Determine which of the lines, if any, are parallel or perpendicular. Explain.

Line a: 4y - 12x = 20
Line b: 3y= -x + 2
Line c: y= 3x - 1

Answers

Answer 1

Answer:

Line [tex]a[/tex] and line [tex]c[/tex] are parallel to each other.

Line [tex]b[/tex] is perpendicular to line [tex]a[/tex].

Line [tex]b[/tex] is perpendicular to line [tex]c[/tex].

Step-by-step explanation:

Rewrite the equation of each line in the slope-intercept form [tex]y = m\, x + b[/tex] to find the slope [tex]m[/tex] of that line.

In the slope-intercept form, [tex]y[/tex] need to be on the left-hand side of the equation while [tex]x[/tex] need to be on the right-hand side. The coefficient of [tex]y[/tex] must be [tex]1[/tex]. The slope of the line would then be equal to the coefficient of [tex]x[/tex].

For example, the equation of line [tex]a[/tex] could be rewritten in slope-intercept form as [tex]y = 3\, x + 5[/tex]. The coefficient of [tex]x[/tex] is [tex]3[/tex], so the slope of this line would be [tex]m_{a} = 3\![/tex].

Similarly, rewrite to obtain the the slope-intercept equation of line [tex]b[/tex]:  [tex]y = (-1/3)\, x + (2/3)[/tex]. The slope of this line would be [tex]m_{b} = (-1/3)[/tex].

The equation of line [tex]c[/tex] is already in slope-intercept form. The slope of that line would be [tex]m_{c} = 3[/tex].

Let [tex]m_{1}[/tex] and [tex]m_{2}[/tex] denote the slopes of two lines in a Cartesian plane.

These two lines are parallel with if and only if their slopes are the same: [tex]m_{1} = m_{2}[/tex]. These two lines are perpendicular to each other if the product of their slope is [tex](-1)[/tex]: [tex]m_{1}\, m_{2} = (-1)[/tex].

In this question, the slope of line [tex]a[/tex] and line [tex]c[/tex] are the same: [tex]m_{a} = m_{c}[/tex]. Thus, line [tex]a\![/tex] and line [tex]c\![/tex] would be parallel.

The product of the slopes of line [tex]a[/tex] and line [tex]b[/tex] is [tex]m_{a}\, m_{b} = 3 \times (-1/3) = (-1)[/tex]. Thus, line [tex]a\![/tex] and line [tex]b[/tex] are perpendicular to each other.

Similarly, line [tex]b[/tex] and line [tex]c[/tex] are perpendicular to each other because the product of their slopes is [tex](-1)[/tex].


Related Questions

3
4
A group of volunteers packed 198 bags of rice. Each bag contained 3
kilo of rice. How many kilograms of rice did the volunteers pack?

Answers

Answer:

No. of bags of rice packed = 198

Amount of rice in each bag = 3 kg

Therefore, total kilograms of rice packed=198×3=594 kg

Step-by-step explanation:

Hope this helps you

Do mark me as brainliest

They packed 594 kilograms of rice.

Given:

Number of bags packed by the group of volunteers = 198

Number of kilo a bag contains = 3 kg

Therefore:

Number of kilograms of rice packed by the volunteers = number of bags packed [tex]\times[/tex] number of kilo one bag of rice weighs

Thus:

Number of kilos of rice packed = [tex]198 \times 3 $ kg\\[/tex]

[tex]= 594 $ kg[/tex]

Therefore, the volunteers packed 594 kilograms of rice.

Learn more here:

https://brainly.com/question/21146374

1.. Use long division to divide.

(2x2 + 10x + 12) = (x + 3)

Answers

Answer:

2(x+2)

Step-by-step explanation:

(2x²+10x+12)/(x+3)=(2(x²+5x+6))/(x+3)=(2(x²+2x+3x+6))/(x+3)=(2(x(x+3)+2(x+3)))/(x+3)=(2(x+3)+(x+2))/(x+3)=2(x+2)

i hope you understand (well it's math)

find the slope of the line passing through the points (-4,1) and (-4,-7)

Answers

Answer:

The slope is undefined.

