Step-by-step explanation:
A transformation(s) of a parent function is

where a is vertical compression/stretched or reflection
B is horinzotnal compression/stretch or reflection
C is horinzontal translation
D is vertical translation.
The parent function is

First, we stretched this by 7
so we have

We need to shift this 12 units to the left so we have

We need to reflect this across x axis so we get

We need to shift this downwards 15 so we get

or because tan is a odd function you could say


This means that we will plug 3 into our x values.
Our rule is 5x.
This means that:
5(3)
This means our final answer will be 15.
Answer:
Step-by-step explanation:
%change=100(final-initial)/(initial)
%change=100(40-32)/32
%change=25%
The diagonal of a rectangle = sqrt(w^2 + l^2)
w = width
l = length
In this problem,
The diagonal = 20 in
w = x
l = 2x + 8
Let's plug our numbers into the formula above.
20in = sqrt((x)^2 + (2x + 8)^2)
Let's simplify the inside of the sqrt
20 in = sqrt(5x^2 + 32x + 64)
Now, let's square both sides.
400 = 5x^2 + 32x + 64
Subtract 400 from both sides.
0 = 5x^2 + 32x - 336
Factor
0 = (5x - 28)(x + 12)
Set both terms equal to zero and solve.
x + 12 = 0
Subtract 12 from both sides.
x = -12
5x - 28 = 0
Add 28 to both sides.
5x = 28
Divide both sides by 5
x = 28/5
The width cant be a negative number so now we know that the only real solution is 28/5
Let's plug 28/5 into our length equation.
Length = 2(28/5) + 8 = 56/5 + 8 = 96/5
In conclusion,
Length = 96/5 inches
Width = 28/5