Answer:
A sequence that has a contant addition/subtraction to get to the next term
for example:
-3, 0, 3, 6, ...
to get to the next term, we'll need to add 3 each time
Step-by-step explanation:
You need the Pythagorean theorem to solve for the side lengths.
Shorter side:
sqrt(6^2+1^2)=sqrt(37)
Longer side:
sqrt(12^2+2^2)=sqrt(148)
Now multiply the sides together to get:
sqrt(37*148)=sqrt(5476)=74
Answer:
f(g(x)) = 722, and g(f(x)) = 154
Step-by-step explanation:
f(x) = 2x²
g(x) = 3x + 4
g(f(x)) = 3(2x²) + 4
g(f(5)) = 3(2 × 5²) + 4
g(f(5)) = 3(2 × 25) + 4
g(f(5)) = 3 × 50 + 4
g(f(5)) = 154
f(g(x)) = 2(3x + 4)²
f(g(5)) = 2(3 × 5 + 4)²
f(g(5)) = 2 × 19²
f(g(5)) = 2 × 361
f(g(5)) = 722
Answer:
8
Step-by-step explanation:
To solve this problem, we need to find the area of the pen, then divide that by the area required by each dog.
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The relationship between circumference and radius is ...
C = 2πr
Solving for r gives ...
r = C/(2π)
The relationship between radius and area of a circle is ...
A = πr²
Substituting for r from above gives ...
A = π(C/(2π))² = C²/(4π)
Filling in the given numbers, we find the area of the pen to be ...
A = (78.5 ft)²/(4·3.14) = 490.625 ft²
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Dividing the pen area by the area per dog gives the number of dogs the pen can hold:
(490.625 ft²)/(60 ft²/dog) ≈ 8.18 dogs
The pen can safely keep 8 dogs.
Answer: Translation: The school will build a fast soccer field that is 120m long and 60m wide, but around it there will be an 8m wide race track. Find the area of the terrain and the area of the track
Step-by-step explanation: