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Olenka [21]
2 years ago
15

In segment AC, the midpoint is B. If segments AC = 5x-9 and AB = 2x, what is the measure of segment AC.

Mathematics
1 answer:
IgorLugansk [536]2 years ago
8 0

Answer:

The measure of segment AC is 36 units

Step-by-step explanation:

- The mid-point divides the segment into two equal parts in length

- B is the mid point of segment AC

- That means B divides segment AC into two equal parts in length

∴ AB = BC

∵ AC = 5x - 9

∵ AB = 2x

- The two parts AB and BC are equal in length

∴ BC = 2x

∵ AC = AB + BC

- Substitute the values of AB and BC in the expression of AC

∴ AC = 2x + 2x

∴ AC = 4x

∵ AC = 5x - 9

- Equate the two values of AC

∴ 5x - 9 = 4x

- Add 9 to both sides

∴ 5x = 4x + 9

- Subtract 4x from both sides

∴ x = 9

- Substitute the value of x in any expression of AC

∵ AC = 4x

∵ x = 9

∴ AC = 4(9) = 36

* The measure of segment AC is 36 units

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Simplify the expression using long division. (10x2 – 85x – 10) ÷ (x – 8) Question 7 options: quotient 10x – 5 and remainder –50
Anna [14]

Answer:

The quotient is (10x - 5) and the reminder is -50 ⇒ 1st answer

Step-by-step explanation:

* Lets solve the long division by easiest way

∵ (10x² - 85x - 10)/(x - 8)

∵ (10x² - 85x - 10) is the dividend

∵ (x - 8) is the divisor

- Divide the first term of the dividend by the first term of the divisor

∴ 10x² ÷ x = 10x ⇒ first term of the quotient

- Multiply 10x by the the divisor

∴ 10x(x - 8) = 10x² - 80x

- Subtract the answer from the dividend

∴ (10x² - 85x - 10) - (10x² - 80x) =

# 10x² - 10x² = 0

# -85x - -80x = -85x + 80x = -5x

# -10

∴ (10x² - 85x - 10)/(x - 8) = 10x + (-5x - 10)/(x - 8)

* Repeat the same steps again with the new dividend -5x - 10

- Divide the first term of the dividend by the first term of the divisor

∴ -5x ÷ x = -5 ⇒ second term of the quotient

- Multiply -5 by the divisor

∴ -5(x - 8) = -5x + 40

- Subtract the answer from the dividend

∴ (-5x - 10) - (-5x + 40) =

# -5x - -5x = -5x + 5x = 0

# -10 - 40 = -50

∴ (-5x - 10)/(x - 8) = -5 + -50/(x - 8)

∴ (10x² - 85x - 10)/(x - 8) = 10x - 5 + -50/(x - 8)

- The quotient is the answer of the division

∴ The quotient is (10x - 5) and the reminder is -50

7 0
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Dahasolnce [82]

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Hope this helps!

6 0
3 years ago
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Tems11 [23]

Answer: There was 5/8 of a foot of board left.

Step-by-step explanation:

Step 1. We need to subtract 1/4 from 7/8. To do this make it where both fractions have the same denominator.

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Answer:

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3 0
2 years ago
What is the answer I need help!
g100num [7]

Answer:

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Step-by-step explanation:

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