You and two friends want to meet up at a location equally distant from each of your homes. One of your friends lives 4 miles north of your home and the other lives 4 miles east. Determine the best place to meet such that you each travel the same distance to that point. A third friend will ride her bicycle to your meeting point from her home 4 miles northwest of your home. Assume that you and your first two friends walk at 4 miles per hour, what speed should the third friend ride to meet the group? Fully explain your answer in essay format to show your work.

Answers

Answer 1

Answer:

The answer is 4√3 MPH. Here's why:

(I refer to North friend as Bob, West friend as Joe, and Northeast friend as Kelly. I also refer to locations as 'points'.  

Another note, just to clarify: To divide 2 radicals (Ex: 6√4 / 2√2), you need to divide the numbers outside the radical symbol by each other, and then divide the numbers inside the radical symbol by each other.  

(6√4 / 2√2 would equal 3√2, because 6 divided by 2 is 3, and 4 divided by 2 is 2.  

1. Ignoring Kelly, for now, we need to find a point that is of equal distance away from the other two friends. We can do this by drawing a square, using the 3 points, with side lengths of 4, since we know that they live 4 miles apart. The middle of this square is the place they have to meet since it is of equal distance from each point

2.  Now we need to find the distance from Bob to Joe, (aka the slope). Pythagorean's Therom says that for a right triangle, (height)²+(base)²=(hypotenuse)². Therefore, (4)²+(4)²=(x)², where x is the hypotenuse. This can be simplified to 32=x². Therefore, the slope is √32. When we simplify the radical, it becomes 4√2. However now, we need to divide this by 2, because each friend is only going halfway across the slope. This means that each friend will travel 2√2 miles.  

3. We know the Time(T)=Distance(D)/Speed(S). Therefore, the time for each friend to reach the location will be 2√2/4. The speed is 4 because the friends go 4 MPH. This information will come into play later on.  

4. Now we need to find out the MPH Kelly should go to reach that same point as the rest of her friends. First, however, we need to find the distance from her point to the meeting point. We can use Pythagorean's Therom again because the meeting point, my point, and Kelly's point all form a right triangle. Again, (height)²+ (base)²= (hypotenuse)². Therefore, (4)²+(2√2)²=y², where y is the distance from Kelly to the meeting point. This simplifies to (16) + (8) = (y²).  16+8=24, therefore y is √24 miles. We can simplify this to 2√6. Now we know that the distance from Kelly to the center point is 2√6 miles, we can find the speed.  

5. As already stated, T=D/S. In order for all friends to meet at the same time,  the amount of time it takes for Group 1 to reach the center point must be equivalent to Kelly's.  

We learned earlier that 2√2/ 4= T. This means that 2√2 / 4 = 2√6 / z. This is because 2√6 was the distance Kelly lived away from the center point, and we know that since the time will be the same, the fractions will be the same.  

6. Now we can cross simplify: (4)(2√6)=(2√2)(z). This reduces to              (8√6)=(2√2)(z). When we divide each side by 2√2, we get our answer, 4√3

Therefore, Kelly needs to ride 4√3 MPH on her bike in order to reach her friends at the same time. Hope this helps :)

Step-by-step explanation:

Answer 2

All 3 friends will meet at 2√2 miles away from my house in the North-East direction.

From, Pythagorean theorem:

(AC)² =  (AB)²+(BC)²

Where,

AC = Distance between first and second friend's home = ?

AB - Distance of first friend's home = 4 miles

BC -  Distance of second friend's home = 4 miles

Put the values in the formula,

[tex](AC)^2 = (4)^2+(4)^2\\\\AC= \sqrt {32}\\\\AC = 4 \sqrt{2}[/tex]

Since the midpoint of the hypotenuse is the point where all friends meet.

So,

[tex]x = \dfrac {4 \sqrt 2}{2} \\\\x = 2\sqrt 2[/tex]

Therefore, all 3 friends will meet at 2√2 miles away from my house in the North-East direction.

Learn more about the Pythagorean theorem:

https://brainly.com/question/22568405


Related Questions

QUICK !!! FAST 15 POINTS
I NEED HELP!!!!!

Answers

Answer:

ECB

Step-by-step explanation:

I noticed they looked exactly the same.

