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oksian1 [2.3K]
3 years ago
10

Which is the equation in slope-intercept form for the line that passes through (-2, 15) and is perpendicular to 2x + 3y = 4?

Mathematics
2 answers:
Ilya [14]3 years ago
4 0

Answer:

B

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Rearrange 2x + 3y = 4 into this form

Subtract 2x from both sides

3y = - 2x + 4 ( divide all terms by 3 )

y = - \frac{2}{3} x + \frac{4}{3} ← in slope- intercept form

with slope m = - \frac{2}{3}

Given a line with slope m then the slope of a line perpendicular to it is

m_{perpendicular} = - \frac{1}{m} = - \frac{1}{-\frac{2}{3} } = \frac{3}{2}, hence

y = \frac{3}{2} x + c ← is the partial equation of the perpendicular line

To find c substitute (- 2, 15) into the partial equation

15 = - 3 + c ⇒ c = 15 + 3 = 18

y = \frac{3}{2} x + 18 → B

DiKsa [7]3 years ago
3 0

Answer:

B and C are both perpindicular to 2x + 3y = 4.

But B passes (-2, 15).

<em>Hope this helps!!!</em>

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It takes a hose 2 minutes to fill a rectangular aquarium 8 inches long, 9 inches wide, and 13 inches tall. How long will it take
nirvana33 [79]
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1st aquarium:
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Now that you've got the volume and rate of the first aquarium, you can find how many inches of the aquarium is filled within a minute, which is also known as the unit rate. To do that, you have to divide both the numerator and denominator by their least common multiple, which is 2. 936 divided by 2 is 468 and 2 divided by 2 is 1.
So the unit rate is 468 in./1 min. Now that you've got the unit rate, you can find out how long it'll take to fill the second aquarium up by finding its volume first.

2nd aquarium:
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V = 21 x 29 x 30
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Calculations:
Now, you divide 18,270 by 468 to find how many minutes it will take to fill up the second aquarium. 18,270 divided by 468 is about 39 (the answer wasn't exact, so I said "about").
 
2nd aquarium's rate:
18,270 in./39 min.

As a result, it'll take about 39 minutes to fill up an aquarium measuring 21 inches by 29 inches by 30 inches using the same hose. I really hope I helped and that you understood my explanation! :) If I didn't, I'm sorry. I tried. :(
7 0
3 years ago
Find the angle of XYZ give your answer to 1 decimal place
miskamm [114]

Answer:

66.4°

Step-by-step explanation:

To find the angle XYZ, we are to use sine rule. For this, we have to first find ∠Z.

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\frac{sin(Z)}{XY}=\frac{sin(X)}{YZ}\\\\Substituting:\\\\\frac{sin(Z)}{6} =\frac{sin(90)}{15}   \\\\sin(Z)=\frac{sin(90)*6}{15}\\\\sin(Z)=0.4\\\\Z=sin^{-1}(0.4)\\\\Z=23.6^o

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90 + ∠Y + 23.6 = 180

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∠Y = 180 - 113.6

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∠Y = ∠XYZ = 66.4°

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