A line segment AB has the coordinates A (2,3) AND B ( 8,11) answer the following questions (1) What is the slope of AB? (2) What is the length of AB? (3) What are the coordinates of the mid point of AB?(4) What is the slope of a line perpendicular to AB ?

Answers

Answer 1

Answer:

1) The slope of the line segment AB is [tex]\frac{4}{3}[/tex].

2) The length of the line segment AB is 10.

3) The coordinates of the midpoint of the line segment AB is [tex]M(x,y) = (5,7)[/tex].

4) The slope of a line perpendicular to line segment AB is [tex]-\frac{3}{4}[/tex].

Step-by-step explanation:

1) Let [tex]A(x,y) = (2,3)[/tex] and [tex]B(x,y) = (8,11)[/tex]. From Analytical Geometry, we get that slope of AB ([tex]m_{AB}[/tex]), dimensionless, is determined by the following formula:

[tex]m_{AB} = \frac{y_{B}-y_{A}}{x_{B}-x_{A}}[/tex] (1)

If we know that [tex]x_{A} = 2[/tex], [tex]x_{B} = 8[/tex], [tex]y_{A} = 3[/tex] and [tex]y_{B} = 11[/tex], the slope of the line segment is:

[tex]m_{AB} = \frac{11-3}{8-2}[/tex]

[tex]m_{AB} = \frac{4}{3}[/tex]

The slope of the line segment AB is [tex]\frac{4}{3}[/tex].

2) The length of the line segment AB ([tex]l_{AB}[/tex]), dimensionless, can be calculated by the Pythagorean Theorem:

[tex]l_{AB} =\sqrt{(x_{B}-x_{A})^{2}+(y_{B}-y_{A})^{2}}[/tex] (2)

If we know that [tex]x_{A} = 2[/tex], [tex]x_{B} = 8[/tex], [tex]y_{A} = 3[/tex] and [tex]y_{B} = 11[/tex], the length of the line segment AB is:

[tex]l_{AB} = \sqrt{(8-2)^{2}+(11-3)^{2}}[/tex]

[tex]l_{AB} = 10[/tex]

The length of the line segment AB is 10.

3) The coordinates of the midpoint of the line segment AB are, respectively:

[tex]x_{M} = \frac{x_{A}+x_{B}}{2}[/tex] (3)

[tex]y_{M} = \frac{y_{A}+y_{B}}{2}[/tex] (4)

If we know that [tex]x_{A} = 2[/tex], [tex]x_{B} = 8[/tex], [tex]y_{A} = 3[/tex] and [tex]y_{B} = 11[/tex], the coordinates of the midpoint of the line segment AB are, respectively:

[tex]x_{M} = \frac{2+8}{2}[/tex]

[tex]x_{M} = 5[/tex]

[tex]y_{M} = \frac{3+11}{2}[/tex]

[tex]y_{M} = 7[/tex]

The coordinates of the midpoint of the line segment AB is [tex]M(x,y) = (5,7)[/tex].

4) From Analytical Geometry we can determine the slope of a line perpendicular to line segment AB as a function of the slope of the line segment:

[tex]m_{\perp} = -\frac{1}{m_{AB}}[/tex] (5)

If we know that [tex]m_{AB} = \frac{4}{3}[/tex], then the slope of a line perpendicular to AB is:

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

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

The slope of a line perpendicular to line segment AB is [tex]-\frac{3}{4}[/tex].


Related Questions

A typical tip in a restaurant is​ 15% of the total bill. If the bill is ​$100​, what would the typical tip​ be

Answers

Answer:

15 dollars

Step-by-step explanation:

Total Bill = Cost of the Meal + tip

Total Bill = 100 + 15/100 * 100

Total Bill = 115

So the tip is 15 dollars.

PLEASE HURRY! (And only respond if you know the answer please.)
A Web music store offers two versions of a popular song the size of the standard version is 2.1 megabytes (MB). The size of the high-quality version is 4.9 MB. Yesterday, the high-quality version was downloaded twice as often as the standard version. The total size downloaded for the two versions was 2737 MB. How many downloads of the standard version were there?​

Answers

Answer:

Step-by-step explanation:

If the no of standard version downloads = 230

Then higher version is twice than that = 460

Total = 2.1 x 230 + 4.9 x 460 = 2737

Do You Know How?
In 3-6, multiply to find the product.
Estimate to check for reasonableness.
3. 205 x 23
4. 108 x 34
5. 410 x 44
6. 302 x 30

Answers

Answer:

3. 4,715 (estimate: 5,000)

4. 3,672 (estimate: 3,300)

5. 18,040 (estimate: 16,000)

6. 9,060 (estimate: 9,000)

Explanation:

It is reasonable if your answer is somewhat close to the estimate.

