A line passes through point A (14,21). A second point on the line has an x-value that is 125% of the x-value of point A and a y-value
that is 75% of the y-value of point A. Use point A to write an equation of the line in point-slope form.

?:(

Answers

Answer 1

Answer:

The equation of the line in point-slope form is [tex]y-21 = - \frac{3}{2}\cdot (x-14)[/tex].

Step-by-step explanation:

According to the statement, let [tex]A(x,y) = (14,21)[/tex] and [tex]B(x,y) = (1.25\cdot x_{A},0.75\cdot y_{A})[/tex]. The equation of the line in point-slope form is defined by the following formula:

[tex]y-y_{A} = m\cdot (x-x_{A})[/tex] (1)

Where:

[tex]x_{A}[/tex], [tex]y_{A}[/tex] - Coordinates of the point A, dimensionless.

[tex]m[/tex] - Slope, dimensionless.

[tex]x[/tex] - Independent variable, dimensionless.

[tex]y[/tex] - Dependent variable, dimensionless.

In addition, the slope of the line is defined by:

[tex]m = \frac{y_{B}-y_{A}}{x_{B}-x_{A}}[/tex] (2)

If we know that [tex]x_{A} = 14[/tex] and [tex]y_{A} = 21[/tex], then the equation of the line in point-slope form is:

[tex]x_{B} = 1.25\cdot (14)[/tex]

[tex]x_{B} = 17.5[/tex]

[tex]y_{B} = 0.75\cdot (21)[/tex]

[tex]y_{B} = 15.75[/tex]

From (2):

[tex]m = \frac{15.75-21}{17.5-14}[/tex]

[tex]m = -\frac{3}{2}[/tex]

By (1):

[tex]y-21 = - \frac{3}{2}\cdot (x-14)[/tex]

The equation of the line in point-slope form is [tex]y-21 = - \frac{3}{2}\cdot (x-14)[/tex].


Related Questions

The diagram below represents the shape of the floor of a hotel lobby. The hotel plans on replacing the carpet in the lobby
12
1
1 14 11

1
1
1121
13 ft
! 11 ft
31 tt
Part A: What is the total area of the hotel lobby floor?
ft?
Part B: If the new carpet costs $1.75 per square foot, how much with the hotel spend on new carpet?

Answers

Answer:.

Step-by-step explanation:

Write the first five terms in the arithmetic sequence. f(n + 1) = f(n) – 19, f(1) = 34

Answers

Answer:

34, 15, -4, -23 and -42

Step-by-step explanation:

We are to find the first five sequence

when n = 1

f(2) = f(1) - 19

f(2) = 34 - 19

f(2) = 15

when n = 2

f(2+1) = f(2) - 19

f(3) = f(2) - 19

f(3) = 15 - 19

f(3) = -4

when n = 3

f(3+1) = f(3) - 19

f(4) = f(3) - 19

f(4) = -4 - 19

f(4) = -23

when n = 4

f(4+1) = f(4) - 19

f(5) = f(4) - 19

f(5) = -23 - 19

f(5) = -42

Hence the first five terms  in the arithmetic sequence are 34, 15, -4, -23 and -42

A hamster is running on a wheel. The diameter of the wheel is 6 inches. The hamster makes the wheel turn 10 times. How far did the hamster run?

Answers

Answer:

60 in or 5 FT

Step-by-step explanation:

6 x 10 = 60 in

:D

Why do parallel lines never cross?

Answers Are

Answers

Answer:

C. Because they have the same slopes and different y-intercepts

Step-by-step explanation:

Answer:

Your answer would be the 3rd one.

Because they have the same slopes and different y-intercepts.

I hope that this is the answer you were looking for!

Have a great day!

Two of your friends go bowling. One friend rents a pair of bowling shoes for $3 and bowls 3 games. The other friend brings his own bowling shoes, bowls 4 games and buys a soda for $0.50. Both friends spend the same amount of money. Show how you can write and solve an equation to find the cost of one game.

Answers

Answer: The cost of each game is $2.50

Step-by-step explanation:

Let's find the equations for each friend:

Friend 1:

Pays $3 for the shoes, and plays 3 games, then if X is the cost of each game, Friend 1 pays a total of:

$3 + 3*X

Friend 2:

This friend buys a soda for $0.50, and he plays 4 games, remember that the cost of each game was X. then this friend pays:

$0.50 + 4*X

And we know that both friends pay the exact same amount, then we can write:

$3 + 3*X = $0.50 + 4*X

And solve this for X.

We need to isolate X, then we can move all the terms with X to the right, and all the terms without X to the left:

$3 - $0.50 = 4*X - 3*X

$2.50 = (4 - 3)*X = X

This means the cost of each game is $2.50

Plz help The population of a specific species of a nocturnal mammal is decreasing at a rate of 3.5%/year. The graph models the number of mammals x years after they were originally counted

How many mammals were there when they were originally counted?

