Gina Wilson unit 4 homework 10 parallel and perpendicular lines PLEASE HELP

Answers

Answer 1

Answer/Step-by-step Explanation:

To determine if segment AB and CD are parallel, perpendicular, or neither, calculate the slope of each.

✍️If the slope of AB and CD are the same value, then they are parallel.✅

✍️If the slope of one is the negative reciprocal of the other, then they are perpendicular.☑️

✍️If their slopes are different, or the slope of one is not the negative reciprocal of the other, then they are neither.❌

1. AB formed by (-2, 13) and (0, 3)

CD formed by (-5, 0) and (10, 3)

Slope of AB = [tex] \frac{y_2 - y_1}{x_2 - x_1} = \frac{3 - 13}{0 -(-2)} = \frac{-10}{2} = -5 [/tex]

Slope of CD = [tex] \frac{y_2 - y_1}{x_2 - x_1} = \frac{3 - 0}{10 -(-5)} = \frac{3}{15} = \frac{1}{5} [/tex].

☑️-5 is the negative reciprocal of ⅕, therefore segments AB and CD are perpendicular

2. AB formed by (3, 7) and (-6, 1)

CD formed by (-6, -5) and (0, -1)

Slope of AB = [tex] \frac{y_2 - y_1}{x_2 - x_1} = \frac{1 - 7}{-6 - 3} = \frac{-6}{-9} = \frac{2}{3} [/tex]

Slope of CD = [tex] \frac{y_2 - y_1}{x_2 - x_1} = \frac{-1 -(-5)}{0 -(-6)} = \frac{4}{6} = \frac{2}{3} [/tex].

✅Segment AB and CD have the same slope value of ⅔. Therefore, they are parallel.

3. AB formed by (-6, 2) and (-2, 4)

CD formed by (-1, 11) and (5, -7)

Slope of AB = [tex] \frac{y_2 - y_1}{x_2 - x_1} = \frac{4 - 2}{-2 -(-6)} = \frac{2}{4} = \frac{1}{2} [/tex]

Slope of CD = [tex] \frac{y_2 - y_1}{x_2 - x_1} = \frac{-7 - 11}{5 -(-1)} = \frac{-18}{6} = -3 [/tex].

❌The slopes of Segments AB and CD are not the same (½ and -3). One is also not the negative reciprocal of the other. Therefore, they are neither parallel nor perpendicular.

4. AB formed by (-3, 8) and (2, 3)

CD formed by (-4, 6) and (-8, 2)

Slope of AB = [tex] \frac{y_2 - y_1}{x_2 - x_1} = \frac{3 - 8}{2 -(-3)} = \frac{-5}{5} = -1 [/tex]

Slope of CD = [tex] \frac{y_2 - y_1}{x_2 - x_1} = \frac{2 - 6}{-8 -(-4)} = \frac{-4}{-4} = 1 [/tex].

❌The slopes of Segments AB and CD are not the same (1 and -1). One is also not the negative reciprocal of the other. Therefore, they are neither parallel nor perpendicular.

5. AB formed by (-8, -1) and (-4, 2)

CD formed by (0, -3) and (12, 6)

Slope of AB = [tex] \frac{y_2 - y_1}{x_2 - x_1} = \frac{2 -(-1)}{-4 -(-8)} = \frac{3}{4} [/tex]

Slope of CD = [tex] \frac{y_2 - y_1}{x_2 - x_1} = \frac{6 -(-3)}{12 - 0} = \frac{9}{12} = \frac{3}{4} [/tex].

✅Segment AB and CD have the same slope value of ¾. Therefore, they are parallel.

6. AB formed by (6, 5) and (3, -1)

CD formed by (2, -5) and (-4, 7)

Slope of AB = [tex] \frac{y_2 - y_1}{x_2 - x_1} = \frac{-1 - 5}{3 - 6} = \frac{-6}{-3} = 2 [/tex]

Slope of CD = [tex] \frac{y_2 - y_1}{x_2 - x_1} = \frac{7 -(-5)}{-4 - 2} = \frac{12}{-6} = -2 [/tex].

❌The slopes of Segments AB and CD are not the same (2 and -2). One is also not the negative reciprocal of the other. Therefore, they are neither parallel nor perpendicular.

