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3 years ago

Help please, im unsure

Mathematics

1 answer:

Helen [10]3 years ago

8 0

Answer:

The value of AM = 43

Step-by-step explanation:

As point M is the midpoint of AB, so

AB = AM + BM

AM = BM

Given

AB = 8x - 50

AM = 2x + 9

so substituting AB = 8x - 50 and AM = 2x + 9 in the equation AB = AM + BM

AB = AM + BM

8x - 50 = 2x + 9 + BM

8x - 2x - 50 - 9 = BM

6x - 50 = BM

Thus,

BM = 6x - 59

AM = BM

so substituting AM = 2x + 9 and BM = 6x - 59 in the equation AM = BM

2x + 9 = 6x - 59

switch sides

6x - 59 = 2x + 9

subtract 2x from both sides

6x - 2x - 59 = 2x + 9 - 2x

4x - 59 = 9

add 59 to both sides

4x - 59 + 59 = 9 + 59

4x = 68

divide both sides by 4

4x/4 = 68/4

x = 17

Thus, the value of x = 17

Therefore, the value of AM will be:

AM = 2x + 9 = 2(17) + 9 = 34 + 9 = 43

Hence, the value of AM = 43

<u>Verification:</u>

AM = BM

2x + 9 = 6x - 59

2(17) + 9 = 6(17) - 59

34 + 9 = 102 - 59

43 = 43

and

AB = 8x - 50 = 8(17) - 50 = 86

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Help please, im unsure ​

Help please, im unsure