Pre-calc What is the remainder when x +4 is divided by x - 2?
1 answer:
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<h3>Answer: As a fraction, HC is 21/4 units long</h3><h3>In decimal form, HC is 5.25 units long.</h3>
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Work Shown:
Let x = HC and y = BH
AH = 12-x since AH = 12-HC and x = HC
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See the attached drawing below. The altitude BH forms three similar triangles which makes the proportion below possible
HC/BH = BH/AH
x/y = y/(12-x) ... substitution
x(12-x) = y^2 ... cross multiply
y^2 = -x^2+12x
note how I isolated y^2 instead of y. We will use this equation later.
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Focus on triangle AHB. Use the pythagorean theorem
(BH)^2 + (AH)^2 = (AB)^2
(y)^2 + (12-x)^2 = (9)^2
y^2 + 144-24x+x^2 = 81
-x^2+12x + 144-24x+x^2 = 81 ... replace y^2 with -x^2+12x
-x^2+12x + 144-24x+x^2-81 = 0
-12x + 63 = 0
-12x = -63
x = -63/(-12)
x = 5.25 <<-- answer in decimal form
x = 5 + 0.25
x = 5 + 1/4
x = 20/4 + 1/4
x = 21/4 <<-- answer as a fraction
Answer:
The value of y that would make O P parallel to L N = 36
Step-by-step explanation:
This is a question on similar triangles. Find attached the diagram obtained from the given information.
Given:
The length of O L = 14
the length of O M = 28
the length of M P = y
the length of P N = 18
Length MN = MP + PN = y + 18
Length ML = MO + OL = 28+14 = 42
For OP to be parallel to LN,
MO/ML = MP/PN
MO/ML = 28/42
MP/PN= y/(y+18)
28/42 = y/(y+18)
42y = 28(y+18)
42y = 28y + 18(28)
42y-28y = 504
14y = 504
y = 504/14 = 36
The value of y that would make O P parallel to L N = 36
