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yawa3891 [41]
3 years ago
11

Brandon mows his lawn once every 5 days. Thomas mows his lawn every 3 days. If they are all mowing there lawn today, how many da

ys will they be mowing there lawn together again?
A. 3


B. 5


C. 8


D. 15
Mathematics
1 answer:
lisov135 [29]3 years ago
4 0

Answer: D. 15

Step-by-step explanation:

Given : Brandon mows his lawn once every 5 days.

Thomas mows his lawn every 3 days.

If they are all mowing there lawn today, then the number of days after which they will be mowing there lawn together again=  LCM (5, 3)

[LCM= Least common multiple]

Since 5 and 3 are co primes (having no common factor other than 1),

so LCM(5,3)= 5 x 3 = 15

Therefore, they will be mowing there lawn together again after 15 days .

Hence, the correct answer is D. 15 .

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Write the equation of the line that is the perpendicular bisector of the segment with endpoints (4, 1) and (2, -5)
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Answer:   \bold{y=-\dfrac{1}{3}x-1}

<u>Step-by-step explanation:</u>

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First, find the slope (m) and then the perpendicular (opposite reciprocal) slope:

m=\dfrac{y_2-y_1}{x_2-x_1}\\\\\\m=\dfrac{-5-1}{2-4} = \dfrac{-6}{-2}=3\quad \rightarrow \quad m_{\perp}=-\dfrac{1}{3}\\

Next, find the midpoint of (4, 1) and (2, -5):

Midpoint=\bigg(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\bigg)\\\\\\.\qquad \qquad=\bigg(\dfrac{4+2}{2},\dfrac{1-5}{2}\bigg)\\\\\\.\qquad \qquad=\bigg(\dfrac{6}{2},\dfrac{-4}{2}\bigg)\\\\\\.\qquad \qquad=(3, -2)

Lastly, input the perpendicular slope and the midpoint into the Point-Slope formula to find the equation of the line:

y - y_1 = m_{\perp}(x - x_1)\\\\y - (-2) = -\dfrac{1}{3}(x - 3)\\\\y + 2=-\dfrac{1}{3}x +1\\\\y =-\dfrac{1}{3}x - 1\\


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