Enter your answer in the box​

Answers

Answer:

The y-intercept represents the number of mammals when they were originally counted.

The y-intercept.is 75.

The asymptote indicates that the number of mammals counted when the study began was 120.

The asymptote indicates that as years pass, the number of mammals will approach 0.

Step-by-step explanation:

im a lil late but here ya go and for anyone further who needs these answers.. Its kind of obvious thugh just by looking at the graph what the answers are.

6. Which graph best represents the solution set of y>3 x-4?

Answers

pictures of the graph ? it should look like this (mark brainliest if correct pls)

The required graph of the solution to the given inequality y>3 x-4 has shown.

What is inequality?

Inequality can be defined as the relation of the equation containing the symbol of ( ≤, ≥, <, >) instead of the equal sign in an equation.

Here,
Given inequality,
y > 3x-4

Illustrating the above inequality on the coordinate plane, the yellow shaded region shows the solution of the given inequality y > 3x-4.

Thus, the required graph of the solution to the given inequality y>3 x-4 has shown.

Learn more about inequality here:

brainly.com/question/14098842

#SPJ6

the dimensions in a rectangle are in the ratio 3:7. if the width is 18 cm, what is the length?

Answers

Answer:

42cm

Step-by-step explanation:

3:7

width:length

18cm width(7cm length/3cm width)=42cm length

What the factor equivalent to x2 + 11x + 24

Answers

Answer:

13x + 24 or 37

Step-by-step explanation:

one of those answers.

Hope this helps and GOOD LUCK :)

Please help me ASAP!!! and please explain it because I do not understand how to do this at all.

Answers

Answer:

The 3 one

Step-by-step explanation:

So first you need to find all the angles.

Triangles all have a total degree of 180.

Then you can start doing trig. To find c I did (4sqrt3)cos60 that equals 3.464 which is 2sqrt3. Then I figured out a by doing the same thing but with sine. (4sqrt3)sin60 and that equals 6. Then I moved to the other triangle. I figured out d next. 6tan45° and that equals 6. Then I did b by doing 6/cos45 and I got 6sqrt2

Mikah and Gracie were running laps at the local gym. Mikah ran 1 and 4/8 laps, and Gracie ran 1 and 1/2 laps. Who ran a further distance?

Answers

Answer:

Trick question they both ran equal distance

Step-by-step explanation:

Gracies distand 1 and 1/2 is already in simplist form, but Mikahs distance 1 and 4/8 can be reduced.

More specifically the fration 4/8 can be reduced, finding the largest common multiple between 4 and 8 we find that 4 is the largest number that goes into both.

This results in the simplification of 1 and 4/8 to 1 and 1/2 which is the same as Gracies distance.

2x + 3 = x -4
what is the answer ​

Answers

Answer:

Step 1: Subtract x from both sides.

2x+3−x=x−4−x

x+3=−4

Step 2: Subtract 3 from both sides.

x+3−3=−4−3

x=−7

Answer:

x=−7

Please answer correctly !!!!!!!!!!!! What is the triangle ?!!!!!! Will mark Brianliest !!!!!!!!!!!!!!

Answers

Isosceles Right

Isosceles, since the two side lengths are equal, and it is a right triangle since it has a 90 degree angle and two other 45 degree angles.

Answer:

Isosceles Right

Step-by-step explanation:

Calculate the total cost for each item.
6. A computer for $450.00 and a 6% sales tax. _____________________________________
7. A pair of pants for $75.00 and a 5% sales tax. ___________________________________

Answers

Answer:

1. 423     2. 71.25

Step-by-step explanation:

450.00-6%=423

75.00-5%= 71.25

The measures of the angles of a triangle are shown in the figure below. Solve
for x.

Answers

Answer:

[tex]x = 46[/tex]

Step-by-step explanation:

Given

The three angles in the triangle are: x, 34 and 100

Required

Determine the value of x

Angles in a triangle add up to 180.

So, we have:

[tex]x + 34 + 100 = 180[/tex]

[tex]x + 134 = 180[/tex]

Subtract 134 from both sides

[tex]x + 134 - 134 = 180 - 134[/tex]

[tex]x = 180 - 134[/tex]

[tex]x = 46[/tex]

Hence, the measure of x is 46

How can you write the equation for a linear function if you know only two ordered pairs for the function?
Drag tiles to complete the explanation. Tiles may be used once, more than once, or not at all.

Answers

Answer: m

one set of ordered pair

b

(In that order)

Step-by-step explanation: Took the test just now, your welcome.