Step-by-step explanation:

m=(y2-y1)/(x2-x1)

m=(-7-1)/(-4-(-4))

m=-8/(-4+4)

m=-8/0

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Only brainliest, 5 stars and a thanks for correct answers.

Answers

Answer:

For 4 yrs the rate is 5%,

but anually, i.e yearly, its 20%.

Please help if you can.

Answers

Answer:

C

Step-by-step explanation:

what is the closest estimate for 2/10

Answers

Answer: 1/5

Step-by-step explanation:

Simplify the fraction by dividing both the numerator and denominator by 2

the budget of a university organizations is split evenly among its various committees . if they have a budget of P 60.000 represents as a function m(n) the amount of money each of the n number of committees would receive

Answers

Answer:

m(n) = 60000

Amount = 60000/n

Step-by-step explanation:

Given

Budget = 60000

Solving (a) Represent as a function mn

To do this simple substitute m(n) for Budget.

This gives;

m(n) = 60000

Solving (b) Amount each committee will receive.

Since the amount will be shared evenly.

Amount = m(n)/n

Substitute 60000 for m(n)

Amount = 60000/n

Solve the following proportion for v.
8/5 = v/6
Round your answer to the nearest tenth.​

Answers

Answer:

[tex]v=\frac{48}{5}=9\frac{3}{5} \\ [/tex]

Step-by-step explanation:

[tex]\frac{8}{5}=\frac{v}{6}[/tex]

Swap sides:

[tex]\frac{v}{6}=\frac{8}{5}[/tex]

Multiply to both sides by 6:

[tex]\frac{v}{6}\cdot6=\frac{8}{5}\cdot6[/tex]

Group like terms:

[tex]\frac{1}{6}\cdot6v=\frac{8}{5}\cdot6[/tex]

Simplify the fraction:

[tex]v=\frac{8}{5}\cdot6[/tex]

Multiply the fractions

[tex]v=\frac{8\cdot6}{5}[/tex]

Simplify the arithmetic:

[tex]v=\frac{48}{5}[/tex]

Please Help!
What is the answer to this question?​

Answers

Answer:

x=8

Step-by-step explanation:

this is a right angle and right angles are 90 degrees. 6*8 equals 48+2 equals 50. 50+40 equals 90!

Answer:

x=8

Step-by-step explanation:

you would subtract 40 from 90 which gives you 50. you would then set 6x+2 equal to 50 and solve from there.


2. Which statement describes the difference in energy between an ice cube and
liquid water?
A. The particles in the ice cube have no energy.
B. The particles in the ice cube have more energy.
C. The particles in the liquid water have more energy.

Answers

Answer:

B

Step-by-step explanation:

The ice has more thermal energy because it is a solid and the water is a liquid. The water has more thermal energy because the molecules of the water are moving faster than the molecules of the ice. The water and the ice have the same amount of thermal energy because they are different forms of the same substance.

Calculate the arithmetic mean of the numbers.
-121 and 49

Answers

Answer: -72 I think

Step-by-step explanation:

Hope this helps :)

Choose the answer that best represents the situation described below.
Mindy is buying a new computer. She knows that the more memory the Computer has, the more expensive it will be

A. The amount of memory is a function of the brand of computer.
B. The cost of the computer is a function of the amount of memory
C. The type of computer is a function of the cost.​

Answers

Answer:

the answer is B

The cost of the computer is a function of the amount of memory.

the question doesn't talk about the brand. only cost of the computer and the amount of memory.

it says that "She knows that the more memory the Computer has, the more expensive it will be"

The school band has 115 members. They are raising money for band camp.
If each member raises $75, what is the total amount of money raised for band camp?
A. $8,625
B. $7,750
C. $8,605
D. $8,305

Answers

A. 8,625 is the answer, $75 times 115 people

6th grade math i mark as brainliest​

Answers

Answer:

c:)

Step-by-step explanation:

The same thing I say bro:)

it cost 42 dollars to rent a bike for 8 hours, how many hours of bike use does the customer get per dollar

Answers

Answer:

About .19 cents for the unit rate

Step-by-step explanation:

Hi please help, if you send me a link, or fake answers your will be reported!

