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2 years ago

A line passes through (-5, -3) and is parallel to -3x - 7y = 10. The equation of the line in slope-intercept form is _____.

1 answer:

4 0

(-5,-3), Parallel to -3x - 7y = 10, Put in slope-intercept form.

So, we must find the slope of this first.

-3x - 7y = 10

Add 3x to both sides.

-7y = 3x + 10

Divide both sides by -7.

y = -3/7x - 10/7

So, our slope is -3/7.

Remember, if you're looking for a line that is parallel to something, the slopes always stay the same.

*Also remember that slope-intercept form is y = mx+b*

Where m = slope, and b = y-intercept.

We have the points (-5,-3) so our y-intercept is -3.

Our slope is -3/7.

So, simply plug in those values into the slope-intercept form equation! :)

y = mx + b

y = -3/7x - 3

~Hope I helped!~

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The width of a rectangle is the length minus 2 units. The area of the rectangle is 35 units. What is the width, in units, of the

Andrews [41]

Answer: width = 5 units

Step-by-step explanation:

Let L represent the length of the rectangle.

The width of a rectangle is the length minus 2 units. It means that the width of the rectangle is (L - 2) units.

The formula for determining the area of a rectangle is expressed as

Area = length × width

The area of the rectangle is 35 units. It means that

L(L - 2) = 35

L² - 2L = 35

L² - 2L - 35 = 0

L² + 5L - 7L - 35 = 0

L(L + 5) - 7(L + 5) = 0

L - 7 = 0 or L + 5 = 0

L = 7 or L = - 5

Since the length cannot be negative, then

L = 7 units

Width = 7 - 2 = 5 units

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Step-by-step explanation:

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2 years ago

Read 2 more answers

The function D(t) defines a traveler's distance from home, in miles, as a function of time, in hours. D(t) = StartLayout enlarge

nalin [4]

- At 2 hours, the traveler is 725 miles from home.

- At 3 hours, the distance is constant, at 880 miles. --> TRUE.

- The total distance from home after 6 hours is 1,062.5 miles --> TRUE.

Step-by-step explanation:

The function D(t) is defined as follows:

$D(t) = 300t+125$ for $t< 2.5$

$D(t) = 880$ for $2.5 \leq 3.5$

$D(t) = 75t+612.5$ for $t\leq 6$

Where

t is the time in hours

D(t) is the distance covered, in miles, after t hours

Now let's analyze the different statements:

- The starting distance, at 0 hours, is 300 miles. --> FALSE. In fact, if we substitute t = 0 into the 1st equation, we get

$D(0) = (300)(0)+125 = 125$

So, the distance at t = 0 is 125 miles.

- At 2 hours, the traveler is 725 miles from home. --> TRUE. In fact, if we substitute t = 2 into the 1st equation,

$D(2) = (300)(2)+125 = 725$

- At 2.5 hours, the traveler is 875 miles from home. --> FALSE. In fact, for t=2.5 we have to use the 2nd equation, which states that the distance is:

D(t) = 880

So, not 875 miles.

- At 3 hours, the distance is constant, at 880 miles. --> TRUE. This is clearly visible from the 2nd equation: for t between 2.5 and 3.5 (so, in this case), the distance is

D(t) = 880

- The total distance from home after 6 hours is 1,062.5 miles --> TRUE. In fact, if we replace t = 6 into the last equation,

$D(6)) = 75(6)+612.5=1062.5$