To determine if the given equations are parallel, perpendicular, or neither, ensure both equations are in the slope-intercept form, y = mx + b, where m is the slope.

7. 3x + 2y = 6 and y = -³/2x + 5

Rewrite the first equation in slope-intercept form

3x + 2y = 6

2y = -3x + 6

y = -3x/2 + 6/2

y = -³/2x + 3

The slope of the first equation is -³/2.

The slope of the second equation is -³/2.

✅Both equations have the same slope value of -³/2. Therefore, they are parallel.

8. 3y = 4x + 15 and 9x + 12y = 12

Rewrite both equations in slope-intercept form.

3y = 4x + 15

y = 4x/3 + 15/3

y = ⁴/3x + 5

And

9x + 12y = 12

12y = -9x + 12

y = -9x/12 + 12/12

y = -¾x + 1

The slope of the first equation is ⁴/3.

The slope of the second equation is -¾..

☑️-¾ is the negative reciprocal of ⁴/3. Therefore both AB equations are perpendicular.

9. 8x - 2y = 4 and x + 4y = -12

Rewrite both equations in slope-intercept form.

8x - 2y = 4

-2y = -8x + 4

y = -8x/-2 + 4/-2

y = 4x - 2

And

x + 4y = -12

4y = -x - 12

y = -x/4 - 12/4

y = -¼x - 3

The slope of the first equation is 4.

The slope of the second equation is -¼..

☑️-¼ is the negative reciprocal of 4. Therefore both AB equations are perpendicular.

10. 3x + 2y = 10 and 2x + 3y = -3

Rewrite both equations in slope-intercept form.

3x + 2y = 10

2y = -3x + 10

y = -3x/2 + 10/2

y = -³/2x + 5

And

2x + 3y = -3

3y = -2x - 3

y = -⅔x - 1

The slope of the first equation is -³/2.

The slope of the second equation is -⅔.

❌The slopes of the first equation and second equation are not the same (-³/2 and -⅔). One is also not the negative reciprocal of the other. Therefore, they are neither parallel nor perpendicular.

11. -4y = -2x + 8 and 3x - 6y = 6

Rewrite both equations in slope-intercept form.

-4y = -2x + 8

y = -2x/-4 + 8/-4

y = ½x - 2

And

3x - 6y = 6

-6y = -3x + 6

y = -3x/-6 + 6/-6

y = ½x - 1

The slope of the first equation is ½.

The slope of the second equation is ½.

✅Both equations have the same slope value of ½. Therefore, they are parallel.

12. y = 8 and x = -1

The first equation is a horizontal line. The slope of am horizontal line is always zero.

The second equation is a vertical line. The slope of a vertical line is undefined.

❌Therefore, they are neither parallel nor perpendicular.

Related Questions

#7 Write an equation in slope-intercept form to represent the line perpendicular to 3x + 2y = -7 passing through the point (1, 1). O y=-3x + 4 O y = -3/2x + 1/3 y = 2/3x + 1/3 O y = 3x + 1

Answers

Answer:

y = 2/3 x + 1/3

Step-by-step explanation:

First find the slope of the given line by solving for "y":

3 x + 2 y = -7

2 y = - 3 x - 7

y = - 3/2 x - 7/2

which shows a slope of "- (3/2)"

Then, the slope of a line perpendicular to it must be "the opposite of the reciprocal" of this slope, that is: "2/3"

We use this info and the requested point (1, 1) to find the complete equation of the perpendicular line:

y = 2/3 x + b

1 = 2/3 (1) + b

1 - 2/3 = b

b = 1/3

Then the equation of the line is:

y = 2/3 x + 1/3

which agrees with the third answer shown in the list of options.

I need to know for you to Awnser my question

Points and brainlest !!!

Answers

Answer:

id c hot hf hdjhdw fhwjfehf v;e

Step-by-step explanation:

id c h

Answer:

2/3

Step-by-step explanation:

theres only 4 less than 5 out of 6 so the fractio is 4/6. 4/6 simplified is 2/3

Which statement correctly describes the relationship represented by the graph?
A.
The relationship is linear and proportional.

