The statement that is true is option A that is Line segment TU is parallel to line segment RS because StartFraction 32 Over 36 EndFraction = StartFraction 40 Over 45 EndFraction.

<h3>What is the line segment about?</h3>

The law of the side- splitter connote that when f the line is parallel to a side of the triangle and if that said line do intersects the other 2 sides, tt is said to divides those given sides proportionally.

So the converse means that when the sides are proportional so therefore, the side TU is said to be parallel to the side RS.

Thus;

$\frac{QT}{TR}$ = $\frac{32}{36} = \frac{8}{9}\\\\ \\$

$\\\frac{QU}{US} =\frac{40}{45} = \frac{8}{9}\\$

Therefore, the ratios are equal and as such TU is parallel to RS

Hence, The statement that is true is option A that is Line segment TU is parallel to line segment RS because StartFraction 32 Over 36 EndFraction = StartFraction 40 Over 45 EndFraction.

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5 0

2 years ago

Three siblings- Kate, Sarah, and Dave- committed themselves to volunteer 160 hours for a homeless charity to build new housing .

liraira [26]

Kate worked for 50 hours, Dave worked for 65 hours and Sarah

worked for 45 hours

Step-by-step explanation:

Three siblings- Kate, Sarah, and Dave- committed themselves to

volunteer 160 hours for a homeless charity to build new housing

1. Dave worked 15 hours more than Kate

2. Sarah worked 5 hours fewer than Kate

3. The total hours for them is 160 hours

Assume that Kate worked for x hours

∵ Kate worked for x hours

∵ Dave worked 15 hours more than Kate

∴ Dave worked for x + 15 hours

∵ Sarah worked 5 hours fewer than Kate

∴ Sarah worked x - 5 hours

∵ They worked for 160 hours

- Add the number of worked hours of them and equate the sum

by 160

∴ x + x + 15 + x - 5 = 160

- Add like terms in the left hand side

∴ 3x + 10 = 160

- Subtract 10 from both sides

∴ 3x = 150

- Divide both sides by 3

∴ x = 50 hours

∵ Kate worked for x hours

∴ Kate worked for 50 hours

∵ Dave worked for x + 15 hours

∴ Dave worked for 50 + 15 = 65 hours

∵ Sarah worked for x - 5 hours

∴ Sarah worked for 50 - 5 = 45 hours

Kate worked for 50 hours, Dave worked for 65 hours and Sarah

worked for 45 hours

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6 0

4 years ago