Given the following two equations determine if they are parallel, perpendicular, or neither.
3x + 6y = 30
4y + 2x = 9

Please show work!

Answers

Answer 1

Answer:

Parallel

Step-by-step explanation:

What you want to do first is to put both equations into the slope intercept form: y=mx+b.

In the first equation, you move the [tex]3x[/tex] to the right side of the equal sign by subtracting on both sides:

[tex]6y = -3x + 30[/tex]

Then you want to divide both sides by 6 to isolate y:

[tex]y = -\frac{1}{2}x + 5[/tex]

Next for the second equation, you do similar steps. You subtract [tex]2x[/tex] from both sides:

[tex]4y=-2x+9[/tex]

Then you want to divide both sides by '4' to isolate y:

[tex]y= -\frac{1}{2}x+\frac{9}{4}[/tex]

Now to check if the two equations are parallel, perpendicular, or neither, you compare the slopes 'm' which is the coefficient next 'x'. If two equations have the same slope, then they are parallel. If the slopes multiplied equal -1, then they are perpendicular. If the slopes are not the same or if the product of the slopes is not -1, then it is neither.

In the case of this problem, the slopes are the same, so the equations are parallel:

[tex]-\frac{1}{2} = -\frac{1}{2}[/tex]


Related Questions

A train traveled from one city to another city in 4 hours at a speed of 70 mph.
The retum trip was made in 5 hours. Find the speed for the return trip.

Answers

Answer:

56miles/hr

Step-by-step explanation:

Given parameters:

Time taken for the to travel  = 4hrs

Speed of the train  = 70mph

  From this data, let us find the distance of the trip;

Distance  =Speed x time

  Therefore, insert the parameters;

          Distance  = 70mph x 4hr = 280miles

Now;

  Return trip took, 5hrs,

Speed  = ?

  Speed  = [tex]\frac{distance}{time}[/tex]  

Insert the parameters and solve;

     Speed  = [tex]\frac{280}{5}[/tex]   = 56miles/hr

Mr Thompson wants to cut a 5-ft rope into a 1/4-ft sections how many 1/4 sections will he have

Answers

Answer:

20 pieces of rope

Step-by-step explanation:

Mr. Thompson has a 5-ft rope. If he cuts the rope into 1/4-ft pieces, that means for every foot, there are 4 pieces of rope. There are 5-ft of rope, so we multiply 5 and 4 to get the number of pieces of rope.

5 x 4 = 20 pieces of rope.

I hope that this helps! :)

Simplify x^-5

please please I need it please please please please please please

Answers

Answer:

[tex]1/x^5[/tex]

Step-by-step explanation:

[tex]x^-^y = 1/x^y[/tex]

Answer:

1/x^5

Step-by-step explanation:

When you have a negative exponent, you have to put 1 over that power without the negative sign in the exponent. You put 1 over x^5

Answer: 1/x^5

Solve for n: n+516=−1n+516=−1

Answers

Answer:

n=-517

n+516=-1

subtract 516

PLEASE PLEASD HELP!!!
A machine produces 480 gel pens per hour. Which equation represents the number of gel pens, p, produced in
m minutes?

Answers

Answer:

8m=p

Step-by-step explanation:

480/60=8

PLEASE HELP ME Find the slope of the line between two points (15,-2) and (-2,1)

Answers

3/17 is the slope good luck with what ur doing

Craig took 20 minutes to swim 14 laps in the school swimming pool.
What is his unit rate per minute?​

Answers

Answer:

0.7 lap per minute

Step-by-step explanation:

Which best represents the greatest amount of change that took place from one day to the next day over the four-day period?

Answers

Answer:

A loss of 93.98 points. Hope this is helpful!

Step-by-step explanation:

Answer:

fat dickaling

Step-by-step explanation:

what is the radius of the cylinder​

Answers

Given height and surface-area-to-volume ratio: r = 2 * h / (h * SA:V - 2) , Given volume and lateral area: r = 2 * V / A_l , Given base area: r = √(A_b / (2 * π)) , Given lateral area and total area: r = √((A - A_l) / (2 * π)) .

identiy why trade improved during the middleages.
this is the question.

