Answer:
x = 6, x = - 6
Step-by-step explanation:
Given
y = x² - 36
To find the zeros let y = 0, that is
x² - 36 = 0 ← x² - 36 is a difference of squares and factors in general as
a² - b² = (a - b)(a + b), thus
x² - 36 = 0
x² - 6² = 0
(x - 6)(x + 6) = 0 ← in factored form
Equate each factor to zero and solve for x
x - 6 = 0 ⇒ x = 6
x + 6 = 0 ⇒ x = - 6
Let h = height of triangle
h^2 + 12^2 = 15^2
h^2 + 144 = 225
h^2 = 225 - 144
h^2 = 81
sqrt{h^2} = sqrt{81}
h = 9 cm
For part B, we need to find surface area because it represents the perimeter of this 3-D figure. The formula needed is SA = B + LA.
1. First find the lateral area.
LA = perimeter of triangle • height
LA = ph
p = 15 + 15 + 24
p = 30 + 24
p = 54 cm
LA = (54)(9)
LA = 486 cm^2
2. We now find the base of each triangle. This is found by finding the area of each triangle and multiplying by 2.
A = (1/2)bh
A = (1/2)(24)(9)
A = 108 cm^2
A = 2•108 cm^2
A = 216 cm^2 = our B in the surface area formula.
SA = B + LA
SA = 216 cm^2 + 486 cm^2
SA = 702 cm^2
The amount of cardboard needed is 702 cm^2.
The sum is 61 for this equation.
Answer:
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