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sergiy2304 [10]
3 years ago
7

if the function f(x) has a domain of -2≤x≤8 and a range of -4≤y≤6 and the function g(x) is defined by the formula g(x)= 5f(2x) t

hen what are the domain and range of g. explain your thought process
Mathematics
1 answer:
Mice21 [21]3 years ago
7 0

Answer:

Domain: -1 ≤ x ≤ 4

Range: -20 ≤ 5f(2x) ≤ 30

Step-by-step explanation:

Inputs of f are between -2 and 8

Input is now 2x, so

-2 ≤ 2x ≤ 8

-1 ≤ x ≤ 4

(Horizontal stretch, factor 1/2)

Range of f is -4 ≤ y ≤ 6

So,

-20 ≤ 5y ≤ 30

(Vertical stretch, factor 5)

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John types 265 words in 5 minutes. At this rate, how many words does he type per minute
Arisa [49]

Answer:

John can type 53 words per minute

Step-by-step explanation:

You would divide 265 by 5 to get the result of 53.

7 0
2 years ago
Read 2 more answers
Tom determines that the system of equations below has two solutions, one of which is located at the vertex of the parabola.
xxTIMURxx [149]

Answer:

Option A: b must equal 7 and a second solution to the system must be located at the point (2, 5)

Step-by-step explanation:

<u><em>The complete question is</em></u>

Tom determines that the system of equations below has two solutions, one of which is located at the vertex of the parabola.

Equation 1: (x – 3)2 = y – 4

Equation 2: y = -x + b

In order for Tom’s thinking to be correct, which qualifications must be met?

A: b must equal 7 and a second solution to the system must be located at the point (2, 5).

B: b must equal 1 and a second solution to the system must be located at the point (4, 5).

C: b must equal 7 and a second solution to the system must be located at the point (1, 8).

D: b must equal 1 and a second solution to the system must be located at the point (3, 4).

step 1

Find the vertex of the quadratic equation

The general equation of a vertical parabola in vertex form is

y=a(x-h)^2+k

where

(h,k) is the vertex

we have

(x-3)^{2}=y-4

so

y=(x-3)^{2}+4

The vertex is the point (3,4)

step 2

Find out the value of b in the linear equation

we know that

If the vertex is a solution of the system of equations, then the vertex must satisfy both equations

substitute the value of x and the value of y of the vertex in the linear equation

y=-x+b

For x=3, y=4

4=-3+b\\b=7

so

y=-x+7

step 3

Find out the second solution of the system of equations

we have

y=(x-3)^{2}+4 -----> equation A

y=-x+7 ----> equation B

solve the system of equations by graphing

Remember that the solutions are the intersection points both graphs

The second solution of the system of equations is (2,5)

see the attached figure

therefore

b must equal 7 and a second solution to the system must be located at the point (2, 5)

5 0
3 years ago
Read 2 more answers
Need help ASAP will mark brainliest
nalin [4]

Answer:

  5x -7y = 21

Step-by-step explanation:

A sketch can convince you that BC is a transversal perpendicular to parallel lines AB and CD. The question asks for an equation for CD, so we just need to write the equation of a line through D that is parallel to AB.

One way to do this is to equate the slopes of the parallel lines:

  ∆y/∆x for AB = ∆y/∆x for CD

  (y2 -y1)/(x2 -x1) = (y -2)/(x -7) . . . . . . where (x1, y1) = A; (x2, y2) = B; (7, 2) = D

  (4 -(-1))/(1 -(-6)) = (y -2)/(x -7)

  5(x -7) = 7(y -2) . . . . . . . . . . . . . cross multiply

  5x -7y = 21 . . . . . . . . . . . . . . . . add 35 -7y, simplify

_____

Note that the graph shows the line CD is named "b", and its equation is shown at upper left. Multiplying that equation by -1 gives the one shown here.

6 0
3 years ago
If I subtract the square of one integer from the square of another, the difference could be
SIZIF [17.4K]

Answer:

The answer is C

Step-by-step explanation:

3 0
3 years ago
Question 2<br> Write an algebraic expression for the verbal expression.<br> a number n less 35
Contact [7]
X < 35
Hope this helps
6 0
3 years ago
Read 2 more answers
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