Answers

Answer:

intermarriage

Step-by-step explanation:

people from different part intermarried

Answer:

dont know

Step-by-step explanation:

Determine the slope and the y-intercept of the table.

Answers

Answer:

Slope: 1.5

Y-Intercept: -1

A quality control group found 7 defects for every 1250 units produced. If 8750 products were produced how many defects were there?

Answers

49 defects hope this helps :)

9. Which point of view is most likely to be uni eliable in a story?
All points of view in a story are equally eliable.
The first person narrator is most likely to be unreliable.
All points of view in a story are equally unreliable.
The third person point of view is most likely to be unreliable.

Answers

This question includes some misspelled words; here is the correct question:

Which point of view is most likely to be unreliable in a story?

All points of view in a story are equally reliable.

The first person narrator is most likely to be unreliable.

All points of view in a story are equally unreliable.

The third-person point of view is most likely to be unreliable.

The correct answer is The first-person narrator is most likely to be unreliable.

Explanation:

In a narrative text, an unreliable narrator implies the narrator lies on purpose to the reader, or his/her version of the story is not completely accurate. This feature of narration occurs mainly if the story, novel, etc. includes a first-person narrator. This is because in a first-person narrator, the thoughts, feelings, and point of view of one of the characters prevail, and this causes the events told are subjective and therefore more likely to be inaccurate. Also, this does not occur if there is a third-person narrator because in this case the narrator acts as an observer and this makes it more objective.

hELLPPLPLP PLEASEE answer 1-3 and please show the work on how to get it

Answers

Answer:

Step-by-step explanation:

Milk consumed in 4 weeks = 20 jugs

Milk consumed in 1 week = 20 ÷ 4 = 5 jugs

Milk consumed in 8 weeks = 5 * 8  = 40 jugs

2) Cost of 20 sets of crayons =  $ 60

Cost of 1 set of crayon  =   60 ÷ 20  = $ 3

Cost of 9 sets of crayons =  3 * 9 = $ 27

3) Number of tomatoes required to make soup for two guest  = 4

Number of tomatoes required to make soup for one guest  = 4 ÷ 2  = 2

Number of tomatoes required to make soup for 6 guests= 2*6= 12 tomatoes

4(2x−9)=4 solve for x

Answers

Answer: x=5

Step-by-step explanation:

Distribute the 4 to the 2 and 9 and you will get (8x-36)=4.

Then you'd add the 36 to 4 to get 40.

Lastly you'd divide 8 and 40 to get 5. Hope this helps!!!

A farmer with 5000 feet of fencing wants to enclose a rectangular field and then divide it into two plots by adding a fence in the middle parallel to one of the sides. Using the function A(x) , analytically find the WIDTH of the field that would maximize its area. (Round your answer to the nearest whole number)

Answers

Answer:

The required width of the field that would maximize the area is = 1250  feet

Step-by-step explanation:

Given that:

The total fencing length = 5000 ft

Let consider w to be the width and L to be the length.

Then; the perimeter of the rectangular field by assuming a parallel direction is:

P = 3L + 2w

⇒ 3L + 2w = 5000

3L = 5000 - 2w

[tex]L = \dfrac{5000}{3} - \dfrac{2w}{3}[/tex]

Recall that:

The area of the rectangle = L×w

[tex]A(w) = ( \dfrac{5000}{3}-\dfrac{2}{3} ) w[/tex]

[tex]A(w) = \dfrac{5000}{3}w-\dfrac{2}{3} w^2[/tex]

Taking the differentiation of both sides with respect to t; we have:

[tex]A' (w) = \dfrac{5000}{3} - \dfrac{2}{3} ( 2 w)[/tex]

[tex]A' (w) = \dfrac{5000}{3} - \dfrac{4w}{3}[/tex]

Then; we set A'(w) to be equal to zero;

So; [tex]\dfrac{5000}{3} - \dfrac{4w}{3}=0[/tex]

5000  = 4w

w = 5000/4

w = 1250

Thus; the required width of the field that would maximize the area is = 1250  feet

Also, the length [tex]L = \dfrac{5000}{3} - \dfrac{2w}{3}[/tex] can now be :

[tex]L = \dfrac{5000}{3} - \dfrac{2(1250)}{3}[/tex]

L = (5000 -2500)/3

L = 2500/3 feet

Suppose, the farmer divides the plot parallel to the width; Then  2500/3 feet = 833.33 feet and the length L = 1250 feet.