Answer:

It should be ΔABD, ΔECD, and ΔECD

Step-by-step explanation:

Since ΔABE is a right triangle, one angle must be 90° with a square to signify it.

solve for x
(21x-9)
27
x=​

Answers

Answer:

x = 6

Step-by-step explanation:

∠ AFB and ∠ EFC are vertically opposite angles and are congruent , then

21x - 9 = 117 ( add 9 to both sides )

21x = 126 ( divide both sides by 21 )

x = 6

The measured valued of x is 6.

What are Vertical Angle?

Vertical angles are generated by the junction of two straight lines that are not contiguous. Vertical angles are positioned across from each other in the corners of the "X" created by two straight lines.

We have,

<AFB = 21x- 9

and, <DFC = 27

Using Vertical Angle

<AFB = (<EFD + <DFC)

21x - 9=  (90 + 27)

21x - 9 = 117

21x = 117 + 9

21x = 126

x = 6

Learn more about vertical angle here:

https://brainly.com/question/24460838

#SPJ2

Expand. 4(5x + 3) 4(5x + 3)

Answers

Wwwwwwww

Hope this helps

If the dress is 90 dollars Nd it’s on sale Nd it’s 35%off how much is the dress

Answers

Answer:

it would be $58.50

Step-by-step explanation:

3/7 x 2/5 will be greater than or less than or equal to 3/7

Answers

Answer:

less than because of 2/5 being so small

ning Attempt 1 of 3 SECTION 3 OF 4 QU Use the rule y=-x+ 7 to fill in the blank. If (1, .y) is on the graph, then y=​

Answers

Answer:chili chuggen

Step-by-step explanation:

Which value of makes this equation true?

12 − 9 + = 12

Answers

Answer:

+9

Step-by-step explanation:

12-9+x=12

3+x=12

x=12-3

x=9

John took a taxi from his house to the airport. The taxi company charged a pick-up fee of $4.70 plus $2.50 per mile. The total fare was $24.70, not including the tip. How many miles was the taxi ride? ​

Answers

Answer:

8

Step-by-step explanation:

You can solve this by creating a linear equation.

Slope: 2.50

Y-intercept: 4.70

y=2.50x+4.70

Since we know that the total fare was 24.70 we can plug it into the y.

24.70=2.50x+4.70

Now solve for the equation.

20=2.50x

8=x

So he went 8 miles with the taxi.

Total number or mile taxi run is 8 miles.

Given that;

Pick up charge = $4.7

Charges per mile = $2.5 per mile

Total fare = $24.7

Find:

Number of mile taxi ride

Computation:

Total fare = Pick up charge + [Total number or mile taxi run][Charges per mile]

24.7 = 4.7 + [Total number or mile taxi run][2.5]

[Total number or mile taxi run][2.5] = 24.7 - 4.7

[Total number or mile taxi run][2.5] = 20

Total number or mile taxi run = 20 / 2.5

Total number or mile taxi run = 8 miles

Learn more:

https://brainly.com/question/3530056?referrer=searchResults

3x + 4x and 5x + 2x are equivalent expressions.
True or False

Answers

Answer:true

Step-by-step explanation:

True because 3+4 =7 5+2=7

A police helicopter descends 128 feet to
hover 468 feet above the ground. Let h
represent the original height of the
helicopter. Write and solve an equation to
represent this situation.

Answers

Answer:

h - d = 477 meters

Where:  h = original height

           d  = amount the helicopter descended

The original height of the helicopter is given to be h

Step-by-step explanation:

fill in the table below by finding the value of the function y = -2x + 3 at each of the inputs x = -1, x = 0, and x = 1.

Answers

Answer:

y=-2(-1)+3 y=5

y= -2(0)+3 y=3

y= -2(1)+3 y=1

would anyone mind helping me out! thanks​

Answers

Answer:

what grade are you if I nay ask so I can asisiy

60in what is the area​

Answers

Answer:

wdym 60 inches measures length (?????)

Answer:

Area = Side2

Step-by-step explanation:

genuinely don’t know how to do geometry.

Answers

Answer:

Im sorry for you this is too complex

The graph is
A. Neither even nor odd
B.odd
C.even
D. Symmetrical about the y axis

Answers

Answer:

Odd

Step-by-step explanation:

The function is odd because cubic functions are always odd.

Elise bought a dress that was discounted 35% off of
the original price of $140. What was
a: the amount of discount and
b : the sale price of the dress?

