The distance between two points is √39 One endpoint is (4,−3). It is known that the y-coordinate of the other endpoint is 2.

What is the x-coordinate of this endpoint?

Answers

Answer 1

Answer:

[tex](4-\sqrt{14}, 2)\text{ or } (4+\sqrt{14}, 2)[/tex]

Step-by-step explanation:

We have the two points: (4, -3) and (x, 2).

We know that the distance between them is √39.

To find our x-coordinate of the second point, we can use the distance formula:

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

Let (4, -3) be (x₁, y₁) and let (x, 2) be (x₂, y₂). We also know that the distance d is √39. Substitute:

[tex]\sqrt{39}=\sqrt{(x-4)^2+(2-(-3))^2[/tex]

Solve for x. First, let's square both sides. This cancels out the square roots:

[tex]39=(x-4)^2+(2+3)^2[/tex]

Evaluate the second term on the right:

[tex]39=(x-4)^2+(5)^2[/tex]

Square:

[tex]39=(x-4)^2+25[/tex]

Subtract 25 from both sides:

[tex]14=(x-4)^2[/tex]

Take the square root of both sides. Since we're taking an even root, we need plus/minus. So:

[tex]x-4=\pm\sqrt{14}[/tex]

Add 4 to both sides:

[tex]x=4\pm\sqrt{14}[/tex]

Therefore, there exists two possibilities for our second point. It can either be:

[tex](4-\sqrt{14}, 2)\text{ or } (4+\sqrt{14}, 2)[/tex]

And we're done!


Related Questions

A costume designer needs some silver and gold thread for the costumes for a school play. She needs a total of 240 yards. At a store that sells thread by the yard, silver thread costs $0.04 a yard and gold thread costs $0.07 a yard. The designer has $15 to spend on the thread.

How many of each color should she get if she is buying exactly what is needed and spending all of her budget?

Write an equation for the length constraint. Write an equation for the cost constraint. solution

Answers

Answer:

Where s represents silver and g represents gold,

Length constraint: s+g=240

Cost constraint: 0.04s+0.07g=15

s= 60

g=180

Step-by-step explanation:

The measurement of silver and gold threads in yards is given as 60 and 180 respectively.

What is a system of linear equations?

A system of linear equations is a group of  equations having same number of variables and degree.

For the n number of variables n number of equations are required.

On the basis of number of solutions a system of equations can be classified as consistent and inconsistent.

The given problem can be solved as follows,

Suppose the number of yards for silver threads be x and that of gold be y.

Then the equation for the total yard is given as,

x + y = 240                  (1)

And, the equation for the cost is,

0.04x + 0.07y = 15      (2)

The value of x from equation (1) is x = 240 - y.

Substitute the value of x in equation (2) to obtain,

0.04(240 - y) + 0.07y = 15  

=> 9.6 - 0.04y + 0.07y = 15

=> 0.03y = 15 - 9.6

=> 0.03y = 5.4

=> y = 180

Substitute the value of y in x = 240 - y to obtain,

x = 240 - 180 = 60

Hence, the costume designer should get  silver and gold thread of 60 yards and 180 yards respectively.

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Solve for :
8x - 3 = 5 (2x + 1)

Answers

Answer:

x = -4

Step-by-step explanation:

8x-3=5(2x+1)

8x-3=10x+5

-3=2x+5

-8=2x

-4=x

Simon began a weight-loss program. He loses weight every two weeks. His weight, in pounds, t months after he began the weight-loss program, is shown by the following expression.

210(0.94)2t

Which statement below best describes the base, 0.94?

A. Simon's weight before he beganm the weight-loss program

B.the rate which Simon loses weight

C. the monthly decrease in Simon's weight

D. the numbers of times Simon has lost weight since he began the weight-loss program

Answers

pretty sure b. not 100% sure.


$8000 is compounded semiannually at a rate of 7% for 20 years.

Answers

i calculated 31674.08 may i please get brainliest for my work

Here are recipes for two mixtures of salt and water that taste different. Mixture A: salt (teaspoons) water (cups) 4 5 7 8 3/4 9 11 1/4 Mixture B is defined by the equation y=2.5x , where x is the number of teaspoons of salt and y is the number of cups of water. Respond to the following questions: 1. If you used 10 cups of water, which mixture would use more salt? How much more? Explain or show your reasoning. 2. Which mixture tastes saltier? Explain how you know.

