The equations of three lines are given below. Line 1: y = - 3/4 x + 3 Line 2/8 x - 6y = 2 Line 3/- 3y = 4x + 7 For each pair of lines, determine whether they are parallel, perpendicular, or neither.

Answers

Answer 1

Answer:

No parallel lines

Lines 1 and 3 are perpendicular

Step-by-step explanation:

Given:

[tex]Line\ 1:y = -\frac{3}{4}x + 3[/tex]

[tex]Line\ 2: \frac{2}{8}x -6y = 2[/tex]

[tex]Line\ 3: 3y = 4x + 7[/tex]

Required

Determine if they are parallel, perpendicular or not

The slope intercept of a line has the form:

[tex]y = mx + b[/tex]

Where

[tex]m = slope[/tex]

First, we calculate the slope of each lines

[tex]Line\ 1:y = -\frac{3}{4}x + 3[/tex]

Compare the above to [tex]y = mx + b[/tex]

[tex]m_1 = -\frac{3}{4}[/tex]

[tex]Line\ 2: \frac{2}{8}x -6y = 2[/tex]

[tex]\frac{2}{8}x -6y = 2[/tex]

Make -6y the subject

[tex]-6y = 2 - \frac{2}{8}x[/tex]

Divide through by -6

[tex]y = -\frac{2}{6} + \frac{2}{8*6}x[/tex]

[tex]y = -\frac{1}{3} + \frac{1}{8*3}x[/tex]

[tex]y = -\frac{1}{3} + \frac{1}{24}x[/tex]

[tex]y = \frac{1}{24}x-\frac{1}{3}[/tex]

Compare the above to [tex]y = mx + b[/tex]

[tex]m_2 = \frac{1}{24}[/tex]

[tex]Line\ 3: 3y = 4x + 7[/tex]

[tex]3y = 4x + 7[/tex]

Divide through by 3

[tex]y = \frac{4}{3}x + \frac{7}{3}[/tex]

Compare the above to [tex]y = mx + b[/tex]

[tex]m_3 = \frac{4}{3}[/tex]

So, we have:

[tex]m_1 = -\frac{3}{4}[/tex]

[tex]m_2 = \frac{1}{24}[/tex]

[tex]m_3 = \frac{4}{3}[/tex]

None of the slopes are the same, so none of the lines are parallel.

However, lines 1 and 3 are perpendicular.

This is shown below

When the slope of two lines satisfy the following condition, then they are  perpendicular.

[tex]m_1 = -\frac{1}{m_3}[/tex]

This gives:

[tex]-\frac{3}{4} = -\frac{1}{4/3}[/tex]

[tex]-\frac{3}{4} = -1/\frac{4}{3}[/tex]

Convert / to *

[tex]-\frac{3}{4} = -1*\frac{3}{4}[/tex]

[tex]-\frac{3}{4} = -\frac{3}{4}[/tex]


Related Questions

HURRY NEED HELP!!!!!!!!!!!

Describe how the graph of y=2x is the same and different from the graph of y=2x-7 . Explain or show your reasoning.

Answers

Answer:

Im guessing

Step-by-step explanation:

The same

Equal

the mid point

The end

your welcome and not for sure

Try it out

3. Fill in the blank

I NEED THIS ASAP

Answers

Answer:

A. Vaccinations give you a small dose of a virus

vaccination because a vaccination injects some of the virus of bacteria into your body so you body properly learns how to fight it off so in case you do ever get the virus it’s not deadly :)

Refer to image below

Answers

Answer:

A ≈ 40°

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right  

Equality Properties

Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtract Property of Equality

Trigonometry

[Right Triangles Only] SOHCAHTOA  [Right Triangles Only] sinθ = opposite over hypotenuse

Step-by-step explanation:

Step 1: Identify

Angle θ = A

Opposite Leg = 27

Hypotenuse = 42

Step 2: Solve for A

Substitute [sine]:                                                                                             sinA = 27/42Simplify:                                                                                                           sinA = 9/14Trig inverse:                                                                                                    A = sin⁻¹(9/14)Evaluate:                                                                                                         A = 40.0052°Round:                                                                                                             A ≈ 40°

PLEASE HELP FOR BRAINLIEST

If y=24, what does ViVi Supremacy = ?

Answers

Answer:

X=2

Step-by-step explanation:

x = ky    (direct variation formula)

8 = 24k

1/3 = k

x = (1/3)(6)

x = 2

I NEED HELP QUICKKK!!!

Answers

Answer:

y = (1/2)x - 1

Step-by-step explanation:

We can find the slope using the equation (y2-y1)/(x2-x1)

(-2- (-3))/6-4 = 1/2

The slope is 1/2 and the equation as of now is y = (1/2)x + C.

