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BaLLatris [955]
3 years ago
13

What would the missing value be?

Mathematics
1 answer:
Dafna11 [192]3 years ago
6 0

Answer:

x = 9

Step-by-step explanation:

Calculate the slope m using the slope formula

m = \frac{y_{2}-y_{1}  }{x_{2}-x_{1}  }

with (x₁, y₁ ) = (2, 6) and (x₂, y₂ ) = (x, - 5 )

m = \frac{-5-6}{x-2} = \frac{-11}{x-2} , then

\frac{-11}{x-2} = - \frac{11}{7} ← numerators are equal, so equate the denominators

x - 2 = 7 ( add 2 to both sides )

x = 9

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Step-by-step explanation:

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3 years ago
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Answer:

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Step-by-step explanation:

Assume your diagram is like the one below.

The intersecting secant angles theorem states, "When two secants intersect outside a circle, the measure of the angle formed is one-half the difference between the far and the near arcs."

For your diagram, that means

\begin{array}{rcl}m\angle L &=&\dfrac{1}{2} \left(m \widehat {JM} - m\widehat {PQ}\right)\\\\(3x + 13)^{\circ}& = &\dfrac{1}{2} \left[(8x + 48)^{\circ} - (5x - 20)^{\circ}\right]\\\\3x + 13& = &\dfrac{1}{2}(8x + 48 - 5x + 20)\\\\3x + 13& = &\dfrac{1}{2}(3x + 68)\\\\6x + 26 & = & 3x + 68\\6x & = & 3x + 42\\3x & = & 42\\x & = & \mathbf{14}\\\end{array}

Check:

\begin{array}{rcl}(3\times14 + 13) & = &\dfrac{1}{2} \left[(8\times14 + 48)^{\circ} - (5\times14 - 20)^{\circ}\right]\\\\42 + 13& = &\dfrac{1}{2}(112 + 48 - 70 + 20)\\\\55& = &\dfrac{1}{2}(110)\\\\55 & = & 55\\\end{array}

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