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3 years ago

Find the equation for the line passing through the point (−1,1) ( − 1 , 1 ) and parallel to the line whose equation is y=2x+12.

1 answer:

7 0

So, parallel lines have the same slope, therefore a parallel line to 2x+12, will have the same slope as that one, so which is it? $\bf y=\stackrel{slope}{2}x\stackrel{y-intercept}{+12}$

so, we're really looking for the equation of a line whose slope is 2, and runs through -1,1.

$\bf \begin{array}{lllll}
&x_1&y_1\\
% (a,b)
&({{ -1}}\quad ,&{{ 1}})
\end{array}
\\\\\\
% slope = m
slope = {{ m}}= \cfrac{rise}{run} \implies 2
\\\\\\
% point-slope intercept
\stackrel{\textit{point-slope form}}{y-{{ y_1}}={{ m}}(x-{{ x_1}})}\implies y-1=2[x-(-1)]
\\\\\\
y-1=2(x+1)\implies y-1=2x+2\implies y=2x+3$

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Algebra public opinion polls reported in newspapers are usually given with a margin of error. for example, a poll with a margin

sweet-ann [11.9K]

Answer:

Minimum percent of the vote that candidate Towne is expected to recieve:

m=51% - 6.3% * 51% =47.787%

Maximum percent of the vote that candidate Towne is expected to recieve:

M=51% + 6.3% * 51% = 54.213%

Solution:

Margin of error: E=6.3%

Minimum percent of the vote that candidate Towne is expected to recieve:

m=51% - E * 51%

m=51% - 6.3% * 51%

m=51% - 51% * 6.3 / 100

m=51% - 3.213%

m=47.787%

Maximum percent of the vote that candidate Towne is expected to recieve:

M=51% + E * 51%

M=51% + 6.3% * 51%

M=51% + 51% * 6.3 / 100

M=51% + 3.213%

M=54.213%

8 0

3 years ago

Area of a Triangle

jek_recluse [69]

Answer:

3.51 (round to the nearest hundreds)

Step-by-step explanation:

PART A

slope of the line passing through AC : (6-1)/(1-2) = 5/-1 = -5

equation of the line passing through B and perpendicular to AC:

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

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

y = 1/5 x - 3/5 + 3

y = 1/5 x + (-3+15)/5

y = 1/5 x + 12/5

PART B

line that passes through the points A and C

y-1 = -5(x-2)

y = -5x+10 + 1

y = -5x + 11

Interception of the lines

y = 1/5x + 12/5

y = -5x + 11

-5x + 11 = 1/5x + 12/5

-25x +55 = x + 12

26x = 43

x = 43/26

y = -5(43/26) + 11

y= -215/26 + 11

y = (-215+286)/26 = 71/26

D (1.65, 2.73)

PART C

AC = $\sqrt{(1-2)^2 + (6-1)^2} = \sqrt{1 + 25} = \sqrt{26}$ = 5,09902

BD = $\sqrt{(3-1.65)^2 + (3-2.73)^2}$ = 1,376735

PART D

AREA = (5,09902 * 1.376735)/2 = 3,509999

8 0

3 years ago

Matt and Anna Killian are frequent fliers on Fast-n-Go Airlines. They often fly between two cities that are a distance of 1680

vladimir1956 [14]

Answer:Wind speed = 30 miles/hour

Plane speed = 450 miles/hour

Step-by-step explanation:

First we have to know the formula for finding speed, which is distance divided by time

Speed = distance/time

Then we label the speed of the plane to be x

And the spend of the wind to be y

From the question, we are told that when the plane flies into the wind, it takes 4 hours to travel a distance of 1680 so we have the time and distance

And since the plane is flying against the wind speed

We can form an equation

x - y = 1680/4

x - y = 420 (1)

Then when the plane is coming back, the wind is going in the same direction with the plane and it take 3.5 hours to cover the same 1680 miles distance, so we form another equation

x + y = 1680/3.5

x + y = 480 (2)

So we solve (1) and (2) simultaneously

x - y = 420 (1)

x + y = 480 (2)

Using elimination method, we eliminate y by adding both equations

2x = 900

x = 450 miles/hour

So therefore, plane speed is 450 miles/hour

Putting the answer in either (1) or (2) to get y

I choose to put it in (2)

x + y = 480

450 + y = 480

y = 480 - 450

y = 30 miles/hour

So therefore, wind speed = 30miles/hour

4 0

3 years ago

NEED HELP ASAP PLZZZUnder a dilation, a square with side lengths 24 yards is transformed a square with side lengths 6 yards. Wha

motikmotik

Answer: 1/4

Step-by-step explanation: i just took the quiz

5 0

3 years ago

Tatum walks her dog 2/3 of a mile every day after school how many miles does she walk her dog in 5 days

alexdok [17]

Answer:

i think it is 3 miles but dunno

Step-by-step explanation:

3 0

3 years ago