.) Mr. Leonard is saving his money for a new Jeep toy. If 30% of the toy Jeep
is $6.00, how much is the toy?

Answers

Answer:

i think its 20 dollars

Step-by-step explanation:

hope its right

Find the median and mean of the data set below: 39, 22, 14, 9, 1, 11​

Answers

Answer:

mean is 16

Step-by-step explanation:

any one here in LISD district

Answers

Answer:

I'm not, but free points?

Step-by-step explanation:

Item Measured Scale Reading (tons) Number of Items on the Scale Weight per Item (tons)
Raul and his friends
1
20
4
cars
7
8
2
baby elephants
ما | ط
001
goats
4
cow NIP
desks
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32

Answers

Answer:

Plato Answer

Step-by-step explanation:

5 divided by 3/12 equals

Answers

Answer:

= 20

Step-by-step explanation:

Turn it into multiplication by doing keep, switch, flip. Keep 5. Switch division to multiplication. Flip 3/12 to 12/3 or 4.

5 x 4 = 20.

Consider this function.
(r) = -3r + 3
Which graph represents the inverse of function ?

Answers

9514 1404 393

Answer:

  C.  graph Y

Step-by-step explanation:

Starting with f(r) = -3r +3, the inverse function can be found from ...

  r = f(y)

  r = -3y +3

  r -3 = -3y

  (r -3)/-3 = y

  y = -1/3r +1

The inverse function will have a slightly negative slope and a y-intercept of 1. This matches graph Y.

Applesauce recipe for 8 uses 3 quarters of water. How much water for 12 people

Answers

Answer:

4.5 quarts

Step-by-step explanation:

We use a proportion to solve this.

8/3 = 12/x

Cross-multiply to get:

8x = 36

x = 4.5

The answer to the question is 4.5

Which statement can you conclude is true from the given information?

Answers

Answer:

angle IJA is a right angle

What is the equation of this line

Answers

Answer:

Y= 2x

Step-by-step explanation:

Two points in that graph are (1,2) and (2,4). you have to do rise over run so 4-2 over 2-1 and the answer is 2/1 or just two.

Based only on the information given in the diagram, it is guaranteed that
AEFG AHJK
K
F
16
E
3
G
00
H
A. True
B. False

Answers

False Also show us the diagram for us to know

The statement that the two triangles are similar based on the given figure is false.

What are Similar Triangles?

Two triangles are said to be similar if the triangles are of the same shape but different size. The angles of the triangle will be equal and the sides are proportional.

So, we know that two similar triangles will have all the corresponding angles equal to each other.

Given two triangles EFG and HJK.

Also, given that,

EG = 8 and HK = 16

EG/ HK = 8/16 = 1/2

∠E = ∠H = 90°

There are no other information given.

If one more corresponding angles are equal, we can use ASA, AAS or AA property, and if one more corresponding side are proportional, we can use SAS postulate.

In this case, we cannot say two triangles are similar.

Hence the statement is false.

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4. Charles claims that he can distinguish between beer and ale 75 percent of the time. Ruth bets that he cannot and, in fact, just guesses. To settle this, a bet is made: Charles is to be given ten small glasses, each having been filled with beer or ale, chosen by tossing a fair coin. He wins the bet if he gets seven or more correct. Find the probability that Charles wins if he has the ability that he claims. Find the probability that Ruth wins if Charles is guessing.

Answers

Answer: Probability that Charles gets 7 or more correctly = 0.776

Probability that Ruth wins = 0.827

Step-by-step explanation:

Given data:

Probability that Charles distinguishes between beer and ale = 0.75

no of glasses = 10

no required to win the bet = 7 or more.

Solution:

a) probability of success p=0.75.

This is a binomial probability problem, what we need to solve for is the probability that ( X >=7 ) this can be gotten as

P(X>=7) = (10Ck) (0.75)^k (1-0.75)^(10-k)

where k=7,8,9,10

Probability that he gets 7 correctly.