Answers

Answer:

1.) Mixture A will use more salt.

Mixture A will require 4 more spoons of salt than mixture B of 10 cups of water is used.

2.) Mixture A

Step-by-step explanation:

Given the daya:

MIXTURE A

___Salt A(teaspoons _____water (Cups)

___4 _____________5

___7 _____________8 3/4

___9 _____________ 11 1/4

Mixture B is defined by the equation'

y = 2.5x ;

x = number of teaspoons of salt ;

y = number of cups of water

Respond to the following questions:

1.) If you used 10 cups of water, which mixture would use more salt? How much more? Explain or show your reasoning.

For mixture B:

If number of cups of water, y = 10

y = 2.5x ; 10 = 2.5x

10/2.5 = x

x = 4 ; 4 teaspoons of salt

Let's write an equation in terms of y and x to represent mixture A.

Mixture A:

5 = k4

k = 5/4

k = 1.25

Equation for mixture A:

y = 1.25x

10 = 1.25x

10/1.25 = x

x = 8 ; 8 teaspoons of salt

Mixture A will use more salt.

Mixture A will require 4 more spoons of salt than mixture B of 10 cups of water is used.

2. Which mixture tastes saltier? Explain how you know.

Mixture A is saltier as it makes use of more teaspoons of salt for the same amount of water.

1. Mixture A will use 4 more teaspoon of salt

2. The mixture that makes use of more teaspoon of salt (4 teaspoon) for the same quantity of water (10 cups) will taste saltier, which is: Mixture A.

Recall:

A proportionate relation is defined by the formula: y = kxk is the constant of proportionality or unit rate between two variables.

From the information given:

x = quantity of salt (teaspoons)y = quantity of water (cups)

Therefore, k = y/x

Equation for mixture B is given as: y = 2.5x

Using a pair of values from the table for mixture A, let's find the constant of proportionality and the equation that defines Mixture A.

Using (4, 5):

k = y/4 = 5/4 = 1.25

Thus, substitute k = 1.25 into y = kx

Equation for Mixture A is: y = 1.25x

1. Let's find the mixture that will have more salt if y = 10 (cups of water).

Substitute y = 10 in each equation that defines each mixtures

Mixture A: y = 1.25x

10 = 1.25x

Divide both sides by 1.25

8 = x

x = 8

Amount of salt you will have in mixture A is you use 10 cups of water is 8 teaspoons

Mixture B: y = 2.5x

10 = 2.5x

Divide both sides by 2.5

4 = x

x = 4

Amount of salt you will have in mixture A is you use 10 cups of water is 4 teaspoons

Thus, Mixture A will use 4 more teaspoon of salt.

2. The mixture that makes use of more teaspoon of salt (4 teaspoon) for the same quantity of water (10 cups) will taste saltier, which is: Mixture A.

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Which is the correct chemical equation for photosynthesis?

Answers

Answer: The process of photosynthesis is commonly written as: 6CO2 + 6H2O → C6H12O6 + 6O2.

Step-by-step explanation: This means that the reactants, six carbon dioxide molecules and six water molecules, are converted by light energy captured by chlorophyll (implied by the arrow) into a sugar molecule and six oxygen molecules, the products.

What is the 8th term of the sequence 12, 17, 22, 27, 32,...​

Answers

Answer:

47

Step-by-step explanation:

just keep adding by 5

Please help answer this ?!

Answers

Answer:

i think you have the right answer

Step-by-step explanation:

good job!

Answer:

A

Step-by-step explanation:

Unless the shape is dialatedthe side lengths remain constant because you are just moving its position ,

Max ran 15 meters, this morning. this afternoon, he ran 48 meters how many more meters did he run this afternoon.

Answers

He ran 33 more meters. (48-15=33 meters)

Can someone please help me?

Answers

Answer:

232.05

Step-by-step explanation:

find out how much it started out with

so divide 46dollars and 50 cents by 3

then you'll have 15dollars and 5 cents

now you know thats how much earned at first you multiply by 15 and you get the answer above

good luck

A ketchup company regularly receives large shipments of tomatoes. For quality control purposes, they take a sample of tomatoes from each shipment. If the sample shows convincing evidence that more than 8\%8%8, percent of the tomatoes in the entire shipment are bruised, then the company will request a new shipment of tomatoes. So the company tests H0 : p = 0.08 versus Ha ​: p > 0.08H, where p is the proportion of tomatoes in the entire shipment that are bruised.
One day, a supervisor takes a random sample of 600 tomatoes from a shipment and finds that 53 of the tomatoes are bruised, which results in a test statistic of z ≈ 0.75. Assuming that the necessary conditions are met, what is the approximate P-value associated with the significance test for this shipment?

