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Vedmedyk [2.9K]
3 years ago
14

What is the arc measure of AD in degrees?

Mathematics
1 answer:
lubasha [3.4K]3 years ago
5 0

Angle ABD measures half of arc AD and angle DBC measures half of arc DC. Therefore angle ABC measures half of arc ADC.

We state this as a theorem:

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Subtract 7 from the product of 4 and a number results in the number added to 29 is what
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4x-7=29 < do you understand how to set that up? Now, the goal is to “get x by itself.”

4x-7=29< now add the 7 to the 29. When you cross an equals sign you change the (+/-) sign of the number you’re moving.

4x= 36< now you will just divide by 4 on both sides. This will give you x by itself on the left side of the equals sign.

x=36/4 which is 9

X=9 :))
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Answer:

A

Step-by-step explanation:

Given

y - 2x - 8 = 0 ( add 2x + 8 to both sides )

y = 2x + 8 → (1)

y² + 8x = 0 → (2)

Substitute y = 2x + 8 into (2)

(2x + 8)² + 8x = 0 ← expand left side using FOIL and simplify

4x² + 32x + 64 + 8x = 0

4x² + 40x + 64 = 0 ( divide through by 4 )

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x + 2 = 0 ⇒ x = - 2

Substitute these values into (1) for corresponding values of y

x = - 8 : y = 2(- 8) + 8 = - 16 + 8 = - 8 ⇒ P (- 8, - 8)

x = - 2 : y = 2(- 2) + 8 = - 4 + 8 = 4 ⇒ Q (- 2, 4 )

Calculate the length of PQ using the distance formula

PQ = \sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2    }

with (x₁, y₁ ) = P (- 8, - 8) and (x₂, y₂ ) = Q (- 2, 4 )

PQ = \sqrt{(-2-(-8))^2+(4-(-8))^2}

      = \sqrt{(-2+8)^2+(4+8)^2}

       = \sqrt{6^2+12^2}

       = \sqrt{36+144}

       = \sqrt{180}

       = \sqrt{36(5)}

       = \sqrt{36} × \sqrt{5}

        = 6\sqrt{5} → A

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