I’m sorry, I don’t know perpendicular but I would love to help.
Answer: 90
Explanation: The pattern is add 3 then the next set is double. [9-6=3 then 18-9=9(or doubled)] and the pattern continues and because 45-42=3 the next number set would be 45 doubles which equals 90.
Y = (x - 1)² + 2
y = (x² - x - x + 1) + 2
y = (x² - 2x + 1) + 2
y = x² - 2x + (1 + 2)
y = x² - 2x + 3
x² - 2x + 3 = 0
x = <u>-(-2) +/- √((-2)² 4(1)(3))</u>
2(1)
x = <u>2 +/- √(4 + 12)</u>
2
x = <u>2 +/- √(16)
</u> 2<u>
</u>x = <u>2 +/- 4
</u> 2<u>
</u>x = 1 <u>+</u> 2
x = 1 + 2 x = 1 - 2
x = 3 x = -1
y = x² - 2x + 3
y = (3)² - 2(3) + 3
y = 9 - 6 + 3
y = 3 + 3
y = 6
(x, y) = (3, 6)
or
y = x² - 2x + 3
y = (-2)² - 2(-1) + 3
y = 4 + 2 + 3
y = 6 + 3
y = 9
(x, y) = (-1, 9)
9 is the square root of 81
final answer: 9
Answers:
- Part (a) 10*sqrt(13)
- Part (b) 10*sqrt(5)
Those values are exact. They approximate to:
10*sqrt(13) = 36.0555
10*sqrt(5) = 22.3607
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Explanation:
Part (a)
If the unknown third side is the hypotenuse then we need to find the value of c when a = 20 and b = 30.
Apply the pythagorean theorem
a^2 + b^2 = c^2
20^2 + 30^2 = c^2
400 + 900 = c^2
1300 = c^2
c^2 = 1300
c = sqrt(1300)
c = sqrt(100*13)
c = sqrt(100)*sqrt(13)
c = 10*sqrt(13) .... exact length
c = 36.0555 ...... approximate length
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Part (b)
If the third side is not the hypotenuse then that must mean c = 30 is the hypotenuse as this side is larger than the 20 cm side. The hypotenuse is always the longest side.
Let a = 20 be the known leg. Let's find the other unknown leg b using the pythagorean theorem.
a^2 + b^2 = c^2
20^2 + b^2 = 30^2
400 + b^2 = 900
b^2 = 900-400
b^2 = 500
b = sqrt(500)
b = sqrt(100*5)
b = sqrt(100)*sqrt(5)
b = 10*sqrt(5) ..... exact length
b = 22.3607 ....... approximate length
