In the circle below, if arc AB is congruent to arc CD, chord AB = 16x - 2 and chord CD = 14x + 8, find x.

Mathematics

1 answer:

erastova [34]2 years ago

5 0

Answer:

d. x = 5

Step-by-step explanation:

Chords that subtend congruent arcs are congruent.

<h3>Setup</h3>

Chord lengths are the same:

AB = CD

16x -2 = 14x +8

<h3>Solution</h3>

2x = 10 . . . . . . add 2-14x

x = 5 . . . . . . . . divide by 2

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Hi there!

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I believe your answer is:

Option B) $y=x-5$

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Here’s why:

Most options (Second, Third, and Fourth) are in slope intercept form.

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$\boxed{\text{Slope-Intercept Form}}\\\\y=mx + b\\\\\boxed{\text{Key:}}\\\\m - \text{The Slope}\\\\b- \text{The Y-Intercept}$

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We are looking for the equation where '-5' is in b's place.

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$\boxed{\text{Which equation shows a y-intercept of -5?}}\\\\---------\\\text{A}) -5y = x\\\\\text{This equation in slope-intercept form is }y=\frac{1}{5}x.\\\\\text{The 'b' part is not shown. This means that the line passes through the}\\\text{origin.}\\\\---------\\\\\text{B})\text{ }y = x-5\\\\\text{This option shows a slope of one and a y-intercept of -5.} \\\\\text{Therefore, \boxed{\text{option B is the correct answer.}}}\\\\----------\\\text{Option C has a y-intercept of 5, and Option D has a}\\$