Solve the following equation(2m)/3 + 1/2 - m/5 = (4m)/5 + 5

Mathematics

1 answer:

Anarel [89]2 years ago

8 0

Answer:

m = - 13.5

Step-by-step explanation:

Given

$\frac{2m}{3}$ + $\frac{1}{2}$ - $\frac{m}{5}$ = $\frac{4m}{5}$ + 5

Multiply through by 30 ( the LCM of 3, 2, 5 ) to clear the fractions

20m + 15 - 6m = 24m + 150 , that is

14m + 15 = 24m + 150 ( subtract 24m from both sides )

- 10m + 15 = 150 ( subtract 15 from both sides )

- 10m = 135 ( divide both sides by - 10 )

m = - 13.5

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One of the same-side exterior angles formed by two lines and a transversal is equal to 1/6 of the right angle and is 11 times sm

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One of the same-side exterior angles formed by two lines and a transversal is equal to 1/6 of the right angle and is 11 times smaller than the other angle. Then the lines are parallel

<h3><u>Solution:</u></h3>

Given that, One of the same-side exterior angles formed by two lines and a transversal is equal to 1/6 of the right angle and is 11 times smaller than the other angle.

We have to prove that the lines are parallel.

If they are parallel, sum of the described angles should be equal to 180 as they are same side exterior angles.

Now, the 1st angle will be 1/6 of right angle is given as:

$\begin{array}{l}{\rightarrow 1^{\text {st }} \text { angle }=\frac{1}{6} \times 90} \\\\ {\rightarrow 1^{\text {st }} \text { angle }=15 \text { degrees }}\end{array}$