Use the Pythagorean Theorem: a² + b² = c².
a and b are the legs of the right triangle, and c is the hypotenuse.
2) 5² + b² = 6²
25 + b² = 36
b² = 11
b = 3.3 cm
3) 7² + b² = 8²
49 + b² = 64
b² = 15
b = 3.9 cm
4) a² + 5² = 13²
a² + 25 = 169
a² = 144
a = 12 cm
Answer:
Step-by-step explanation:
The discriminant is found in
which is part of the quadratic formula. In
, a = 4, b = 10, c = -16. Filling in for the discriminant:
It's positive so we know we have real roots; it's not a perfect square, so our solutions are 2 complex rational.
In 
, a = -16, b = -7, c = 3. Filling in for the discriminant:
It's positive and not a perfect square so the 2 solutions are complex rational
Answer:
2094.4yds cubed
Step-by-step explanation:
V=pi*r^2*h/3
V=pi*100*20/3
V≈2094.4
32 students choose a favorite topping for their slices.
Let x be the total number of students.
1/2 of the total students, or 1/2x, choose pepperoni.
1/4 of the total students, or 1/4x, choose extra cheese.
1/8 of the total students, or 1/8x, choose sausage.
4 students choose mushrooms.
We know that together, these equal the total number of students, x:
1/2x+1/4x+1/8x+4=x
We will use 8 as the common denominator:
4/8x+2/8x+1/8x+4=x
Combining like terms:
7/8x+4=x
Subtract 7/8x from both sides:
7/8x+4-7/8x=x-7/8x
4=1x-7/8x
4=1/8x
Divide both sides by 1/8:
4÷(1/8) = 1/8x÷(1/8)
4/1÷(1/8) = x
4/1×8/1 = x
32/1 = x
32 = x
