)
(5, 1)
(−1, 5)

Answers

Answer with Step-by-step explanation:

We have to find the points which lie in the solution set of the following system of inequalities:

y < −3x + 3

y < x + 2

(1, −5)

when x=1

y < −3x + 3⇒ y<0

y < x + 2⇒ y<3

and y= -5 satisfies the above inequalities

So, it lies in the solution set

(1, 5)

when x=1

y < −3x + 3⇒ y<0

y < x + 2⇒ y<3

and y= 5 does not satisfy the above inequalities

So, it does not lie in the solution set

(5, 1)

when x=5

y < −3x + 3⇒ y< -12

y < x + 2⇒ y<7

and y= 1 does not satisfy the above inequalities

So, it does not lie in the solution set

(−1, 5)

when x= -1

y < −3x + 3⇒ y<6

y < x + 2⇒ y<1

and y= 5 does not satisfy the above inequalities

So, it does not lie in the solution set

Hence, Correct answer is:

(1,-5)

(1,-5) would be the answer. I used a graphing calculator to solve this. I plugged in the equation and looked at the intersection of the 2 graphs. Hope this helps.

Penn stacks all of his snowballs in a square pyramid. The number of snowballs, P(n), in n layers of the square pyramid is given by P(n) = P(n-1) + n^2 Which could not be the number of snowballs Penn has? 5, 30, 25, 14

Answers

Naturally, a pyramid of zero layers doesn't need any snowballs, so P(0) = 0. Then using the given recurrence, we find

P(1) = 1

P(2) = 1 + 4 = 5

P(3) = 1 + 4 + 9 = 14

P(4) = 1 + 4 + 9 + 16 = 30

and so on; luckily, three of these are listed among the answer choices, which leaves 25 as an insufficient number of snowballs to make such a pyramid.

More generally, we would end up with

P(n) = 1^2 + 2^2 + 3^2 + \cdots + n^2 = \displaystyle \sum_(k=1)^n k^2 = \frac{n(n+1)(2n+1)}6

Then given some number of snowballs S, you could try to solve for n such that

S = n (n + 1) (2n + 1)/6

and any S that makes n a non-integer would be the answer.

What is the slope that is perpendicular to the line 4x-6y=12?.?.

Answers

Answer:

It might be -2/3

I tried doing the way I did in school but also on ---- and got the same answer so sorry if it's wrong

Answer:

-3/2

Step-by-step explanation:

4x-6y=12

-6y=12-4x

6y=4x-12

y=2/3x-2

Slope= 2/3

Perpendicular Slope= -3/2

The perpendicular line's slope is the opposite reciprocal of the original slope, so you answer is -3/2.

the expression 3x + 20 represents the elevation above sea level, in meters, of a rock climber after x minutes of climbing. what is the rock climber’s initial height above sea level?

Answers

Answer:

The rock climber’s initial height above sea level was 20 meters.

Step-by-step explanation:

This is because y-intercept is 20, meaning at time 0 minutes, the rock climber was at 20 meters.