P(X>=7) = (10Ck) (0.75)^k (1-0.75)^(10-k)

Substitute k = 7 into the equation

= 0.250

Probability that he gets 8 correctly.

P(X>=7) = (10Ck) (0.75)^k (1-0.75)^(10-k)

substitute k = 8 into the equation

= 0.282

Probability that he gets 9 correctly.

P(X>=7) = (10Ck) (0.75)^k (1-0.75)^(10-k)

Substitute k = 9 into the equation

= 0.188

Probability that he gets 10 correctly.

P(X>=7) = (10Ck) (0.75)^k (1-0.75)^(10-k)

Substitute the k= 10 into the equation.

= 0.0563

Probability that Charles gets 7 or more correctly

= 0.250 + 0.282 + 0.0563 + 0.188

= 0.776

b) Probability that Ruth wins

K = 1,2,3,4,5,6

p=0.5

P(X < 7)

P(X < 7) = (10Ck) (.5)^k (1-.5)^(10-k)

Probability that he gets one correctly

P(X = 1 ) = (10Ck) (.5)^k (1-.5)^(10-k)

substitute k= 1 into the equation.

= 0.0098

P(X=2) = (10Ck) (.5)^k (1-.5)^(10-k)

Substitute k= 2 into the equation

= 0.0439

P(X =3) = (10Ck) (.5)^k (1-.5)^(10-k)

Substitute k=3 into the equation.

=0.117

P(X=4) = (10Ck) (.5)^k (1-.5)^(10-k)

Substitute k= 4 into the equation

= 0.2051

P(X=5) = (10Ck) (.5)^k (1-.5)^(10-k)

Substitute k =5 into the equation

= 0.246

P(X= 6 ) = (10Ck) (.5)^k (1-.5)^(10-k)

Substitute k = 6 into the equation

= 0.205

Probability that Ruth wins

= 0.205 + 0.246 + 0.2051 + 0.117 + 0.0439 + 0.0098

= 0.827

ANSWER NEEDED ASAP PLS HELP show your work and give me the answer pleae

Answers

1. 5
2. 2
3. 1,000
4. -6
5. -12
6. 1
7. -5
8. -11
9. 13
10. 6

What is the answer and plz give me step by step explaining

Answers

Answer:

7

Step-by-step explanation:54x=60x-42, -6x=-42, divide both sides by six then you get 7

In the parallelogram below,
z = [ ? ]°

Answers

Z is equal to 124 degrees

if the point (6,3) lies on the graph of a direct variation, what is the constant of variation?

Answers

Answer:

[tex]k = 0.5[/tex]

Step-by-step explanation:

Given

[tex](x,y) = (6,3)[/tex]

Required

Determine the constant of variation

Since it is a direct variation, the following relationship exists:

[tex]y = kx[/tex]

Where k represents the constant.

Substitute 6 for x and 3 for y

[tex]3 = k * 6[/tex]

[tex]3 = 6k[/tex]

Make k the subject

[tex]k = \frac{3}{6}[/tex]

[tex]k = 0.5[/tex]

Hence, the constant of variation is 0.5

Garfield always catches 40% of the total flies that he sees on Monday Garfield saw 60 Total

flies how many flies did he catch

Answers

Answer:

24

Step-by-step explanation:

since 40% of 60 is 24 then the answer is 24 because garfield catches 40% of 60 of the files he sees

PLEASE HELP!!! (20 POINTS)

Is it true that [20+(−1)0]0=1? Explain.
A.No, because the negative sign will cancel the values, resulting in zero.
B.Yes, because the negative sign will cancel the values, resulting in one.
C.No, because any number raised to the zero power is zero.
D.Yes, because any number, except zero, raised to the zero power is one.

Answers

It’s either b or d give me a moment to get the positive answer

write a function for the table
please help I don't get it ​

Answers

Answer:

y = 2x - 5

Step-by-step explanation:

Let us consider the points (- 2, - 9) & (0, - 5)

Equation of line in two point form is given as:

[y-(-9)]/[-9-(-5)] = [x - (-2)]/[-2 - 0]

(y + 9)/(-9 +5) = (x + 2)/ (-2)

(y + 9)/(-4) = (x + 2)/(-2)

(y + 9)/(2) = (x + 2)/(1)

(y + 9) = 2(x + 2)

y + 9 = 2x + 4

y = 2x + 4 - 9

y = 2x - 5

This is the required function.