Answers

Answer:

The value is   [tex]p-value  =  0.22663[/tex]

Step-by-step explanation:

From the question we are told that

    The proportion of bruised tomatoes p =  0.08

    The  null hypothesis is  [tex]H_o  :   p =  0.08[/tex]

    The alternative hypothesis is  [tex]H_a  :  p >  0.08[/tex]

    The sample size is  n  =  600

    The number of bruised tomatoes from the sample selected is  k  =  53

    The test statistics is  z =0.75

Generally the p-value is mathematically represented as

      [tex]p-value  =  P(Z > z)[/tex]

=>    [tex]p-value  =  P(Z > 0.75)[/tex]

From the z-table  

    [tex]P(Z > 0.75) =  0.22663[/tex]

So  

    [tex]p-value  =  0.22663[/tex]

     

Answer:

P-value ≈ 0.2266

Step-by-step explanation:

find the midpoint (-6,-10) (-2,-8)

Answers

The Answer is (-4,-9)

If Coach Smith has 12 players and each player needs three uniforms, three shin guards, two balls, and three pairs of cleats. How much will he end up spending on his equipment for the entire soccer team?

Answers

you can't do that. there isn't enough detail. we don't know how much each item costs

A fruit salad recipe calls for 3/4 pound of apples and 2/5 pound of dates. What is the least common denominator of the fractions?
(1 Point)

Answers

Answer:

20

Step-by-step explanation:

because 4x5 equals 20

A pump fills an empty pool at a rate of 500 cubic meters per hour. If one liter is equivalent to one cubic decimeter and 1 meter is equal to 10 decimeters, how many liters of water are in the pool half an hour after the pump starts?

Answers

If a liter equals a cubic decimeter and a meter equals ten decimeters, then 250,000 liters of water is filled in the pool in half an hour.

What is meant by cubic decimeter?

1000 cubic centimeters make up one cubic decimeter. Repeating this procedure would allow us to translate between cubic centimeters and meters or between cubic decimeters and meters. We must keep in mind three conversions. 1000 cubic centimeters is equal to one cubic decimeter.

1 cubic meter = 1000 liters

because, 1 liter = 1 decimeter³

1 meter = 10 decimeters

1 decimeter= 0.1 meters

1 liter = 0.1³ meter³

1 m³ = 1000 liters

Given:

In 1 hour the amount of water filled = 500 cubic meters

In half an hour the amount of water filled = 250 cubic meters

= 250,000 liters.

Therefore, 250,000 liters of water exists filled in the pool in half an hour.

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just a quick question!!​

Answers

Answer:

The scale is by 4 becuase if you mutiply 4 by the numbers on the smaller triangle then you will get the numbers on the larger triangle.

Step-by-step explanation:

52x16 please add explaining to show me how to do it

Answers

Answer: 832

Step-by-step explanation:

Below is how I solved it

You do 2 times 6, then 2 times 10, then 6 times 50, then 50 times 10. Make a table!

2 x 6 = 12

2 x 10 = 20

6 x 50 = 300

50 x 10 = 500

500 + 300 + 20 + 12 = 832

52 x 16 = 832

Need help ASAP !!! I am failing MATH

Answers

Answer:

i think it is D

Step-by-step explanation:

HARRY I NEED HELP FAST 15POINTS

Which expressions are quadratic expressions? Check all that apply
z^2
2x + 7x - 10
2x^2 + 9x - 7
500(0,25)^t -1
13x^3 + 21x^2-5

Answers

Answer:

First,Third Only

Step-by-step explanation:

Quadratic expression are those expression where the variable has a degree of maximum 2 and only the first and third expression have the degree of 2 in the choices. 2nd choice is a linear expression because both the variables have degree 1. 4th choice has a degree of t which means its an exponential expression, and 5th choice has the degree 2 and 3 but the maximum degree is 3 so it isn't a quadratic is a cubic equation.

