Longer leg = x + 4
Shorter leg = x
Hypotenuse = x + 8
Using Pythagorean Theorem:
a^2 + b^2 = c^2
(x + 4)^2 + x^2 = (x + 8)^2
x^2 + 8x + 16 + x^2 = x^2 + 16x + 64
2x^2 + 8x + 16 = x^2 + 16x + 64
2x^2 +8x = x^2 + 16x + 48
2x^2 - 8x = x^2 + 48
x^2 - 8x = 48
x^2 - 8x - 48 = 0
You can complete the square from here or use the quadratic formula.
Completing the square:
x^2 - 8x = 48
x^2 - 8x + (-8/2)^2 = 48 + (-8/2)^2
x^2 - 8x + 16 = 48 + 16
(x - 4)(x - 4) = 64 or (x - 4)^2 = 64
x - 4 = +√64 OR x - 4 = -√64
x - 4 = +8 OR x - 4 = -8
x = 12 OR x = -4
However, you can't use negative 4 as a length because your length needs to be a positive.
So x will be 12.
Shorter leg: 12
Longer leg: 12 + 4
Hypotenuse: 12 + 8
Answer:
The answer is c = 2 + 3d .
Step-by-step explanation:
It is given that a cab ride cost $2 which is a fixed amount and charges additional $3 per mile. So you have to make an equation of c in terms of d :
Let c be the cost,
Let d be the distance,
c = 2 + 3d
Part A)
The coin landed on heads 9 times out of 30 flips, so the experimental probability is 9/30, which reduces to 3/10 probability.
Part B)
Theoretically a coin has a 1/2 probability of landing on heads each flip
Answer:
The area of the building in terms of y in its simplest form is 12(y + 2)
Step-by-step explanation:
Since the area of a rectangle is A = LW where L = length and W = width. From our question, the width of the rectangular building is 3 feet. So, W = 3 feet and its length is 4y + 8 feet. So, L = 4y + 8 feet.
So, the area of the building in terms of y is A = LW
= (4y + 8) × 3
Factorizing out 4 from the expression, we have
= 4(y + 2) × 3
= 12(y + 2)
So, the area of the building in terms of y in its simplest form is 12(y + 2)