Answers

Answer:

a: $49

b: $91

Explaination:

a: 35% of 140 = 49

b: 140 - 49 = 91

You're welcome! <3

The amount of discount is $49 and  the sale price of the dress is $91 and this can be determined by using the unitary method.

Given :

Elise bought a dress that was discounted 35% off of  the original price of $140.

a) The unitary method can be used in order to determine the amount of discount. If the original price is $140 then the discounted price is given by:

[tex]=\dfrac{35}{100}\times 140[/tex]

Simplify the above expression.

= $49

b) The unitary method can be used in order to determine the sale price of the dress. If the original price is $140 then the selling price is given by:

[tex]=\dfrac{65}{100}\times 140[/tex]

Simplify the above expression.

= $91

For more information, refer to the link given below:

https://brainly.com/question/12116123

answer this pls
don't send me a link ​

Answers

Answer:

2-1

4-2

6-3

8-4

Step-by-step explanation: It is a pattern

Answer:

6 adults to 3 children

8 adults to 4 children

Step-by-step explanation:

it is a pattern

Find the volume of the cylinder in terms of pi

Answers

Answer:

It's B

Step-by-step explanation:

Answer:

115.52

Step-by-step explanation:

The formula for finding the volume of a cylinder is [tex]\pi r^{2} *h[/tex]

Since this is in terms of [tex]\pi[/tex], we dont need to solve for that part.

3.8 * 3.8 = 14.44, then 14.44 * 8 = 115.52

I suggest writing down that formula, It comes in handy.

3) A packet of
rice is 821 g. It is divided into a
equal portions. What is the mass of each portion?​

Answers

821 divid 2 equals 410 but your not saying how many portions it is equal to

The base area of a square-based prism is 25 ft squared. One of the lateral faces of the prism is 30 ft squared. What is the surface area of the prism?

Answers

Step-by-step explanation:

Given data

lateral surface area= 30ft

base area of squared prism = 25 ft means height= 25

(therefore, square object length breadth and height same )

total surface area = lateral surface * height

= 30ft*25ft

=750 ft square.

it may be help you . please mark me as brainlist

thanks.

What is 972 divided by 5? PLEASE HELP!! AND IF THERE IS A REMAINDER PLS TELL ME. Ty!

Answers

Answer:

194.4

Step-by-step explanation:

The remainder is 4

194 with a remainder of 4

Help me please thanks

Answers

Answer:

-5/9

Step-by-step explanation:

also for this one, you have to put x as 3, y as 4, and z as 1

4/3(3)-1

=4/9-1

=4/9-9/9

=-5/9

hope this helps xD

What is the length of the line?

Answers

Answer:

Im going to say 8

Step-by-step explanation:

Answer:

OK i know this is not exactly the answer but find out the area or how big the squares are the add it up and u got it i would be saying C but i dont know

Step-by-step explanation:

List and count all the outcomes for event E, in which the product of the two numbers rolled is odd.

Answers

there’s no attachment, i can try to help tho what does the problem look like
Where is the attachment

Explain WHY the function y = tan x is graphed like
this such that it does not for a continuous function

Answers

Answer:

Those asymptotes give you some structure from which you can fill in the missing points. Find the vertical asymptotes so you can find the domain.

Please help, will give brainliest!!!!

Find the values of angles A, B, and C in this diagram and explain their
relationships to each other.

Answers

Answer:

A=20, B=60, C=80

Step-by-step explanation:

Supplementary angles are those which add to 180 o. Complementary angles are those which add to 90°

find the particular solution to the exact differentiable equation dy/dx=(2e^x)-cosx passing through the point (0,3)

Answers

Answer:

y = 2eˣ - sin x + 1  

Step-by-step explanation:

dy/dx = 2eˣ - cos x

(0, 3)

Integrate dy/dx to find the original function.

y = 2eˣ - sin x + C

Solve for C by substituting the point given.

3 = 2e⁰ - sin(0) + C 3 = 2 - 0 + C 1 = C

Now we can substitute C into the original function.

y = 2eˣ - sin x + 1  

This is the particular, or explicit, solution to the differentiable equation.

simplify (a2+5)(a+3)​

Answers

Answer:

[tex]a^{3}[/tex] + [tex]3a^{2}[/tex] + 5a + 15

Step-by-step explanation:

The L shape is reflected in the y axis. Which one of the following shows the correct image

Answers

Answer:

B

Step-by-step explanation:

The image gets flipped across the y-axis.