Standard form of a quadratic expression

[tex]ax^2+bx+c[/tex]

First and third! Hope this helps!

A family on vacation took a road trip to Florida. Use the table to determine whether an equation in the form y=ke can be written for the situation. Explain your answer.​

Answers

Answer:

No. Since the value of the ratio

is not the same for each pair of​ values, the relationship is not proportional.​ So, an equation cannot be written for the situation. its c

Step-by-step explanation:

Give the 10th term of the following sequence:
1, 4, 7. 10

Answers

Answer:

28

Step-by-step explanation:

Answer:

29

Step-by-step explanation:

Read the problem in the box below. Make a list to help you find the correct
answer.
Radio listeners were asked to call in and pick their
two favorite rodents. The listeners had 4 choices:
Woodchuck, Prairie dog, Beaver and Chipmunk.
Which of the following is the complete list of the
possible pairs of rodents?
A. WP, PW, WC, PB, PC, BP
0 0
B. WP, WB, WC, PB, PC, BW
C. WP WB, WC, PB, PC, BC
D. WP CB, WC, CP, PC, BC

Answers

Answer:

C. WP WB, WC, PB, PC, BC

Step-by-step explanation:

List the possible combinations. (With no duplicates)

WP, WB, WC

PB, PC

BC

Now check your options for the answer with the combinations you had.

That is your answer.

The distance (d) in meters that an ant can travel varies directly with the amount of time (t) in hours it spends walking. assume that an ants constant off proportionality is 18.write the equation to the represent the proportional relationship between d and t using the information given. What does the constant of proportionality represent in this problem?

Answers

The constant is 18

To find distance (d) you would multiply the constant by the time(t).

D = 18t

Distance is speed x time, so the given constant would be the speed of the ant.

Pls help i dont understand :( will give Brainliest + 25 Points

Answers

The answer I think is C

I WILL MARK BRAINLIST
A photograph is dilated to fit in a frame, so that its area after the dilation is 9 times greater
than the area of the original photograph. What is the scale factor of the dilation?
A photograph is dilated to fit in a frame, so that its area after the dilation is 9 times greater
than the area of the original photograph. What is the scale factor of the dilation?

Answers

Answer:

i think its 3

Step-by-step explanation:

PLEASE NEED HELP!!

ASAPPP

Answers

Answer:

Its the third option.

Step-by-step explanation:

No,  all points on the line are solutions of the equation.

Answer:

answer the last    yes because all the points meet

Step-by-step explanation:

Write 3.6 x 10^-3 in standard form.

Answers

Answer: 33

Step-by-step explanation: hope this helps

A liquid solution is slowly leaking from a container. The graph shows the milliliters of solution, y, remaining in the container after x minutes.



How many minutes will it take for the container to empty if the solution continues leaking at the same rate? Show your work or explain how you know.

Answers

Answer:

90 minutes

Step-by-step explanation:

See attachment for graph.

First, we need to determine the slope.

When y = 900, x = 0

When y = 600, x = 30

The slope is then calculated as:

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

m = (600 - 900)/(30 - 0)

m = -300/30

m = -10

Next, we determine the equation of the line using

y - y1 = m(x - x1)

So, we have:

y - 900 = -10(x - 0)

y - 900 = -10x

y = 900 - 10x

When the container is empty, y = 0.

So, we have:

0 = 900 - 10x

Collect Like Terms

10x = 900

Solve for x

x = 900/10

x = 90

im kinda dumb here ... need help again

Answers

Answer:

with what lol

Step-by-step explanation:

Answer:need me points

Step-by-step explanation:

Write the equation of a line through (5, -3) with a slope of
1/5 in standard form.​

Answers

Answer:

[tex]\frac{1}{5} x-4[/tex]

Step-by-step explanation:

I graphed it on desmos by inserting the point (5,-3) and [tex]\frac{1}{5} x[/tex] for the slope then translated [tex]\frac{1}{5} x[/tex] down 4 so it would go through the point

Answer:

y = 1/5x - 4

Step-by-step explanation:

y = mx + b

simply plug in the slope,

y = 1/5x + b

now put in the cooridinates for b,

-3 = 1/5 ( 5) + b

now solve for b,

-3 - 1 = b

-4 = b

now put -4 into the equation,

y = 1/5x - 4

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