Calculate the sales tax for each item.
1. A sweater for $19.99 and a 6% sales tax. _______________________________________
2. A purse for $45.00 and a 5% sales tax.___________________________________________
3. A bicycle for $120.00 and a 7% sales tax.________________________________________
4. A TV for $3000.00 and a 4% sales tax.___________________________________________
5. A radio for $35.00 and a 6% sales tax.____________________________________________

Answers

Answer:

$19.99 + $1.19 tax = $21.18$45.00 + $2.25 tax = $45.25$120.00 + $8.40 tax = $128.40$3,000.00 +$120.00 tax = $3,120.00$ 35.00 + $2.10 tax = $37.10

1. The sales tax of a sweater = $1.2

2. The sales tax of a purse = $2.25

3. The sales tax of a bicycle =  $8.4

4. The sales tax of a TV = $120

5. The sales tax of a radio = $2.1

What is a percentage?

A ratio or value that may be stated as a fraction of 100 is called a percentage. Moreover, it is indicated by the symbol "%."

Given:

1. A sweater for $19.99 and a 6% sales tax.

The sales tax of a sweater = 19.99 x 0.06 = $1.2

2. A purse for $45.00 and a 5% sales tax.

The sales tax of a purse = 45 x 0.05 = $2.25

3. A bicycle for $120.00 and a 7% sales tax.

The sales tax of a bicycle = 120 x 0.07 = $8.4

4. A TV for $3000.00 and a 4% sales tax.

The sales tax of a TV = 3000 x 0.04 = $120

5. A radio for $35.00 and a 6% sales tax.

The sales tax of a radio = 35 x 0.06 = $2.1

Therefore, all the required sales tax is given above.

To learn more about the percentage;

https://brainly.com/question/24159063

#SPJ2

I NEED HELP ASAP IT IS FOR CHRISTMAS!!!!!!THESE ARE ALL MY POINTS!!
If three kids that want to buy something that cost $35.99 how much would each of them have to pay? Any ideas for what i should get my mom and dad?!!!! please help

Answers

Answer:

They should pay $12 each

Answer:

about 12 dollars probably more with tax maybe around 12.03

There are 15 female performers in a dance recital. The ratio of men to women is 4:5. How many men are in the dance recital?

Answers

Answer:

12 Men

Step-by-step explanation:

Since the ratio is 4:5 (men:women) 15/5 = 3, so you use 3 as your multiplier and write 3 x 4 = 12 :D

A scuba diver is 20 feet below the surface of the water 14 seconds after he entered the water and 100 feet below the surface after 30 seconds.  What is the scuba divers rate of change?

Answers

Answer:

1 foot = 0.7 secs

Step-by-step explanation:

14 seconds divided by 20 feet = 0.7 seconds per foot descended.

Hope this helps and good luck :)

Please answer correctly !!!!!!!!!!!!!! Will mark Brianliest !!!!!!!!!!!!!!

Answers

Answer:

The third side is 36 units.

Step-by-step explanation:

Given that this is a 90° triangle so you can apply Pythagoras Theorem :

[tex] {a}^{2} + {b}^{2} = {c}^{2} [/tex]

[tex] {a}^{2} = {c}^{2} - {b}^{2} [/tex]

[tex] {a}^{2} = {( \sqrt{90}) }^{2} - {6}^{2} [/tex]

[tex] {a}^{2} = 90 - 36[/tex]

[tex] {a}^{2} = 54[/tex]

[tex]a = \sqrt{54} = \sqrt{9 \times 6} = 3 \sqrt{6} [/tex]

just use theorem pythagoras

Look at points C and D on the graph. What is the distance (in units) between points C and D? Round your answer to the nearest hundredth. I REALLY NEED IT FAST

Answers

Answer:

The distance between points C and D is 5.83

Step-by-step explanation:

We need to find distance between points C and D

Looking at the graph we can find coordinates (x,y) of points C and D

Coordinates of point C are: (-4,3)

Coordinates of point D are: (1,0)

The formula used to calculate Distance is:

[tex]Distance=\sqrt{(x_2-x_1)^+(y_2-y_1)^2}[/tex]

Putting values and finding distance between points C and D

[tex]x_1=-4, y_1=3, x_2=1, y_2=0[/tex]

[tex]Distance=\sqrt{(x_2-x_1)^+(y_2-y_1)^2}\\Distance=\sqrt{(1-(-4))^2+(0-3)^2} \\Distance=\sqrt{(1+4)^2+(-3)^2} \\Distance=\sqrt{(5)^2+(-3)^2} \\Distance=\sqrt{25+9}\\Distance=\sqrt{34}\\ Distance=5.83[/tex]

So, the distance between points C and D is 5.83

What is the value of f(-1)?
O f(-1) = -3
Of(-1) = -1
O f(- 1) = 0
Of(-1) = 6

Answers

Answer: C: f(-1)=0

Step-by-step explanation:

To find f(-1), we look for the value under f(x) that corresponds to x=-1. This value is 0.

