Amy wants to run the 26 miles of the marathon in 4.5 hours. at what rate will she have to run to reach thisbgoal??

1 answer:

5 0

The answer is:
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5.778 mi/ h;
→ or; write as: 5 ⁷/₉ mph {"miles per hour"}.
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Explanation:
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We shall solve in miles ("mi.") per hour ("h"); denoted as "mi / h" ; or sometimes, "mph".
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Given 26 mi / 4.5 h ; we want to solve for the number of miles (mi) per unit hour (h),
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The answer is (26/ 4.5) mi / h l
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26 ÷ 4.5 = 5.7777777777777778→ Round to: 5.778 mi/ h;
→ or; write as: 5 ⁷/₉ mi /h
_____________________________________________________

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Find an equation of the line through these points (15,2.2) (5,1.6). Write answer in a slope-intercept form

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$y=\frac{\displaystyle 3}{\displaystyle 50}x+\frac{\displaystyle 13}{\displaystyle 10}$

Step-by-step explanation:

Hi there!

Slope-intercept form: $y=mx+b$ where $m$ is the slope and $b$ is the y-intercept (the value of y when x is 0)

1) Determine the slope (m)

$m=\frac{\displaystyle y_2-y_1}{\displaystyle x_2-x_1}$ where two given points are $(x_1,y_1)$ and $(x_2,y_2)$

Plug in the given points (15,2.2) and (5,1.6):

$m=\frac{\displaystyle 1.6-2.2}{\displaystyle 5-15}\\\\m=\frac{\displaystyle -0.6}{\displaystyle -10}\\\\m=\frac{\displaystyle 0.6}{\displaystyle 10}\\\\m=\frac{\displaystyle 0.3}{\displaystyle 5}\\\\m=\frac{\displaystyle 3}{\displaystyle 50}$

Therefore, the slope of the line is $\frac{\displaystyle 3}{\displaystyle 50}$ . Plug this into $y=mx+b$ :

$y=\frac{\displaystyle 3}{\displaystyle 50}x+b$

2) Determine the y-intercept (b)

$y=\frac{\displaystyle 3}{\displaystyle 50}x+b$

Plug in a given point and solve for b:

$1.6=\frac{\displaystyle 3}{\displaystyle 50}(5)+b\\\\1.6=\frac{\displaystyle 3}{\displaystyle 10}+b\\\\1.6-\frac{\displaystyle 3}{\displaystyle 10}=\frac{\displaystyle 3}{\displaystyle 10}+b-\frac{\displaystyle 3}{\displaystyle 10}\\\\\frac{\displaystyle 13}{\displaystyle 10}=b$