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lorasvet [3.4K]
2 years ago
15

Which equations below represent lines that are perpendicular to the line that contains (1, -2) and (3, 4)? (CHECK PICS FOR ANSWE

R CHOICES, CHOOSE MORE THAN ONE IF NECESSARY)

Mathematics
1 answer:
Gala2k [10]2 years ago
8 0

First, let's find the slope of the line from the points given.

m = (4 - - 2) / (3 - 1)

m = 6 / 2

m = 3

Secondly, we know that a line perpendicular to the original must have a slope that is the opposite reciprocal of the original. For the given points, the opposite reciprocal slope would be -1/3.

Now, we can put all of the equations below into slope intercept form and find the ones that have a slope of -1/3.

Equation 1: Correct

y = -1/3x - 5

Equation 2: Incorrect

y = 3x - 3

Equation 3: Incorrect

y - 2 = 3(x + 1)

y - 2 = 3x + 1

y = 3x + 2

Equation 4: Correct

x + 3y = 9

3y = -x + 9

y = -1/3x + 3

Equation 5: Incorrect

3x + y = -5

y = -3x - 5

Hope this helps!! :)

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2 years ago
Rajan needs 1 liter of 15% hydrochloric acid solution for an experiment. He checks his storage cabinet, but he only has a 5-lite
yarga [219]

Answer:

<em>Rajan must use </em><em>0.75</em><em> liters of 5% hydrochloric acid solution and </em><em>0.25</em><em> liters of 45% hydrochloric acid solution.</em>

Step-by-step explanation:

Let us assume that, x liters of the 5% hydrochloric acid and y liters of the 45% hydrochloric acid solutions are combined.

As Rajan need total of 1 liter of solution, so

x+y=1

i.e x=1-y --------------------1

As Rajan needs 5% hydrochloric acid and 45% hydrochloric acid to make a 1 liter batch of 15% hydrochloric acid, hence acid content of the mixture of two acids will be same as of the final one, so

0.05x+0.45y=1\times 0.15

i.e 5x+45y=15 -------------2

Putting value of x from equation 1 in equation 2,

\Rightarrow 5(1-y)+45y=15

\Rightarrow 5-5y+45y=15

\Rightarrow 5+40y=15

\Rightarrow 40y=15-5=10

\Rightarrow y=0.25

Putting the value of y in equation 1,

x=1-0.25=0.75

Therefore, Rajan must use 0.75 liters of 5% hydrochloric acid solution and 0.25 liters of 45% hydrochloric acid solution.

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3 years ago
У
o-na [289]
1 - 10
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