The secant-tangent theorem states that when a tangent and a secant meet outside a circle, the product of the secant length and it's segment outside the circle is equal to the square of the tangent segment length.

Applying the tangent-secant theorem or rule, we will have this equation:

$AB \times EB= DB^{2}$

AB = $(x-7)+4 = x -3$

EB = 4

Substitute:

$(x - 3)(4) = 8^{2} \\\\4x - 12 = 64\\\\$

Add 12 to both sides

$4x = 64 +12\\\\4x = 76$

Divide both sides by 4

x = 19

Therefore the value of x is 19.

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4 0

3 years ago

What is the length of the third side of the window frame below? (Figure is not drawn to scale.) A picture of a right triangular

dmitriy555 [2]

78^2-72^2= 900
√900= 30

a. 30in

7 0

4 years ago

Read 2 more answers

Samantha loves to download new music. She originally had 52 songs but plans to purchase 2 new songs each week. She wants to know

aleksley [76]

Answer:

Step-by-step explanation:

a93 = 93 + 2(52 − 1)

a93 = 93 + 2(52 + 1)

a93 = 52 + 2(93 + 1)

a93 = 52 + 2(93 − 1)

Originally 52 - Get rid of the first 2

a93 = 52 + 2(93 + 1)

a93 = 52 + 2(93 − 1)

2 each week. - Annoying. That doesn't help.

a93 = 52 + 2(93 + 1)

a93 = 52 + 2(93 − 1)

We're not buying any new ones in the first week, so purchases are one down.

a93 = 52 + 2(93 − 1)

I think we made it.

5 0

3 years ago

In ΔKLM, the measure of ∠M=90°, KM = 40, LK = 41, and ML = 9. What ratio represents the tangent of ∠K?

melomori [17]

Answer:

The ratio representing the tangent of ∠K is 40 : 9.

Step-by-step explanation:

Consider the right-angles triangle KLM below.

The angle M is 90°.

KM = perpendicular (p) = 40

ML = base (b) = 9

LK = hypotenuse (h) = 41

The tangent of an angle is the ratio of the perpendicular length to the length of the base.

Compute the tangent of ∠K as follows:

$tan (K)=\frac{p}{b}=\frac{40}{9}$

Thus, the ratio representing the tangent of ∠K is 40 : 9.

5 0

3 years ago