<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
The equation of the line is y = 3x + 6
<h3>What are linear equations?</h3>
Linear equations are equations that have constant average rates of change.
Note that the constant average rates of change can also be regarded as the slope or the gradient
<h3>How to determine the
equation of the line?</h3>
The given parameters are
Slope, m = 3
y-intercept, c = 6
A linear equation is represented as
y = slope * x + y-intercept
i.e.
y = mx + c
So, we have
y = 3x + 6
Hence. the linear equation is y = 3x + 6
Read more about linear equation at
brainly.com/question/14323743
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Since they are asking you who swam the fastest not the longest etc but the fastest. So the answer would be tawni. I believe this because they never said who swam more BUT JUST THE FASTEST PERIOD! Sorry, i went too far. Hope this helps! :)
Answer:
(9x +12y) & (9x - 12y)
Step-by-step explanation:
Hence, dimensions of the pool are (9x + 12y) & (9x - 12y)