Answers

Answer:

Your answer is going to be A) a number decreased by seven

Step-by-step explanation:

A number which is m, decreased which is the subtraction sign, and seven.

find the difference between 8.136kg and 5.387kg

Answers

Answer:

2.74900 kilograms

Step-by-step explanation:

8.136kg-5.387kg=2.74900 kilograms

how to list the first ten multiples of 7

Answers

Answer:

7,14,21,28,35,42,49,56,63,70

Step-by-step explanation:

just add 7 lol anyways here ya go :)

Exponent Rule of algebra
New volume of cube
Please help me

Answers

64x^15 because (4x^5)^3

Answer:

above me is maybe a yes or no

Step-by-step explanation:

brainlles to above me

42.3 subtracted by 14.742

Answers

Answer:

-27.558

Step by Step:

I subtracted it

Find three consecutive even integers whose sum is -48.

Answers

Answer:

48 then it would be 32? im not sure that what i caculated

Step-by-step explanation:

Can someone plz help

Answers

Answer:

9. answer: -3, 10. answer: 5

Write the slope-intercept form of an equation for a line with y-intercept -5 and slope 2.

Answers

Answer:

y = -5 + 2x

Step-by-step explanation:

Naiomis parents want to have $50,000 saved for her college education if they invest $20,000 today and earns 7% interest compounded annually about how long would it take them to save the $50,000

Answers

Answer:

13.54 years

Step-by-step explanation:

Saw the answer to this before

Hope this helps!

13.54 years hope it helps

A stereo marked down $75. If this is a 15% decrease, find the sale price.

Answers

I believe the sale price is $63.75

Answer:

The Marked Price is 63.75

Step-by-step explanation:

15/100 * 75 = 11.25

75 - 11.25 = 63.75

Hence the Marked Price is 63.75


8. Which set of numbers is arranged in increasing order?
A 23 873. 24 765,25 000.5 678)
B. (16 287. 16 728.16 827, 16 872
C. 98 782.98 728.98 287.98 278)
D. 78 082.78 802.78 208.78 028)​

Answers

B because it has a chain the is increasing

Answer:

its B :)

Step-by-step explanation:

i took the test

7= 4x + 7
can someone please help me solve this :,)

Answers

Answer:

Here

Step-by-step explanation:

7 = 4x + 7

Cancel out the 7's on each side by adding negative 7 to both sides...

0 = 4x

Now find how much for x alone

4x = 0

divide both sides by 4

x = 0

X = 0

7 = 0 + 7

7 = 7

how many lbs is 200 oz

Answers

The answer should be 12.5 lbs !!!!

Answer:

your answer will be 12.5!

passes through (1, -1) and (2,0)

Answers

Answer:

y = x - 2

Step-by-step explanation:

1. Find the slope - change in y/change in x

[tex]\frac{0-(-1)}{2-1}[/tex] = 1

Slope is 1

2. Find y-intercept

y = x + b

Substitute a point (2,0)

0 = 2 + b

b = -2

3. Put the equation together

y = x - 2

Need help so much on Circle

Please help me for my geometry honors work please! Thank you

Answers

Answer:

x = 95

Step-by-step explanation:

The total degree of a circle is 360. The twp arcs on each side of the parallel lines are equal.

Subtract 135 and 35 from your total

360 - 135 - 35 = 190

Divide your answer by 2

190 ÷ 2 = 95

Your answer would be 95
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