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Natasha_Volkova [10]
1 year ago
5

From the diagram below, if the sides AD = 3 and DC = 27, and BD = X + 3, find x.

Mathematics
1 answer:
Colt1911 [192]1 year ago
4 0

Given:

• AD = 3

,

• DC = 27

,

• BD = x + 3

Let's solve for x.

To solve for x, apply the altitude formula:

\frac{AD}{BD}=\frac{BD}{DC}

Where BD is the altitude.

Cross multiply:

BD^2=AD*DC

Plug in the values and solve for x:

\begin{gathered} (x+3)^2=3*27 \\  \\ (x+3)^2=81 \end{gathered}

Take the square root of both sides:

\begin{gathered} \sqrt{(x+3)^2}=\sqrt{81} \\  \\ x+3=9 \\  \\ \text{ Subtract 3 from both sides:} \\ x+3-3=9-3 \\  \\ x=6 \end{gathered}

Therefore, the value of x is 6 .

ANSWER:

d. 6

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2 years ago
1. A circle with center (-5, 2) is tangent to the y-axis. What is the radius of the circle? What is the equation of the circle?
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Answer:

Step-by-step explanation:

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2)  Starting with (x - h)^2 + (y - k)^2 = r^2 and comparing this to the given

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we see that h = 4, k = -3 and r = 6.  The center is at (4, -3) and the radius is 6.

3)  Notice that A and B have the same x-coordinate, x = 15.  The center of the circle is thus (15, -2), where that -2 is the halfway point between the two given points in the vertical direction.   Arbitrarily choose A(15, 4) as one point on the circle.  Then the equation of this circle is

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2 years ago
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