Answer:
Exact answer = 10.41666666666666666666666666666pi
Estimated answer = 32.70938
Step-by-step explanation:
Semi circle formula: 1/2 * 4/3 * pi * r^3
r = 2.5
1/2 * 4/3 * pi * 2.5^3
2/3 * pi * 2.5^3
2/3 * pi * 15.625
10.416..... * pi
Exact answer = 10.417pi
We can estimate pi as 3.14
So, 10.417 * 3.14 = 32.70938
Exact answer = 10.41666666666666666666666666666pi
Estimated answer = 32.70938
Answer:
Step-by-step explanation:
1. Set 3x + 20 and 5x - 50 equal to each other
3x + 20 = 5x - 50
3x = 5x - 70
-2x = -70
x = 34
2. Once you've solved for x plug that in to 3x + 20 or 5x + 50
3(35)+ 20
105 + 20
125
3. After plugging in the x take that answer and subtract from 180 which will give you y
180 - 125 = y
55 = y
We have an triangle:
base=4 in
height=3 in,
This triangle can be dividided into two equal triangles, we need calculate the hypotenuse.
leg₁=4 in/2=2 in
leg₂=3 in
Pythagoras law:
hypotenuse²=leg₁²+leg₂²
hypotenuse²=(2 in)²+(3 in)²
hypotenuse²=4 in²+9 in²
hypotenuse²=13 in²
hypotenuse=√13 in.
Now, we can find the surface area.
Surface area=2 *(rectangle area)+base area + 2(triangle area)
rectangle area=10 in x √13 in=10√13 in²
base area=10 in x 4 in=40 in²
Triangle area=(4 in x 3 in)/2=6 in²
Surface area=2(10√13 in²)+40 in²+2(6 in²)=(20√13+52) in²≈124.11 in²
Answer: 124.11 in²
Answer:
The vertex will be at ( -1,-2)
Step-by-step explanation:
g(x) = |x + 1| - 2.
The vertex of g(x) = |x | is ( 0,0)
y = f(x) + C C < 0 moves it down
y = f(x + C) C > 0 moves it left
We shift this to the left 1 unit and down 2 units
( 0 -1, 0-2)
The vertex will be at ( -1,-2)
