Answer:
A. 27°
Step-by-step explanation:
Given that s is perpendicular to r, and <1 = 3x, <2 = 5x + 18, therefore:
m<1 + m<2 = 90°
3x + (5x + 18) = 90°
Solve for x using this equation
3x + 5x + 18 = 90
8x + 18 = 90
Subtract 18 from both sides
8x + 18 - 18 = 90 - 18
8x = 72
Divide both sides by 8
x = 9
Find m<1
m<1 = 3x
Plug in the value of x
m<1 = 3(9) = 27°
The common factor of 7 and 15 is 1
Answer:
3x+1.
Step-by-step explanation:
First we divide g(x)/f(x) (the process is in the first image):
5x-15 in Z7[x] is 5x-1 and 
is 
in Z7[x]. So
g(x)/f(x) = 
Now gcd(g,f) = gcm(f,r).
f(x)/r(x) = 
Then, gcd(f,r) = gcd(r,3x+1).
r/(3x+1) = 
Then, gcd(r, 3x+1) = gcd(3x+1,4) = 3x+1.
So, gcd(f,g) = 3x+1.
Answer:
7%
Step-by-step explanation:
Answer:
262 square feet
Step-by-step explanation:
The lateral surface is the side surfaces, except top and bottom.
There are 3 lateral surfaces.
The 2 sides are triangles with length 20 and height 8.5
And
The back is a rectangle with length 12 and height 8.5
We sum up all the 3 surface areas, that will give us the answer.
Area of triangle is (0.5) * length * height
So,
Area of 1 triangle = 0.5 * 20 * 8.5 = 80
Area of 2 triangles = 80 * 2 = 160
Area of rectangle = length * height
so,
Area of back rectangle = 12 * 8.5 = 102
Total Lateral Surface Area = 160 + 102 = 262 square feet