Now we can plug in any of the given data to find C in the equation.

-3 = 1/2(4) + C

-1 = C

C = -1

We now plug in -1 for C and get y = (1/2)x - 1 as our answer.

Drag to the correct place

Answers

Answer

5xcoefficient

3y → Variable

9 → Constant

3÷2.58=
what's the answer i'm fr wut is the answer

Answers

Answer:

1.1627907

Step-by-step explanation:

Answer:

1.162

Step-by-step explanation:

use lond divison but it goes on forever

What is the slope of the line through(-5, -10) and(-1, 5)?

Answers

Answer:

15/4

Step-by-step explanation:

to find the slope with two coordinates use

y2 - y1 / x2 - x1

first find the difference between the ys

the 2nd y point is 5, and the 1st y point is -10, so subtract them from each other

5 - (-10) = 5 + 10 = 15

then find the difference between the xs

the 2nd x point is -1, and the 1st x point is -5, so subtract them from each other

-1 - (-5) = -1 + 5 = 4

now put the difference in ys over the difference in xs

15 / 4

So thats your slope

Ryan cut away 7.85 meters of rope. Before that, he had 13 meters of rope. How much rope does Ryan have left?

Answers

Answer:

5.15

Step-by-step explanation:

13 - 7.85 = 5.15 ( I may be wrong lol )

Answer:

sawarasenaikimiwa⛓shoujonano?✨böKùWâÿARiçHiñBįCChīńOoSûDàYO

-by-step explanation:

...................????

Answers

Answer:

it is 14 hours because there is no fraction and its multiplication

Paulina has read 58 pages of the 234-page book she is doing a book report on for Language Arts. She plans to finish her book by reading 25 pages each day. Using d for the number of days, write a two-step equation to model this situation that you could solve to find out how many days Paulina took to read the rest of her book. Multiple choice question.
A) 25d – 58 = 234
B) 25d + 58d = 234
C) 25 + 58d = 234
D) 25d + 58 = 234

Answers

The answer is d) 25d + 58= 234

Answer:

D

Step-by-step explanation:

A:

25d - 58 = 234

Add 58 to 58 and 234

25d = 292

Divide 25 from both sides

d = 11

A is incorrect because you need to subtract the pages that have been read.

B:

25d + 58d = 234

Combine Like Terms

83d = 234

Divide 83 from both sides

d = 83

B is incorrect because 58 pages aren't days, those are the pages read so this equation is overall incorrect.

C:

25 + 58d = 234

Subtract 25 from both sides

58d = 209

Divide both sides by 58

d = 3.603 and so on

C is incorrect because, again, 58 isn't the days its the pages read.

D:

25d + 58 = 234

Subtract 58 from 58 and 234

25d = 176

Divide 25 from both sides

d = 7.04

D is the correct answer because 25 is the days and 58 is the pages read. You subtracted 58 from each side, making the number of pages in the book go down because you read those pages. You also divided 176 (the pages left) by the days, so 7.04 is your answer. 7 is the answer rounded down. D is your answer.

If y = 3x^4 -2x^3-7x+5, find dy/dx.

Answers

Dy/dx = 12x^3 - 6x^2 - 7

The derivative of [tex]y = 3x^4 - 2x^3 - 7x + 5[/tex] with respect to x is

dy/dx = 12x³ - 6x² - 7.

We have,

The power rule states that if we have a term of form a[tex]x^n[/tex], the derivative with respect to x is given by [tex]d/dx(ax^n) = nax^{n-1}.[/tex]

Applying the power rule, we differentiate each term as follows:

[tex]d/dx(3x^4) = 3 \times 4x^{4-1} = 12x^3\\d/dx(-2x^3) = -2 \times 3x^{3-1} = -6x^2\\d/dx(-7x) = -7 \times 1x^{1-1} = -7[/tex]

d/dx (5) = 0 (since 5 is a constant)

Combining these derivatives, we get:

dy/dx = 12x³ - 6x² - 7

Therefore,

The derivative of [tex]y = 3x^4 - 2x^3 - 7x + 5[/tex] with respect to x is

dy/dx = 12x³ - 6x² - 7.

Learn more about derivatives here:

https://brainly.com/question/29020856

#SPJ4

What is full of holes but still holds water?

Answers

Answer:

I believe it's a sponge because it's filled with holes although it can still hold water.

Answer:

sponge

Step-by-step explanation:

help me quick and i’ll give brainliest

Answers

Answer:

2nd one

Step-by-step explanation:

factorise x^2 - 9???????

