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3 years ago

What is the equation of a line passing through (5,2) and parallel to the line represented by the equation y - 2x + 1?

Mathematics

1 answer:

34kurt3 years ago

4 0

Step-by-step explanation:

Im not sure if its supposed y = -2x + 1 or y = 2x + 1 but I'll solve the problem for both.

First for y = -2x + 1

Since the line has to be parallel to y = -2x + 1

the slopes would be the same.

so, so far the equation would be

y = -2x + b

now we substitute (5,2) into the equation

2 = -2(5) + b

2 = -10 + b (Add 10 to both sides of the equation)

+10 +10

12 = b

Now that we solved for b

The equation would be

y = -2x + 12

^^ This equation is parallel to y = -2x + 1

Now to solve for an equation parallel to y = 2x + 1

Both equations would have the same slope

So far we would have

y = 2x + b

Now we solve for be by substituting the point (5,2)

2 = 2(5) + b

2 = 10 + b (subtract 10 from both sides)

-10 -10

-8 = b

After solving for b

The equation is

y = 2x - 8

This equation is parallel to y = 2x + 1

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Which is a true statement?

erastova [34]

A. because the lease amount of negative is actually more. if that makes any sense

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3 years ago

Write the point slope form of the equation of the line through the given points.

oee [108]

Answer:

$\displaystyle y - 3 = -1\frac{1}{5}x\:OR\:y + 3 = -1\frac{1}{5}x - 5$

Step-by-step explanation:

First, find the rate of change [slope]:

$\displaystyle \frac{-y_1 + y_2}{-x_1 + x_2} = m \\ \frac{3 + 3}{-5 ± 0} = -\frac{6}{5} = -\frac{1}{5}$

Then plug these coordinates into the Point-Slope Formula Remember, in this formula, all the negative symbols give the OPPOSITE terms of what they really, so be EXTREMELY CAREFUL inserting the coordinates into the formula with their CORRECT SIGNS. It does not matter which ordered pair you choose:

$\displaystyle y - y_1 = m[x - x_1] \\ \\ y - 3 = -1\frac{1}{5}x\:OR\:y + 3 = -1\frac{1}{5}x - 5$

I am joyous to assist you anytime.

5 0

3 years ago

The ubiquitous 12oz aluminum cans used to distribute drinks in this country have a diameter of approximately 2.75 inches and a h

gayaneshka [121]

Answer:

3.5%

Step-by-step explanation:

The volume of a cylinder = $\pi r^2h$

r = radius of cylinder,

h = height of cylinder

For the non-optimal can,

r = 2.75/2 = 1.375

h = 5.0

$V = \pi(1.375^2)\times 5.0 = 9.453125\pi$

For the optimal can,

d/h = 1,

d = h

2r = h

r = h/2

$V = \pi\left(\dfrac{h}{2}\right)^2\times h = \pi\left(\dfrac{h^3}{4}\right)$

They have the same volume.

$\pi\dfrac{h^3}{4} = 9.453125\pi$

$h^3 = 37.8125$

$h=3.36$ (This is the height of the optimal can)

$r = \dfrac{3.36}{2} = 1.68$ (This is the radius of the optimal can)

The area of a cylinder is

$A = 2\pi r(r+h)$

For the non-optimal can,

$A = 2\pi\times\dfrac{2.75}{2}\left(\dfrac{2.75}{2}+5.0\right) = 17.53125\pi$

For the optimal can,

$A = 2\pi\times1.68\left(1.68+3.36\right) = 16.9344\pi$

Amount of aluminum saved, as a percentage of the amount used to make the optimal cans = $\dfrac{17.53125\pi - 16.9344\pi}{16.9344\pi}\times 100\% = 3.5\%$

5 0

3 years ago

Which on the following is the converse of the statement “if it is summer ,then it is warm outside”?

Elodia [21]

The converse of the statement "If it is summer, then it is warm outside' would be "if it is warm outside then it is summer" Hope this helped!

8 0

3 years ago

Gamers charges $8 to rent a video game. The Discount Club charges $4 to rent a video game after a membership fee of $10 is paid.

tatiyna

Answer

8x>10+4x for x=>3

Just two games.

for the third game you would have paid $24 in total

Step-by-step explanation:

Given that

gamers charge $8

Discount Club charges $4 after a membership of $10

total for the Discount club is given by the expression

let x be the number of games rent

Y=10+4

So at the first rent, you will pay Discount Club

$14 and the second rent you would have spent

14+4= $18

and the third rent you would have spent

18+4= $22

the inequality is given as

for x=>3

8x>10+4x

8 0

3 years ago