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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:

Zina [86]3 years ago

4 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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Which expression does the number line represent?

seropon [69]

Answer:

I think the answer is 3÷3/4

Step-by-step explanation:

im not sure, when i worked it out in my head that's the answer that made the most sense

5 0

2 years ago

Please help thank you.

marusya05 [52]

This problem can be completed in 2 ways. Both are acceptable.

Option 1:

This is an isosceles trapezoid that can be divided into a rectangle and two congruent triangles.

The area of the rectangle is the base times the height.

$9 \times 4=36$

The area of one of the triangles is half the base times the height.

$\dfrac{1}{2} \times 5 \times 4 = 10$

The other triangle must have that area too.

$36+10+10=56$

The area is 56 square centimeters.

Option 2:

We can use the area formula for the trapezoid.

$A=\dfrac{b_1+b_2}{2} \times h$

Where $b_1$ is the length of the shorter base
and $b_2$ is the length of the longer base
and $h$ is the height.

The length of the shorter base is 9.
The length of the longer base is 9+5+5, or 19.

The height is 4.

$A=\dfrac{9+19}{2} \times 4$

$=56$

Same answer. The area is 56 square centimeters.

Both options are two acceptable ways the problem can be tackled.

7 0

3 years ago

Help please, I need to figure this problem out

yarga [219]

Answer:

AB is parallel to BE because it is an equilateral triangle.

BE is parallel to EC because it has 2 of the same angles to the same sides are equal.

Hope that helps, it's a tad hard to explain

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3 years ago

Which of the following is true concerning hull fouling from commercial shipping and recreational boating?

user100 [1]

Answer: C. It is difficult to prevent since ship hulls begin, conduct, and end voyages in water.

Step-by-step explanation:

4 0

3 years ago

Read 2 more answers

Find x, y and ab and how to check if the answer is right

iris [78.8K]

Answer:

x = 2, y = -2, AB = 142

Step-by-step explanation:

The fact that X is the midpoint gives you two relations:

AX = XB

AX + XB = AB

Since you have two unknowns, this number of equations is sufficient to find their values. Substituting the given expressions in the above equations, you have ...

8(3x+5) -3(y-7) -22x = 5x +y +23 -4(x-12)
8(3x+5) -3(y-7) -22x + 5x +y +23 -4(x-12) = 2x -5y +128

Simplifying the first of these can make simplifying the second one easier.

24x +40 -3y +21 -22x = 5x +y +23 -4x +48

2x -3y +61 = x +y +71 . . . . . . we can use this simplification

x -4y = 10 . . . . . . . . . . . . . . . . subtract x+y+61

Now, we can simplify the second equation to ...

2x -3y +61 +x +y +71 = 2x -5y +128

3x -2y +132 = 2x -5y +128 . . . . . simplify the left side

x +3y = -4 . . . . . . . . . . . . . . . add -2x+5y-132

Then the two equations we need to solve are ...

x -4y = 10
x +3y = -4

Subtracting the second from the first, we get

-7y = 14

y = -2

Substituting into the first of these simplified equations, we get

x -4(-2) = 10 . . . . substitute for y

x +8 = 10 . . . . . . .evaluate

x = 2 . . . . . . . . . .subtract 8

So, the solution is (x, y) = (2, -2).

Now, the values of AX and XB are ...

AX = 2x -3y +61 = 2·2 -3(-2) +61 = 71

XB = x+y+71 = 2 +(-2) +71 = 71 . . . . . . . . matches AX, a good sign

AB = 2x -5y +128 = 2·2 -5(-2) +128 = 142 . . . . = AX+XB, another good sign

The desired values are x = 2, y = -2, AB = 142.

_____

You check the answer by filling the values into the expressions given in the problem statement and seeing if you get consistent results. Here, we used the simplified expressions, rather than the original expressions, so if we did the simplification wrong, we may have the wrong answer. It is always best to use the original equations. (A machine solver working with the original equations confirms our result, so "confidence is high.")

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3 years ago