Answers

Answer:

Step-by-step explanation:

(−3)(+3) here is the answer short and simple (:

hope this helps

if I'm wrong i am so sorry

Answer: (x+3) (x-3)  im pretty sure!

PLEASE HELP
THE ANSWER ARE A.MILLIMETERS OR CENTIMETERS OR METERS OR KILOMETERS
ANSWER FOR B IS A. GRAMS OR KILOGRAMS
ANSWER FOR C IS A. MILITMETERS OR LITERS

Answers

Answer:

(a) kilometer

(b) Kilograms

(b) Milliliters

Answer:

(a)= kilometer

(b)= kilogram

(c)= millimeters

Step-by-step explanation:

You need to try and figure out which answer is more reasonable.

where might be a lesser sooty owl be found sleeping?

Answers

The Lesser Sooty Owl is a strictly nocturnal bird. Hides & sleeps during the day in dense foliage, between tangles of aerial roots, in all kinds of crevices, or beneath overhanging banks. Hunts in clearings and near roads, but also inside forest.

1/3 + a = 5/4
What does the a equal?

Answers

Answer:

1/3 + a = 5/4 = 4/15

Answer:

[tex]a = \frac{11}{12}[/tex]

Step-by-step explanation:

In order to find the value of a we just solve the equation as follows....

[tex]\frac{1}{3} + a = \frac{5}{4} \\[/tex]

[tex]a = \frac{5}{4} - \frac{1}{3}[/tex]

[tex]a = \frac{15}{12} - \frac{4}{12}[/tex]

[tex]a = \frac{11}{12}[/tex]

Find the value of x to the nearest centimeter.
48 cm
Х
60 cm

Answers

Answer:

60cm

Step-by-step explanation:

x0.40

2880—> 7315.2cm hope this helps

due in a few hours, i'll give brainliest to the correct answer!!!

Answers

Answer:

Angle a=45, Angle b=45

Step-by-step explanation:

The angles are complementary angles which means they both add up to 90 degrees.  And if angles a and b are equal then its 90/2 which is 45.

I need help with these 2 questions

Answers

Answer:

1. a

2. c

Step-by-step explanation:

14.2=2(-5.8+t) i dont know the answer

Answers

Answer:

t = 12.9

Step-by-step explanation:

Here  is the answer (i think)

t = 1 2. 9

10 POINTS!!! WILL MARK BRAINLIEST

Answers

Answer:

y=5

Step-by-step explanation:

75+3x+(4x+10)

ok look at the triangle 2 sides are congruent means 2 angles are congruent

that means that 75 and 3x are congruent

75=3x

divide by 3 both sides

x=25

75+75=150

30=4y+10

y=5

I got it to be 2(2y+5)

Question 5
2 pts
(9x + 16)°
(5x - 14)
The value of
is
The measure of the exterior angle is
degrees

Answers

Answer:

Value is 15 and measure is 151

Bill weighs 110 pounds and is gaining one pound per week. James weights 200 pounds and is losing two pounds per week. After how many weeks will they weigh the same?

Answers

Answer:

After 50 weeks

Step-by-step explanation:

Answer:

150

Step-by-step explanation:

because one gaining a month and one not gaining

Solve:

2a - b + c = 0
a - b = -9
2a + b = 0

Answers

Answer:a=b/2-c/2

b=9+a

b=-2a

Step-by-step explanation:

k - 873 = -695
What is the answer

Answers

Answer:

k= -1,568

Step-by-step explanation:

I am pretty sure this is the answer if not I am soo sorry

Answer:

178 is the answer......

6 + 6(x + 4) + 15y + x

Answers

Answer:

7x + 15y + 30

Step-by-step explanation:

6 + 6x + 24 + 15y + x

= 7x + 15y + 30

Please help!!!
You're shopping for a guitar and find one
with an original price of $160. The store is
offering a 30% discount on all guitars. Wait!
There is an additional 25% off all purchases.
What is the sale price of the guitar?

Answers

$84

$160 * 0.30 = $48

$160 - $48 = $112

$112. * 0.25 = $28

$112 - $28 = $84

Use what you know.
Guitar cost =$160 w/ 30% off
30% = 30/100 = 0.30.

30% off means 30% of the price $160 will be taken off so that is why I multiplied 160 by 0.30 (30/100).

30% of 160 is 48 so I subtracted 48 from 160 which equals $112.

With an extra 25% off I repeated the same steps above.

25/100 = 0.25

$112 * 0.25= $28
$112 - $28 = $84

If you need me to break it down more just let me know. I HOPE THIS HELPS

help me please i need help on my hw

Answers

Answer:

111.707317073

Step-by-step explanation:

111.707317 or 11 with a remainder of 29
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