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leva [86]
3 years ago
5

Write an equation of the line that passes through the given point and is parallel to the given line.

Mathematics
1 answer:
Margaret [11]3 years ago
3 0

Answer:

Part 40) y=-2x+9

Part 41) y=5x+6

Part 42) y=\frac{2}{3}x+\frac{4}{3}

Step-by-step explanation:

Remember that

If two lines are parallel, then their slopes are the same

Part 40) Write an equation of the line that passes through the given point

and is parallel to the given line

we have

Point (4,1)

Given line y=-2x+7

step 1

Find the slope of the given line

The given line is a equation of the line in slope intercept form

y=mx+b

where

m is the slope

b is the y-intercept

so

The slope of the given line is

m=-2

step 2

Find the y-intercept b

we have

m=-2

(4,1)

substitute in the linear equation

1=(-2)4+b

solve for b

b=1+8

b=9

step 3

Find equation of the line that passes through the given point and is parallel to the given line

we have

m=-2

b=9

substitute

The equation of the line is

y=-2x+9

Part 41) Write an equation of the line that passes through the given point

and is parallel to the given line

we have

Point (0,6)

Given line y=5x-3

step 1

Find the slope of the given line

The given line is a equation of the line in slope intercept form

y=mx+b

where

m is the slope

b is the y-intercept

so

The slope of the given line is

m=5

step 2

Find the y-intercept b

b=6 ----> because the y-intercept is the point (0,6) (value of y when the value of x is equal to zero)

step 3

Find equation of the line that passes through the given point and is parallel to the given line

we have

m=5

b=6

substitute in the linear equation

y=5x+6

Part 42) Write an equation of the line that passes through the given point

and is parallel to the given line

we have

Point (-5,-2)

Given line y=(2/3)x+1

step 1

Find the slope of the given line

The given line is a equation of the line in slope intercept form

y=mx+b

where

m is the slope

b is the y-intercept

so

The slope of the given line is

m=\frac{2}{3}

step 2

Find the y-intercept b

we have

m=\frac{2}{3}

(-5,-2)

substitute in the linear equation

-2=(\frac{2}{3})(-5)+b

solve for b

-2=-\frac{10}{3}+b

b=-2+\frac{10}{3}

b=\frac{4}{3}

step 3

Find equation of the line that passes through the given point and is parallel to the given line

we have

m=\frac{2}{3}

b=\frac{4}{3}

substitute

The equation of the line is

y=\frac{2}{3}x+\frac{4}{3}

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KiRa [710]

Answer:

Null Hypothesis, H_0 : \mu = 1,100 square feet

Alternate Hypothesis, H_A : \mu < 1,100 square feet

Step-by-step explanation:

We are given that the mean area of several thousand apartments in a new development is advertised to be 1,100 square feet.

A consumer advocate has received numerous complaints that the apartments are smaller than advertised.

<u><em>Let </em></u>\mu<u><em> = mean area of several apartments.</em></u>

So, Null Hypothesis, H_0 : \mu = 1,100 square feet

Alternate Hypothesis, H_A : \mu < 1,100 square feet

Here, <u>null hypothesis states that</u> the mean area of apartments are same as advertised.

On the other hand, <u>alternate hypothesis states that</u> the mean area of apartments are smaller than advertised.

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4 0
2 years ago
Which inequality represents 17 less than twice a number is no more than 35?
alexandr402 [8]

Answer:

A

Step-by-step explanation:

"17 less than twice a number" is 2n - 17

"No more than 35" is \leq 35

2n - 17 \leq 35

7 0
1 year ago
How do you find the slope for 6x=8y+10
Jlenok [28]
<span>6x=8y+10

Well you must first get your equation set up into the form called "Slope intercept." 
</span>6x=8y+10
Add 8y on both of your sides because your y is suppose to be alone.
8y + 6x = 10
Subtract 6x on both sides since it is in fact the opposite of addition.
8y = 6x + 10
Now, you will divide by 8 on both sides. When doing this your y will be alone.
y= 6/8x + 10/8
Note: You can leave it like this but you want to probably simplify.
y = 3/4x + 5/2
       or
y = 3/4x + 2 1/5

THERE YA GO BUDDY! :D

-Gives you a thumbs up-



4 0
2 years ago
Read 2 more answers
Last week, Jane made deposits of $64,$25 and $37 into her checking account. She then wrote checks for $52 and $49. What is the o
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Answer:

$25 added to her account

Step-by-step explanation:

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3 years ago
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What is the slope line that passes through the points (10, 8) and (-15, 18)? Write your answer in simplest form
klasskru [66]

Answer: y=-\frac{2}{5}x+12

<em>y = mx + b</em>

m = slope = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}=\frac{18-8}{-15-10}=\frac{10}{-25}=\frac{2(5)}{-5(5)}=-\frac{2}{5}

<u>The y-intercept(b) can be found by substituting a point into the function.</u>

y = -\frac{2}{5}x + b \\\\8=-\frac{2}{5}(10) + b\\\\8=-4+b\\\\b=8+4=12

<u>Therefore, the function is:</u>

y=-\frac{2}{5}x+12

3 0
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