B.
The relationship is linear and non-proportional.

C.
The relationship is non-linear and proportional.

D.
The relationship is non-linear and non-proportional.

Answers

Answer: A

Step-by-step explanation: The line is linear as it changes at a constant rate which means it’s also proportional as proportional means as x changed so does y.

....................

Answers

Answer:

10.7%

Step-by-step explanation:

Hope this helps :)

.................... what do u mean bruh

what is 5 8/12 as a mixed number in simplest form

Answers

Answer:

= [tex]5\frac{2}{3}[/tex]Step-by-step explanation:

Let a=(-7,3) and b=(-2,-12), and c=a+b. What is the magnitude and direction angle of c?

A. |c|=18; theta=135°
B. |c|=18; theta=225°
C. |c|=9sqrt2; theta=135°
D. |c|=9sqrt2; theta=225°

Answers

Answer:

D is correct

Step-by-step explanation:

I got it right on my edge math unit test review.

The value of |c| = 9√2 and θ = 225⁰

What is Magnitude?

The magnitude or size of a mathematical object is a property which determines whether the object is larger or smaller than other objects of the same kind.

Here, given values;

a = (-7, 3) and b = (-2, -12)

Now, c = a + b

c = (-7, 3) + (-2, -12)

c = (-9, -9)

Now, |c| = √(9²+9²)

|c| = 9√2

Now, tan θ = |y/x|

tan θ = |-9/-9|

tan θ = 1

tan θ = tan 225⁰

θ = 225⁰

Thus, the value of |c| = 9√2 and θ = 225⁰

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The college student senate is sponsoring a spring break Caribbean cruise raffle. The proceeds are to be donated to the Samaritan Center for the Homeless. A local travel agency donated the cruise, valued at $2000. The students sold 2629 raffle tickets at $5 per ticket. (a) Kevin bought forty-one tickets. What is the probability that Kevin will win the spring break cruise to the Caribbean

Answers

Answer: the probability that Kevin will win the spring break cruise to the Caribbean is 0.01559

Step-by-step explanation:

Given that;

the total number of raffle ticket sold by the student is 2629

Kevin bought 41 tickets

the probability that Kevin will win the spring break cruise to the Caribbean?

The required probability will be:

Probability

Answer:

1) The function that represents how the money in her suit case is s(x) = 450

The function that represents the amount she is able to make from baby sitting is a(x) = 6(x - 2)

Given that the values of the two function are the same units, dollars, and the amount are to be put to the same use for spending money for her first year of college, the combination of the two functions is the sum of their values given as follows;

f(x) = s(x) + a(x) = 450 + 6(x - 2)

2) For simplification, we expand the second term and add the constant terms as follows;

f(x) = 450 + 6·x - 12

f(x) = 438 + 6·x

The sum of the two terms becomes, f(x) = 438 + 6·x

are there sample worksheets for accounting

Answers

Yes, there are! Hope this helps! Have a great day! :)

Can someone help answer this

Answers

Answer:

968 - 744 = 224

Step-by-step explanation:

if Fatima's lettuce broccoli and peas all weigh 968 grams when weighed together and her lettuce and broccoli way 744 grams, as shown in the photo, when weighed together you would subtract the weight of the lettuce and broccoli from the weight of the peas, lettuce, and broccoli together.

you would then get 224 as your answer. your number sentence then should be:

968 - 744 = 224

Step-by-step explanation: 968-744=224 is the answer

Answer subtract 744 and 968 and you will get the answer

On a field trip, there are 2 girls for every 3 boys.

If there are 20 kids total, how many girls are there?

Answers

Answer:

8 Girls

Explanation:

The ratio is 2:3. For every two girls, there are three boys. So 2+3=5. Now we are gonna divide 20 by 5 and you get 4. 4 equals one person. So fitting it into the ratio, 4x2=8. And to make sure it is correct, we also have to try it with the boy. 4x3=12. 12+8=20. Have a good day

The tread life of a particular brand of tire is a random variable best described by a normal distribution with a mean of 60,000 miles and a standard deviation of 1600 miles. What warranty should the company use if they want 94% of the tires to outlast the warranty?