Which is not a correct way to represent the relation "the second number is 1 less than three times the first number"?

y=1 - 3x

y= 3x + (-1)

y= -1 + 3x

y= 3x - 1

Answers

Answer:

3x-1

Step-by-step explanation:

Answer:

y = 3 x - 1

Step-by-step explanation:

-3(ñ-4)+15=-5(ñ-7)-10

Answers

Answer:

ñ = -1

Step-by-step explanation:

29 + 15x = -x - 3. Simplified

Answers

for this equation the answer is x= -2

Heeeeellpppp
x^5 + 6x + 11x + 6 = 0

Answers

Answer:

The answer for x is

x=0.35262048

if Ad = 2x + 2 and cd= x +11, what is the value of x​

Answers

Answer: the answer is 9

Step-by-step explanation:

PLS help me asap
A motorboat moves across a lake at a constant speed. When it begins, it is 64
km from the shore. After 17 minutes, it is 30 km from the shore. Which
function describes the motorboat's distance from the shore?

The answer
A. y= 2x+64
B. y=-2x+64
C. y=-17x+ 30
D. y=-17x+64

Answers

Answer:

y=-2x+64 i think

Step-by-step explanation:

The answer is B hope this helps

which number are composite numbers-49,35,32,41,47

Answers

Answer:

49, 35, 32

Step-by-step explanation:

A prime number is a number whose factors are 1 and itself

Eg 7

7 is a prime number because it only comes in table one and 7

Or it’s only factors are 1 and itself

A composite number comes in 1, itself and other tables

Eg. 16

It comes in table 1, 2, 4 and 16

Answer: 49,32,35.

Hope this helps!

decimals that equals 1

Answers

Answer:

0.01

Step-by-step explanation:

Please help me I am confused

Answers

Add 8 to both sides of the equation

Help I Dont Understand?

Answers

I am worry I tried but I think its the wrong answer good luck!

Cho flipped a coin 20 times. The coin landed on tails 8 times. What is the ratio of the number of times the coin landed on heads to the number of flips?​

Answers

Answer:

The answer is

A ) 12 to 20

Step-by-step explanation:

Cho flipped heads 12 times. She flipped the coin a total of 20 times, making the ratio 12 to 20.

I hope this helped you! If it did, please consider rating, pressing thanks, and giving my answer 'Brainliest.' Have a fantastic day! :)

HELP!!! Parallel Line Proofs

Answers

They add to 180 when you connect the two lines

Describe how the graph of y=2xy=2x is the SAME as the graph of y=2x-7y=2x−7.



Select all statements that are true.





They both have a slope of 2.


They cross the x-axis at the same point.


They are parallel to each other.


They have the same slope.


They are in the same location.


They cross the y-axis at the same point.

Answers

Answer:

-They both have a slope of 2.

-They are parallel to each other.

-They have the same slope.

Step-by-step explanation:

The 2 equations are;

y = 2x and y = 2x - 7

Now, from slope intercept equation,

y = mx + c

Where m is slope and c is the intercept on the y-axis

From the 2 equations y = 2x and y = 2x - 7, Comparing with y = mx + c, we can see they both have a slope of 2.

For 2 lines to have same slope, it means that they are parallel and have different y-intercepts.

They should cross the x-axis when y = 0.

But at x = 0,we have;

y = 2x = 0. And x = 0

Also,for y = 2x - 7 is y = 2x - 7 = 0

2x = 7 and x = 7/2.

Thus,they don't cross the x - axis at the same point

Looking at the options, we can see that there are 3 correct ones from what we've described above namely;

-They both have a slope of 2.

-They are parallel to each other.

-They have the same slope.

Answer:

its

Step-by-step explanation:

please helppp ppppñpñp

Answers

Answer:

I tried my best to explain it, hope it helps!

Step-by-step explanation:

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