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3 years ago

Find the equation of a line passing through (3, -5) that is parallel to 2x + 6y =10

Mathematics

1 answer:

PtichkaEL [24]3 years ago

7 0

Answer:

The equation of the line would be y = -1/3x - 4

Step-by-step explanation:

In order to find this, we first need to find the slope of the original line. We do this by solving for y.

2x + 6y = 10

6y = -2x + 10

y = -1/3x + 5/3

Now that we see the slope as -1/3, we know the new line will have the same slope thanks to the definition of parallel lines. So, we can use this slope and the point in point-slope form to find the equation.

y - y1 = m(x - x1)

y - -5 = -1/3(x - 3)

y + 5 = -1/3x + 1

y = -1/3x - 4

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Find x so that (x,-14) is a solution to 2x+3y=12

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Answer:

Question:

Find $x$ so that $(x,-14)$ is a solution to $2x+3y=12$ .

Step-by-step explanation:

So we are asked to replace $y$ with -14 and solve for $x$ in the equation:

$2x+3y=12$ .

$2x+3y=12$ with $y=-14$ :

$2x+3(-14)=12$

$2x-42=12$

Add 42 on both sides:

$2x=54$

Divide both sides by 2:

$x=27$ .

So the $x$ -coordinate that corresponding to $y=-14$ is $27$ .

Verify that:

$(27,-14)$ is a point satisfying $2x+3y=12$ .

Replace $x$ with 27 and $y$ with -14:

$2(27)+3(-14)=12$

$54+-42=12$

$12=12$ is true so our work must be right.

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3 years ago

What is the value of m in the figure below? If necessary,round your answer to the nearest tenth of a unit

bogdanovich [222]

Answer:

Step-by-step explanation:

It turns out from similar triangles, that 7/BD = BD / 18. Use triangles ABD and BDC to show this relationship. Solving this equation will give you BD

BD^2 = 7*18

BD^2 = 126 Just leave it in this form. Do your rounding at the end.

Because triangle BDC is a right angle triangle, use the Pythagorean Theorem to solve for m

m^2 = BD^2 + 7^2

m^2 = 126 + 49

m^2 = 175 Take the square root of both sides.

sqrt(m^2) = sqrt(175)

m = 13.22

so the answer is D

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3 years ago