Answers

Answer:

The warranty the company should use is of 57,520 mile.

Step-by-step explanation:

Let X denote the tread life of a particular brand of tire.

It is provided that, [tex]X\sim N(60,000, 1600^{2})[/tex].

Also provided that the company wants 94% of the tires to outlast the warranty.

Let x denote the warranty .

That is, P (X > x) = 0.94.

⇒ P (X < x) = 0.06

⇒ P (Z < z) = 0.06

The corresponding value of z is -1.55.

Where and

We are interested on this probability

And the best way to solve this problem is using the normal standard distribution and the z score given by:

If we apply this formula to our probability we got this:

And we can find this probability using the normal standard table or exce:

answer

Write an equation in slope-intercept form of the line perpendicular to the given line that contains D

Answers

if would be the last answer i believe

a. Estimate of the population mean number of units sold per month

n = Number of Data Values = 5

Sum of Data Values = Σxi =97 + 120 + 88 + 97 + 93 = 495

Sample Mean = X = Σxi/n = 495 / 5 = 99

The population mean number of units sold per month is 99

b. Estimate of the population standard deviation

Month Data (x) X x - X (x - X)^2

1 97 99 -2 4

2 120 99 21 441

3 88 99 -11 121

4 97 99 -2 4

5 93 99 6 36

Sum of deviation squared 606

s^2 = Sample Variance = Σ(xi - X)2/(n - 1)

Sample Variance = 606/4 = 151.5

Sample Standard Deviation = √Sample Variance

Sample Standard Deviation = √151.5

Sample Standard Deviation = 12.30853362509117

Sample Standard Deviation = 12.31

The point estimate of the population standard deviation is 12.31

Factor 15x-10x^3

PLEASE ASNWER ASAP

Answers

Answer:

[tex]\huge\boxed{\sf 5x(3-2x^2)}[/tex]

Step-by-step explanation:

[tex]\sf 15x-10x^3\\\\Greatest Common Factor = 5x\\\\So, We'll \ take \ 5x \ common\\\\= 5x ( 3-2x^2)\\\\Thus, this \ is \ the \ factorized\ form\\\\\rule[225]{225}{2}[/tex]

Hope this helped!

~AnonymousHelper1807

Michael wants to purchase a jeep. The purchase price of the Jeep is $37,000. The
dealership will allow him to pay cash or finance the Jeep with a down payment of
$5,000.00 and 60 monthly payments of $625.00. Michael chose to finance the jeep.
Answer the following questions.
a) What is the amount financed?
b) What is the total amount of monthly payments?
C} What is the amount of the finance charge?

Answers

Answer:

A) $32,000 B) $37,500 C) $5,500

Step-by-step explanation:

Price of jeep: $37,000

Michael uses $5,000 of his own money toward that total $37,000-$5,000= $32,000

Monthly payments $625.00×60months=$37,500

After paying $5,000 of his own money, & bringing theamount owed to $32,000. Michael still has to pay back $37,500. Making, the finance chardge $5,500. ($37,500-$32,000= $5,500)

Amount financed = $32000, total amount of monthly payment = $37500 and total amount of the finance charge = $5500.

What is dealership finance ?

"Dealer financing is a type of loan that is originated by a retailer to its customers and then sold to a bank or other third-party financial institution. The bank purchases these loans at a discount and then collects principle and interest payments from the borrower. This is also called an indirect loan."

According to the question,

Given,

Price of jeep = $37000

Down payment = $5000

Total number of monthly payment = 60

Amount to be paid after down payment

= $37000 - $5000

= $32000 ____( 1 )

Amount paid in Monthly payments = $625.00 × 60months

= $37500 ____( 2 )

From ( 1 ) and ( 2 ) we get,

Finance charge amount = Total monthly amount - Total amount financed

= $37500 - $32000

= $5500

Hence, amount financed , total amount monthly payment and total amount of the finance charge is $32000 , $37500 and $5500.

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Marianne is 15 years old and her brother is 5 years old; is the relationship between their ages proportional?

Answers

Answer:

The ratio is 15:5 or 3:1. If Marianne is 3 years old, her brother is 1. And it is proportional...

Step-by-step explanation:

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