Which decimal has the greatest value ? 0.2 , 0.27 , 0.029 , 0.231

Answers

Answer:

0.27

Step-by-step explanation:

Greatest decimal value is 0.27

What is decimal value?

Decimals are based on the preceding powers of 10

Given decimal values are

0.2,0.27,0.029,0.231

Order the decimal numbers from low to high

0.029<0.2<0.231<0.27

Hence, the greatest decimal value is 0.27

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Helppp... last question on the test lol
(Will mark brainliest)

Answers

Answer:

A. Y=1.4x

Step-by-step explanation:

HELP URGENT !!!!!!!!!!!!!!

Answers

Answer:

D

Step-by-step explanation:

Solve the equation for x. 25x = 275

x =​

Answers

Answer:

x = 11

Step-by-step explanation:

So the equation is  25x = 275. In order for us to find out what x is we need to get rid of 25 that is next to x, so we are going to have to divide 25x by 25. What you do to one side you do to the other so the equation will look like this:

25x/ 25 = 275/ 25

25x/25 = x

275/25 = 11

so x = 11

Urgently need this my kid is confused and so am I.

The length, x, of a rectangle is five more than the width, y, and the perimeter of the rectangle is 42 meters. If y = x – 5 is one equation used to solve the system of equations, select the other equation that can be used to solve the for the length and width of the rectangle. What are the values of the length and width?

Answers

Answer:

The other equation is [tex]x + y = 21[/tex]

The length and width are 13 and 8

Step-by-step explanation:

Given

[tex]Perimeter = 42[/tex]

[tex]y = x - 5[/tex]

Required

What is the other equation for the length and width?

x and y represents the length and width respectively.

The perimeter of a rectangle is calculated using:

[tex]Perimeter = 2 * (length + width)[/tex]

In this case, it is:

[tex]Perimeter = 2 * (x + y)[/tex]

Substitute 42 for perimeter

[tex]42 = 2 * (x + y)[/tex]

Divide through by 2

[tex]21 = x + y[/tex]

[tex]x + y = 21[/tex]

Required: The values of length and width

We have that:

[tex]y = x - 5[/tex]

[tex]x + y = 21[/tex]

Substitute x - 5 for y in the second equation

[tex]x + x - 5 = 21[/tex]

[tex]2x - 5 = 21[/tex]

Add 5 to both sides

[tex]2x - 5 + 5 = 21 + 5[/tex]

[tex]2x = 26[/tex]

Divide through by 2

[tex]x = 13[/tex]

Substitute 13 for x in [tex]y = x - 5[/tex]

[tex]y = 13 - 5[/tex]

[tex]y = 8[/tex]

Hence, the length and width are 13 and 8 respectively

What are the answers pls?

Answers

Answer:

B)

Step-by-step explanation:

I believe the answer is B).

Hope this helps! Do you give brainlliest?

Find the slope and y-intercept of the line in each graph. (Explore Activity 1) Please help me

Answers

Answer:

1. Slope = -2 , y-intercept = 1

2. Slope = 5 , y-intercept = -15

3. Slope = 1.5 , y-intercept = -2

4. Slope = -3 , y-intercept = 9

Step-by-step explanation:

1. The slope is -2 because using the formula y₁-y₂÷x₁-x₂ you can use the points given to you to get -2. It doesn't matter which one you pick as y1 or y2, just make sure you keep it consistent with the x numberings. I did 1--3 (which becomes 1+3) and 0-2. Those equal 4/-2 which gives you -2. Use these same steps for all of them, but with ones that don't have the points given, just pick two that are whole numbers and not decimals. For finding the y-intercept, just find the point that is on the y axis line. It is given on number one as (0,1). So, the y-intercept is 1. Hope this helps!

If the equation 5(3x + 7) – 1 = 3(52 + k) + 4 has infinitely many solutions, what is the value of k?

Answers

Answer:

k = 5x - 42

Step-by-step explanation:

Ellen already knew 50 appetizer recipes before starting culinary school, and she will learn 4 new appetizer recipes during each week of school. After 73 weeks of culinary school, how many total appetizer recipes will Ellen know? Write and solve an equation to find the answer.

Answers

Answer:

342

Step-by-step explanation:

50+4x=y

x=73

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