Answer:
A. 162 m²
Step-by-step explanation:
==>Given:
Isosceles trapezoid with:
base a = 19m
base b = 35m
Perimeter = 74meters
==>Required:
Area of trapezoid
==>Solution:
Recall: the length of the legs of an isosceles trapezoid are equal.
Perimeter of isosceles trapezoid = sum of the parallel sides + 2(length of a leg of the trapezoid)
Let l = leg of trapezoid.
Perimeter = 74m
Sum of parallel sides = a+b = 19+35 = 54m
Thus,
74 = 54 + 2(l)
74 - 54 = 2(l)
20 = 2(l)
l = 20/2 = 10m
Let's find area:
Area = ½(a+b)*h
a = 19
b = 35
h = ?
Using Pythagorean theorem, let's find h as follows:
h² = l² - [(35-19)/2)²
h² = 10² - [16/2]²
h² = 100 - 64
h² = 36
h = √36 = 6m
Area = ½ x (a+b) × h
= ½ × (19+35) × 6
= ½ × 54 × 6
= 27 × 6
Area = 162m²
The solution to the equation includes both the positive and negative portions of the solution. x = 12, -12
Answer: a) -13/16
Step-by-step explanation: Start by setting equations equal and rearrange X^3 - x^2 + 1 = 0. Visual inspection of graph shows x between -1 and -1/2. Start with x = 3/4 plug in and calculate: just a little too small. Try going halfway towards -1: x =-7/8 Plug in and the answer is very far from 0. Go halfway back towards -3/4: -13/16 and the equality is very close.
The answer you are looking for is -17/44
