Answer:
22 units
Step-by-step explanation:
The perimeter of a polygon is said to be the sum of the length of it's sides.
From the question, we have 5 vertices. This means the polygon is a pentagon. It's given vertices are
A = (−1, 3)
B = (−1, 6)
C = (2, 10)
D = (5, 6)
E = (5, 3)
To find the distance between two points, we use the formula
d = √[(y2 - y1)² + (x2 - x1)²]
Between A and B, we have
d(ab) = √[(6 - 3)² + (-1 --1)²]
d(ab) = √(3²) + 0
d(ab) = √9 = 3
Between B and C, we have
d(bc) = √[(10 - 6)² + (2 --1)²]
d(bc) = √[4² + 3²]
d(bc) = √(16 + 9) = √25 = 5
Between C and D, we have
d(cd) = √[(6 - 10)² + (5 - 2)²]
d(cd) = √[(-4)² + 3²]
d(cd) = √(16 + 9) = √25 = 5
Between D and E, we have
d(de) = √[(3 - 6)² + (5 - 5)²]
d(de) = √(-3)² + 0
d(de) = √9 = 3
Between E and A, we have
d(ea) = √[(3 - 3)² + (5 --1)²]
d(ea) = √[0 + (6)²]
d(ea) = √36 = 6
The perimeter is given as
d(ab) + d(bc) + d(cd) + d(de) + d(ea) =
3 + 5 + 5 + 3 + 6 = 22 units
Answer:
-36
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
Step-by-step explanation:
<u>Step 1: Define</u>
x⁴ - 3x² - 90
x = -3
<u>Step 2: Evaluate</u>
- Substitute in <em>x</em>: (-3)⁴ - 3(-3)² - 90
- Exponents: 81 - 3(9) - 90
- Multiply: 81 - 27 - 90
- Subtract: 54 - 90
- Subtract: -36
<span>To find the z-scores, find the difference in the number of inches for each value from the mean and then divide that by the standard deviation. For women at 72 inches (6'), this would be (72-64) / 2.7, or a z-score of +2.963. For a male at 72 inches, this would be (72-69.3)/2.8, or +0.964. This shows that the woman at 6 feet tall is more rare in the distribution than a man at 6 feet tall.</span>