Pythagorean theorem: a² + b² = c²
a = long leg
b = short leg
c = hypotenuse
graph can form a right triangle:
JK: a = 7 - 3 = 4 ; b = 5 - 3 = 2
⇒ 4² + 2² = c² ⇒ 16 + 4 = 20 ; c = √20 = 4.47 or 4.5 units
VW: a = 6 - (-2) = 6 + 2 = 8 ; b = -3 - (+4) = 7
⇒ 8² + 7² = c² ⇒ 64 + 49 = 113 ; c = √113 = 10.63 units
EG: a = 7 - (-2) = 7 + 2 = 9 ; b = 9 - 1 = 8
⇒ 9² + 8² = c² ⇒ 81 + 64 = 145 ; c = √145 = 12.04 units
EG: a = -1 - 6 = 7 ; b = 2 - (-2) = 2 + 2 = 4
⇒ 7² + 4² = c² ⇒ 49 + 16 = 65 ; c = √65 = 8.06 units
Trapezoid: Rectangle and right triangle.
Rectangle = 1 side of the width is the long leg of the right triangle.
a = 8 - 2 = 6 ; b = 12 - 9 = 3
6² + 3² = c² ; 36 + 9 = 45 ; c = √45 = 6.71 units
upper base:CD: 9 - 2 = 7
lower base: BA: 12 - 2 = 10
side: DA: 8 - 2 = 6
side: CB: 6.71
Perimeter = 7 + 10 + 6 + 6.71 = 29.71 units
Answer:
347.1 and the standard deviation is
Step-by-step explanation:
the standard deviation you subtract the mean from each number then you square the results then you work out the mean of those results then square root that
A+b+c=56
a=√625=25
b=2√81 = 2x9=18
c = 56-25-18=13
X + y = 33
x - y = 9 Add the 2 equations together
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2x = 42 Divide both sides by 2
x = 21
Use the original equation and plug 21 in for x, then solve.
x + y = 33
21 + y = 33
Subtract 21 from both sides
y = 12
One list had 21 items on it and the other list had 12 items on it.
Answer:
a₆ = 12
Step-by-step explanation:
The nth term of an arithmetic sequence is
= a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Given a₂ = 5 and a₁₀ = 19 , then
a₁ + d = 5 → (1)
a₁ + 9d = 19 → (2)
Subtract (1) from (2) term by term to eliminate a₁
8d = 14 ( divide both sides by 8 )
d = 1.75
Substitute d = 1.75 into (1)
a₁ + 1.75 = 5 ( subtract 1.75 from both sides )
a₁ = 3.25
Then
a₆ = 3.25 + 5(1.75) = 3.25 + 8.75 = 12