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dusya [7]
3 years ago
13

Find the equation of the line passing through the point (4,−1) that is parallel to the line 2x−3y=9.

Mathematics
1 answer:
motikmotik3 years ago
7 0

Hey there!

Line passes through (4, -1) & is parallel to 2x -3y=9

Let's start off by identifying what our slope is. In the slope-intercept form y=mx+b, we know that "m" is our slope.

The given equation needs to be converted into slope-intercept form and we can do this by getting y onto its own side of the equal sign.

Start off by subtracting 2x from both sides.

-3y = -2x + 9

Then, divide both sides by -3.

y = (-2x + 9)/-3

Simplify.

y = 2/3x - 3

"M" is simply a place mat so if we look at our given line, the "m" value is 2/3. Therefore, our slope is 2/3.

We should also note that we're looking for a line that's parallel to the given one. This means that our new line has the same slope as our given line. Therefore, our new line has a slope of 2/3.

Now, we use point-slope form ( y-y₁=m(x-x₁) ) to complete our task of finding a line that passes through (4, -1). Our new slope is 2/3 & it passes through (4, -1).

y-y₁=m(x-x₁)

Let's start by plugging in 2/3 for m (our new slope), 4 for x1 and -1 for y1.

y - (-1) = 2/3(x - 4)

Simplify.

y + 1 = 2/3 + 8/3

Simplify by subtracting 1 from both sides.

y = 2/3x + 8/3 - 1

Simplify.

y = 2/3x + 5/3

~Hope I helped!~

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How can i read, write, and represent decimal numbers
snow_tiger [21]

Answer:

When reading decimal numbers, read the whole number part as normal, use "and" to represent the decimal point and continue reading the number as normal, but end with the last place value.

For example: how do you read 36.57 --> thirty-six and fifty-sevens hundredths

When writing decimals it is like reading them. You write the whole part as normal, and write a decimal to represent where you would say "and". Continue writing the number.

For example: Write eighty-five and sixty-four hundredths --> 85.64

Step-by-step explanation:

7 0
3 years ago
Find the length of each diagnol and the area
katrin [286]

Answer:

The length of diagonal BD is 11·(1 + √3)

The length of diagonal AC = 22

Step-by-step explanation:

The given data are;

Quadrilateral ABCD = A kite

The length of segment AD = 22

The measure of ∠DAE = 60°

The measure of ∠BCEE = 45°

Whereby, triangle ΔADE = A right triangle, and DE is the perpendicular bisector of AC, by trigonometric ratio, we have;

AE = EC

DE = 22 × sin(60°) = 11·√3

AE = 22 × cos(60°) = 11

∴ AE = EC = 11

BE = EC × tan(∠BCE) = 11 × tan(45°) = 11

The length of the diagonal BD = BE + DE (By segment addition property)

∴ BD = 11 + 11·√3 = 11·(1 + √3)

The length of diagonal BD = 11·(1 + √3)

The length of diagonal AC = AE  + EC

∴ AC + 11 + 11 = 22

The length of diagonal AC = 22.

7 0
3 years ago
You use 4 gallons of water on 14 plants in your graden. At this rate, how much water will it take to water 35 plants
Jlenok [28]

It will take 10 gallons of water to water the 35 plants

8 0
3 years ago
Six more than the product of a number and 7 is 4
Scilla [17]
6+7(n)=4


7n+6=4


If they ask you to solve for n you subtract 6 on each side giving you

7n=-2

Divide by 7


n= -2/7

You’re welcome. Let me know if you have questions
6 0
3 years ago
(2x2 +5x+6) + (8x2 +3x+2)
Wewaii [24]

Hey there!

Answer:\boxed{10x^2+8x+8}

Explanation:

(2x^2+5x+6)+(8x^2+3x+2)

Let's start off with combining like terms.

2x^2+5x+6+8x^2+3x+2\\(2x^2+8x^2)+(5x+3x)+(6+2)\\10x^2+8x+8

\boxed{10x^2+8x+8}\text{ is your answer.}

Hope this helps!

\text{-TestedHyperr}

4 0
3 years ago
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