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2 years ago

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A rectangle with the length of 75 miles and width of 25 miles can be used to model building usage at one of Florida's universiti

es. Only 70% of the buildings at this university are used for instruction. If 32,125 students are enrolled at this university, what is the average student population density per square mile of building space used for instruction, rounded to the nearest student?

1 answer:

HACTEHA [7]2 years ago

8 0

Answer:

24 students per mile

Step-by-step explanation:

Given in the question,

Length of rectangle for building university = 75 miles

Width of rectangle for building university = 25 miles

Total area:

Length x Width

= 75 x 25

= 1875 miles²

Only 70% of the buildings at this university are used for instruction

70% of 1875 miles²

70/100 x 1875

= 1312.5 miles²

32,125 students are enrolled at this university

So,

1312.5 miles² = 32,125 students

1 mile = 32,125/1312.5

= 24 students per mile

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What is the equation of the line that has a slope of m = 2 and passes through the point (-5, -6)?

Alenkinab [10]

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$y=2x+4$

Step-by-step explanation:

You can solve this two ways: insert the values into point-slope form and simplify to solve for y, converting it to slope-intercept form, <em>or</em><em> </em>insert the values into slope-intercept form, solve for b, and insert b. We'll do both :)

<em><u>Point-slope form:</u></em>

$y-y_{1}=m(x-x_{1})$

Where:

$m$ is the slope

$x_{1}$ and $y_{1}$ are corresponding coordinate points $(x,y)$

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Solve for y. Expand the right sie using the distributive property:

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Isolate the variable. Subtract 6 from both sides, canceling out the 6 on the left:

$y+6-6=2x+10-6\\\\y=2x+4$

<em>OR</em>

<em></em>

<em><u>Slope-intercept form:</u></em>

$y=mx+b$

Where:

$m$ is the slope
$b$ is the y-intercept
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Insert the given values:

$m=2\\\\(-5_{x},-6_{y})\\\\-6=2(-5)+b$

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3 years ago

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$(0,0)\ and\ (2,1)$

Required

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Where

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To determine which point is on the line, we simply plug in the values of x to in the equation check.

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<em></em>

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<em></em>

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<em></em>

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<em></em> $\frac{2}{8} = \frac{1}{2} * \frac{4}{8}$ <em></em>

<em></em> $\frac{2}{8} = \frac{1 * 4}{8 * 2}$ <em></em>

<em></em> $\frac{2}{8} = \frac{4}{16}$ <em></em>

<em></em> $\frac{1}{4} = \frac{1}{4}$ <em></em>

<em></em>

<em>This point is on the graph</em>

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