In the right ∆ABC, the hypotenuse AB = 17 cm. M is the midpoint of the hypotenuse. Find the legs if PAMC=32 cm and PBMC=25 cm
Answers
Answer:
The length of the legs is 8.64cm and 14.64cm respectively
Step-by-step explanation:
I've added an attachment to aid my explanation.
At different intervals, I'll be making reference to it.
Given
[tex]AB = 17[/tex]
[tex]PAMC = 32[/tex]
[tex]PBMC = 25[/tex]
From the attachment, we have:
[tex]y + z = AB[/tex]
Since, M is the Midpoint
[tex]y = z = \½AB[/tex]
Substitute 17 for AB
[tex]y = z = \½ * 17[/tex]
[tex]y = z = 8.5[/tex]
Also, from the attachment
[tex]v + x + z = PAMC[/tex]
[tex]v + x + y = 32[/tex]
Substitute 8.5 for y
[tex]v + x + 8.5 = 32[/tex]
[tex]v + x = 32 - 8.5[/tex]
[tex]v + x = 23.5[/tex] --------- (1)
Also, from the attachment
[tex]v + w + z = 25[/tex]
Substitute 8.5 for z
[tex]v + w + 8.5 = 25[/tex]
[tex]v + w = 25 - 8.5[/tex]
[tex]v + w = 17.5[/tex] ----------- (2)
Subtract (2) from (1)
[tex]v - v + x - w = 23.5 - 17.5[/tex]
[tex]x - w = 6[/tex]
Make x the subject
[tex]x = 6 + w[/tex]
Apply Pythagoras Theorem:
We have that:
[tex]AB^2 = AC^2 + BC^2[/tex]
The above can be replaced with
[tex]17^2 = x^2 + w^2[/tex] (see attachment)
[tex]289 = x^2 + w^2[/tex]
Substitute 6 + w for x
[tex]289 = (6 + w)^2 + w^2[/tex]
[tex]289 = 36 + 12w + w^2 + w^2[/tex]
[tex]289 - 36 = 12w + 2w^2[/tex]
[tex]253 = 12w + 2w^2[/tex]
Reorder
[tex]2w^2 + 12w - 253 = 0[/tex]
Solve using quadratic equation:
[tex]w = \frac{-b \± \sqrt{b^2 - 4ac}}{2a}[/tex]
Where
[tex]a = 2[/tex]
[tex]b = 12[/tex]
[tex]c = -253[/tex]
[tex]w = \frac{-12 \± \sqrt{12^2 - 4 * 2 * -253}}{2 * 2}[/tex]
[tex]w = \frac{-12 \± \sqrt{144 + 2024}}{4}[/tex]
[tex]w = \frac{-12 \± \sqrt{2168}}{4}[/tex]
[tex]w = \frac{-12 \± 46.56}{4}[/tex]
Split:
[tex]w = \frac{-12 + 46.56}{4}[/tex] or [tex]w = \frac{-12 - 46.56}{4}[/tex]
[tex]w = \frac{34.56}{4}[/tex] or [tex]w = \frac{-58.56}{4}[/tex]
[tex]w = 8.64[/tex] or [tex]w = -14.64[/tex]
But length can't be negative
So:
[tex]w = 8.64[/tex]
Recall that: [tex]x = 6 + w[/tex]
[tex]x = 6 + 8.64[/tex]
[tex]x = 14.64[/tex]
Hence, the length of the legs is 8.64cm and 14.64cm respectively
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A dietician gathered data about the amounts of flour, baking powder, and butter used for several different muffin recipes. She used a graphing tool to organize the data in different scatter plots and found the following lines of best fit:
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plato master test
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The coefficient of determination - R - squared value is square of the correlation coefficient.
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Since, on comparing the R - squared values of the three relationships, we find that the R - squared value of the relationship between baking powder and flour used is largest. Thus, line of best fit between baking powder and flour is expected to produce the most reliable predictions.
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Step-by-step explanation:
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Answers
Answer:
Step-by-step explanation:
if it includes the point should verify the equation
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Answers
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Step-by-step explanation:
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Answers
Answer:
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Step-by-step explanation:
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