Hong's gas tank is 1/2 full. After he buys 5 gallons of gas, it is 5/6 full. How many gallons can Hong's tank hold?

1) find the equation of the line parallel to

In-s [12.5K]

Answer:

1) The equation of the line parallel to x-5y=6 and through (4,-2) is 5y = x -14

2) The equation of the line perpendicular to y= -2/5x + 3 and through (2,-1) is 2y = 5x -12

Solution:

1) find the equation of the line parallel to x-5y=6 and through (4,-2).

Given, line equation is x – 5y = 6

We have to find the line equation that is parallel to given line and passing through the point (4, -2)

Now, let us find slope of the given line.

$\text { Slope }=\frac{-x \text { coefficient }}{y \text { coefficient }}=\frac{-1}{-5}=\frac{1}{5}$

Now, we know that, slope of parallel lines are equal.

So, slope of required line is 1/5 and it passes through (4, -2)

Now, using point slope form

$y-y_{1}=m\left(x-x_{1}\right) \text { where } m \text { is slope and }\left(x_{1}, y_{1}\right) \text { is point on line. }$

$y-(-2)=\frac{1}{5}(x-4) \rightarrow 5(y+2)=x-4 \rightarrow 5 y+10=x-4 \rightarrow x-5 y=14$

Hence, the line equation is 5y = x -14

2) find the equation of the line perpendicular to y= -2/5x + 3 and through (2,-1)

$\text { Given, line equation is } y=-\frac{2}{5} x+3 \rightarrow 5 y=-2 x+15 \rightarrow 2 x+5 y=15$

We have to find the line equation that is perpendicular to given line and passing through the point (2, -1)

Now, let us find slope of the given line.

$\text { Slope }=\frac{-x \text { coefficient }}{y \text { coefficient }}=\frac{-2}{5}=-\frac{2}{5}$

Now, we know that, product of slopes of perpendicular lines equals to -1.

So, slope of required line $\times$ slope of given line = -1

slope of required line = $-1 \times \frac{5}{-2}=\frac{5}{2}$

And it passes through (2, -1)

Now, using point slope form

$\begin{array}{l}{\text { Line equation is } y-(-1)=\frac{5}{2}(x-2) \rightarrow 2(y+1)=5(x-2)} \\\\ {\rightarrow 2 y+2=5 x-10 \rightarrow 5 x-2 y=12}\end{array}$

Hence, the line equation is 2y = 5x -12

4 0

3 years ago

What is the value of x? Assume that the line is tangent to the cirlce.

Vanyuwa [196]

It’s definitely not D or A but the closest one would be C, that’s what I would put. So the answer might be C.90

4 0

3 years ago

Read 2 more answers

Half of a pizza was broccoli and half was mushroom. george ate 2/3 of the broccoli part and 1/4 of the mushroom part. how much o

VladimirAG [237]

1/2 was broccoli and 1/2 was mushroom...

he ate 2/3 of the broccoli part......2/3 of 1/2 = 2/3 * 1/2 = 2/6 = 1/3
he ate 1/4 of the mushroom part....1/4 of 1/2 = 1/4 * 1/2 = 1/8

so he ate 1/3 + 1/8 = 8/24 + 3/24 = 11/24 <==

5 0

3 years ago

Solve by both sides variable josh has two leaking pipes in his basement. while waiting for the plumber to come, josh puts a buck

Phoenix [80]

First off, you misspelled some words, second WHICH BUCKET does josh's brother take? That's important!

4 0

3 years ago

Ob's wife Bobette is looking for a new phone plan for their home because ever since the pandemic, all the kids have been using u

Alex Ar [27]

Answer:

5 gigabyte

Step-by-step explanation:

Let the GB data at which the charge for both company is same be x

For Kodu

monthly fixed charge = $50

Per GB data charge over limit = $36

charge for X GB data = Per GB data charge over limit *x = $36*x = 36x

Total charge for Kodu for x gb data = monthly fixed charge +charge for X GB data = $50 +$36

For Fidu

monthly fixed charge = $35

Per GB data charge over limit = $39

charge for X GB data = Per GB data charge over limit *x = $39*x = 39x

Total charge for Fidu for x gb data = monthly fixed charge +charge for X GB data = $35 +$39

Given that at at X GB data charge for both the company is same then

50 +36x = 35 +39x

39x - 36x = 50-35

=> 3x = 15

=> x = 15/3 = 5

Thus, at 5 GB over the limit, charge for both the company will be same.

8 0

3 years ago