It might help if you think about it like flipping a piece of paper cut into that shape horizontally.

also (x, y) -> (-x, y)

Answer:

B

Step-by-step explanation:

Help fast help fast help fast help fast

Answers

Answer: T(x) = 18x + 65

Step-by-step explanation:

T(x) = A(x) + B(x)

T(x) = 10x + 50 + 8x + 15             [Plug in the number for A(x) and B(x)]

T(x) = 10x + 8x+ 50 + 15

T(x) = 18x + 65

Other Questions
What can be changed when a style is modified?tablesspellingtext contentfontanswer fast! Cost of Spoiled Units Lieu Company is a specialty print shop. Usually, printing jobs are priced at standard cost plus 50 percent. Job 631 involved printing 400 wedding invitations with the following standard costs: Direct materials $220 Direct labor 80 Overhead 80 Total $380 Normally, the invitations would be taken from the machine, the top one inspected for correct wording, spelling, and quality of print, and all of the invitations wrapped in plastic and stored on shelves designated for completed jobs. In this case, however, the technician decided to go to lunch before inspecting and wrapping the job. He stacked the unwrapped invitations beside the printing press and left. One hour later, he returned and found the invitations had fallen on the floor and been stepped on. It turned out that about 50 invitations were ruined and had to be discarded. An additional 50 invitations were then printed to complete the job. Required: 1. Calculate the cost of the spoiled invitations. If required, round your answer to the nearest cent. $fill in the blank 1 2. What is the price of Job 631 Use the volume formula to find the volume of the prism. (look at the pic for the options) Jasmine made a scale drawing of an office. The scale of the drawing was 4 inches: 3 feet. The desk is 8 inches long in the drawing. How long is the actual desk? How did the Aboriginal people travel over to Australia from Asia At 5:00 a.m., the temperature outside was 6F below zero. By 12:00p.m., it rose by 9F. At 7:00 p.m., the temperaturedropped by 5F. What was the evening temperature?A. -20FB. 8FC. 20FD. -2F Someone please explain how to do this!! I was doing my homework when I come across this question, it says "substitute each given value of the variable to find which, if any, is a solution of the inequality." what does this mean? 2x - y + 4z + 11. how many terms are there in the algebraic expression?2. what is the coefficient of y?3. what are the variables in the algebraic expression?4. what os the constant? According to Goldratt: Two activities scheduled to be carried out sequentially and using the same scarce resource benefit from having the same project manager. Two activities scheduled to be carried out in parallel and using the same scarce resource are independent. Two activities scheduled to be carried out in parallel and using the same scarce resource are not independent. Two activities scheduled to be carried out sequentially and using the same scarce resource require different project managers. What is Hamilton finally able to do in "My Shot?" Classification is done by asking a series of yes or no questions. This questioning method iscalled a dichotomous key. Each question is about physical structures and is based onwhatever it is that divides members of that kingdom, phylum, class, order, family orgenus. Questions might include: Does it bear its young live or lay an egg? Does it have gillsor lungs? Does it have hair, fur, scales or feathers? The dichotomous key helps us to classifyorganisms in an organized manner."Dear King Phillip Come Over For Good Soup" is a mnemonic device that can help youremember the order and names of the different levels of classification. The first letter ofeach word is the same as the first letter for the different levels of classification-Domain,Kingdom, Phylum, Class, Order, Family, Species.The dichotomous keyAhelps classify organisms through yes or no questions.Bunlocks the names of different organisms in a family.groups animals that lay eggs with animals that have live births.asks multiple questions about how organisms behave and act. Which statement best describes behavioral adaptations? anyone know how to do this PLEASE....pic below 20pts.. What effect will increasing numbers of high-profile green building projects likely have on thinking about building?More thought will be given to the total impact of a construction project.Thinking about building will focus more on the specific needs of any given project.Thinking will become more collaborative and team based.Thinking about building will center on location and maximizing local labor sources. The ideas Roosevelt articulated in this excerpt led to which foreign policy initiative? plzz help me to do this please for all fnaf fans (five night at Freddy's) name all of the Afton family and their roles. worth 10 points the monthly income of B is twice the monthly income of A and the income of C is twice the monthly income of B. if there total income is Rs 12600. find the monthly income of each of them Christian influence in the Kingdom of Axum led to: A. the creation of illuminated manuscripts. O B. the increased demand for iron tools. O C. the growth of salt and gold trade routes. O D. the collapse of its trading empire.