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Dvinal [7]
3 years ago
11

If m∠JKM = 43, m∠MKL = (8 - 20), and m∠JKL = (10x - 11), find each measure.

Mathematics
1 answer:
Brut [27]3 years ago
3 0

Correct Question: If m∠JKM = 43, m∠MKL = (8x - 20), and m∠JKL = (10x - 11), find each measure.

1. x = ?

2. m∠MKL = ?

3. m∠JKL = ?

Answer/Step-by-step explanation:

Given:

m<JKM = 43,

m<MKL = (8x - 20),

m<JKL = (10x - 11).

Required:

1. Value of x

2. m<MKL

3. m<JKL

Solution:

1. Value of x:

m<JKL = m<MKL + m<JKM (angle addition postulate)

Therefore:

(10x - 11) = (8x - 20) + 43

Solve for x

10x - 11 = 8x - 20 + 43

10x - 11 = 8x + 23

Subtract 8x from both sides

10x - 11 - 8x = 8x + 23 - 8x

2x - 11 = 23

Add 11 to both sides

2x - 11 + 11 = 23 + 11

2x = 34

Divide both sides by 2

\frac{2x}{2} = \frac{34}{2}

x = 17

2. m<MKL = 8x - 20

Plug in the value of x

m<MKL = 8(17) - 20 = 136 - 20 = 116°

3. m<JKL = 10x - 11

m<JKL = 10(17) - 11 = 170 - 11 = 159°

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What is the rate of change and initial value for the linear relation that includes the points shown in the table?
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The initial value: 25, rate of change: -5 ⇒ answer C

Step-by-step explanation:

The table:

→  x  :    1    :    3    :    5    :    7

→  y  :    20 :    10  :    0    :    -10

The linear relation between x and y is y = m x + b, where

  • m is the rate of change
  • b is the initial value

Let us use the table to find m and b

∵ m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} , where (x_{1},y_{1})

   and (x_{2},y_{2}) are any two ordered pairs in the table

∵ (x_{1},y_{1}) = (1 , 20)

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∴ m=\frac{10-20}{3-1}=\frac{-10}{2}=-5

∵ m is the rate of change

∴ The rate of change is -5

Substitute the value of m in the form of the linear relation

∴ y = -5 x + b

To find b substitute x and y in the equation by the coordinates of any points in the table, let us chose point (5 , 0)

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- Add 25 to both sides

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∴ The initial value is 25

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