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tino4ka555 [31]
3 years ago
10

One week Alaina ran 12 miles in 131.25 minutes. The next, Alaina ran 12 miles in 119.5 minutes. If she ran in a constant pace du

ring each run, about how much faster did she run each mile in he second week than in the first week?
Mathematics
2 answers:
vlabodo [156]3 years ago
6 0
Ou should not increase to more than 12 miles next week<span>; ... </span>25 miles<span> a </span>week<span>, usually a 7 </span>milerun<span> ... before I </span>run<span> a half. Using that method</span>
Ronch [10]3 years ago
5 0

Answer:

0.98 minutes

Step-by-step explanation:

First, we have to determine how much time it took for Alaina to run one mile on the first and the second week:

First week:

12 miles → 131.25 minutes

1 mile     →     x

x=(131.25 minutes*1 mile)/12 miles= 10.93 minutes

Second week:

12 miles → 119.5 minutes

1 mile     →     x

x= (119.5 minutes*1 mile) /12 miles= 9.95 minutes

Now, we have to find the difference between the time it took to run 1 mile in the first and the second week:

10.93-9.95= 0.98 minutes

She run 0.98 minutes faster in the second week.

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Consider the line y = 7x-9.
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y = \frac{-1}{7}x -\frac{8}{7} is the equation of the line that is perpendicular to this line and passes through the point (6, -2)

y = 7x - 44 equation of the line that is parallel to this line and passes through the point (6, -2)

<em><u>Solution:</u></em>

<em><u>Given that line is:</u></em>

y = 7x - 9

<em><u>The equation of line in slope intercept form is given as:</u></em>

y = mx + b ------ eqn 1

Where, "m" is the slope of line and "b" is the y intercept

On comparing eqn 1 with y = 7x - 9 we get,

m = 7

<h3><u>Find the equation of the line that is perpendicular to this line and passes through the point (6, -2)</u></h3>

We know that,

Product of slope of a line and slope of line perpendicular to given is always -1

Therefore,

7 \times \text{ slope of line perpendicular to it } = -1\\\\\text{ slope of line perpendicular to it } = \frac{-1}{7}

Now find the equation of line:

\text{ Substitute } m = \frac{-1}{7} \text{ and } (x, y) = (6, -2) \text{ in eqn 1}

-2 = \frac{-1}{7} \times 6 + b\\\\-2 = \frac{-6}{7} + b\\\\b = -2+\frac{6}{7}\\\\b = \frac{-14+6}{7}\\\\b = \frac{-8}{7}

\text{Substitute } m = \frac{-1}{7} \text{ and } b = \frac{-8}{7} \text{ in eqn 1}\\\\y = \frac{-1}{7}x -\frac{8}{7}

Thus the equation of line perpendicular to given line is found

<h3><u>Find the equation of the line that is parallel to this line and passes through the point (6, -2)</u></h3>

Slopes of parallel lines are equal

Therefore,  m = 7

<em><u>Substitute m = 7 and (x, y) = (6, -2) in eqn 1</u></em>

-2 = 7(6) + b

-2 = 42 + b

b = -44

<em><u>Substitute m = 7 and b = -44 in eqn 1</u></em>

y = 7x - 44

Thus equation of line parallel to given line is found

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Step-by-step explanation:

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