The length and width of the rectangle is 60 and 40. If the scale factor is ¼, what are the new measurements?

Answers

Answer:

15 and 10

Step-by-step explanation:

I hope this helps :)

Logan multiplied 54,216 by a number less than 1. He thinks the product will be greater than 54,216. Explain why he is incorrect.

Answers

He is incorrect because anything mutipled by 0 is 0!

Find the inverse function of f(x)=−32x+4
(Hint: f(x) is the same thing as y. Swap your x and y then get in slope-intercept form (y= form))

f−1(x)=____x+____=____

Answers

The answer equals 24

a scientist is studying the growth of bacteria the bacteria double every 20 min if there are 5 bacteria at the beginning how many bacteria will be there in 2 hours?

Answers

Answer:

15,625

Step-by-step explanation:

2h=120m

120/20 = 6

5^6 = 15,625

There are three times as many girls as boys in a school .Find an expression in term of x for the total number of student in school ,where x represent the number of boys in the school

Answers

Answer:

Total number of students = 4x

Step-by-step explanation:

Let the number of boys be x

Since, no of girls = 3 times the no of boys

So, number of girls = 3x

Total number of students = no of boys + no of girls

Total number of students = x + 3x

Total number of students = 4x

Answer:

The total number of students is 4x

Step-by-step explanation:

Hope this helped have an amazing day!

please help!! I'm going to fail!! ​

Answers

B ( the second one)

Answer:

3rd one

Step-by-step explanation:

look t the form x equals up to a diviser

What is the simplified form of 15 x to the eighth power over 24 y to the fifth power divided by 4 x to the fourth power over 8 squared ? (6 points)

4 y cubed over 5 x to the fourth power
4 y to the fourth power over 5 x cubed
5 x to the fourth power over 4 y cubed
5 x cubed over 4 y to the fourth power

Answers

Answer:

5 x to the fourth power over 4 y cubed

Other Questions
Explain how asexual reproduction works. what organisms undergo asexual reproduction? Many shark species have experienced a great deal of decline in population sizes due to a variety of factors. In the Bahamas, sharks are plentiful, but still experience a decline as populations reach their carrying capacity. Which of the following factors does not affect the carrying capacity of all shark species? If anybody needs help, please let me know. I only do writing and English. Answer this so I can help you. Have a great day. plzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz What does gaslighting mean? help me please i'll give braneliest The first person to answer my questions wins a brainlist IF THERE RIGHT. alrightI speak without a mouth and hear without ears. I have no body, but I come alive with wind. What am I? This riddle relies on tricking you into thinking about ears and a mouth. You get a tiny hint about wind to encourage you to think broadly and avoid the literal. Why do people, animals, and all other organisms do cellular respiration?O To make food/glucose for themselves. As a byproduct they make the oxygen that we need.O To make carbon dioxide and water that animals can use.O To make ATP (cell energy). Carbon dioxide and water are also produce as byproducts.To make oxygen, carbon dioxide, and glucose for themselves. thank yaal for answerin ;) The powers not delegated to the United States by the Constitution,nor prohibited by it to the States, are reserved to the Statesrespectively, or to the people.-Tenth Amendment, U.S. ConstitutionWhich principle of U.S. government is most clearly reflected in the amendmeabove? a 10 kilogram steel ball is dropped from the top of a tower 100 meters high the kinetic energy of the ball just before it sttikes the ground is most nearly What are the Vedas?A. regions ruled by a Vedic kingB. a group of female Hindu saintsC. a tribe native to North IndiaD. a collection of ancient Hindu scripturesE. the autobiography of a saint find the area of Rhombus if its diagonals measure 18 cm and 21 cm Finish the statement: Epic poems...a) tend to be about taking risks.b) tend to be about the American dream.c) tend to be about the common people.d )tend to be about big heroic rulers. 15 is what % of 60:( 3 fun facts about Japan f(x)=2x 5 13x 4 +22x 3 187x 2 160x+336 If you have done everything correctly, you might realize that stagflation creates a dilemma for the Fed. Why? Choose one or more: A. If the Fed wants to reduce unemployment, it must be willing to accept more inflation. B. If the Fed wants to reduce inflation, it must be willing to accept higher unemployment. C. If the Fed wants to reduce unemployment, it must be willing to accept less inflation. D. If the Fed wants to reduce inflation, it must be willing to accept lower unemployment. A major arc will have a measure that is A. less than 180 B. equal to 180C. greater than 180 The mural of your school mascot is $4$ feet by $12$ feet and is to be completely framed using a single row of square tiles each $2$ inches on an edge. If the tiles are $\$0.10$ each, find the cost, in dollars, of the tiles needed to frame the mural.