Fran and Alex ride their bicycles from school. Fran rides 3 miles west and 2 miles south to get home. Alex rides 4 miles east and 3 miles north to get home. How many miles apart are Fran's and Alex's homes?

Answers

Answer 1

Answer:

The number of miles the homes of Fran's and Alex's homes are apart is approximately 8.602 miles

Step-by-step explanation:

The given displacements, d in vector form are;

For Fran;

3 miles west and 2 miles south gives d₁ = -3·i - 2·j

For Alex;

4 miles east and 3 miles north gives d₂ = 4·i + 3·j

The number of miles apart between Fran's and Alex's homes = d₂ - d₁

d₂ - d₁ = 4·i - (-3·i) + 3·j - (-2·j) = 7·i + 5·j

∴ The number of miles between Fran's and Alex's homes = 7·i + 5·j

The magnitude in miles in the distance between Fran's and Alex's homes = √(7² + 5²) = √74

∴ The magnitude in miles in the distance between Fran's and Alex's homes ≈ 8.602 miles

The magnitude in miles in the distance between Fran's and Alex's homes = The number of miles the homes of Fran's and Alex's homes are apart

∴ The number of miles the homes of Fran's and Alex's homes are apart ≈ 8.602 miles


Related Questions

If my current slope is 7 what is the perpendicular slope?
A- -7
B-7
C- -1/7
D- 1/7

Answers

The correct answer is: B-7

Answer

-7

Step-by-step explanation:

opposite of 7

How many packages of gum can you buy with $18 if one package cost $2?

Which equation best represents this word problem?

Group of answer choices

18 x 2 = p

p - 18 = 2

p + 2 = 18

2p = 18

Answers

Answer:

2p = 18

Step-by-step explanation:

A bowling alley charges $2.50 per game plus $4 to rent shoes. A second bowling alley charges $4 per game plus $1 to rent shoes. How many games would a
person have to play for the two bowling alleys to cost the same amount?

Answers

Answer:

The person would have to play 2 games for the two bowling alleys to cost the same amount

Step-by-step explanation:

Assume that the number of games that makes the two costs equal is x

∵ A bowling alley charges $2.50 per game plus $4 to rent shoes

∵ The number of games is x

The cost = 2.50x + 4

∵ A second bowling alley charges $4 per game plus $1 to rent shoes

∵ The number of games is x

The cost = 4x + 1

∵ They have the same cost

→ Equate the 2 expressions above

4x + 1 = 2.50x + 4

→ Subtract 2.50x from both sides

∵ 4x - 2.50x + 1 = 2.50x - 2.50x + 4

1.50x + 1 = 4

→ Subtract 1 from both sides

∵ 1.50x + 1 - 1 = 4 - 1

1.50x = 3

→ Divide both sides by 1.50

x = 2

The person would have to play 2 games for the two bowling alleys to

   cost the same amount

Question 1 of 10
Which of the following best describes the slope of the line below?

O A. Zero
O B. Positive
O C. Negative
O D. Undefined

Answers

Answer:

B

Step-by-step explanation:

Based on the housing data below, use linear regression to estimate a fair price for a 1900 ft2 home. Square Feet House Price (in thousands) 1400 1700 105 135 1500 183 O A. $140,000 B. $156,000 C. $160,000 D.- $176,000​

Answers

The solution is Option D.

The fair price of a 1900 ft² home is given by the equation A = $ 176,000

What is an Equation of a line?

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

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

Given data ,

Let the square feet of the house be represented as x

Let the number of houses be represented as y

Let the first point be P ( 1400 , 105)

Let the second point be Q ( 1500 , 183 )

Now , the slope of the equation is given by

Slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Slope m = ( 183 - 105 ) / 1500 - 1400

Slope m = 78 / 100

Slope m = 0.78

Now , the equation of line is y - y₁ = m ( x - x₁ )

Substituting the values in the equation , we get

y - 1400 = 0.78 ( x - 105 )

On simplifying the equation , we get

y - 1400 = 0.78x - 81.9

Adding 1400 on both sides of the equation , we get

y = 0.78x + 1318.1

Therefore , the value of y is 0.78x + 1318.1

Hence , the equation of line is 0.78x + 1318.1 and the price is $ 176,000

To learn more about equation of line click :

https://brainly.com/question/14861637

#SPJ2

Answer:

Step-by-step explanation:

b i think

ANSWER THIS IS FOR EXTRA CREDIT

Answers

Answer:

The answer is c

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

A top swimmer would be able to swim across a 25-meter pool in about 15 of a minute. How fast can a top swimmer go?

Answers

Answer:

1.66 or 1 and 2/3 fast

Step-by-step explanation:

Answer:

ಠ ,,ಠ

 ____

Step-by-step explanation:

because earth is round the amount of time it takes to eat a tortilla chip is honey bunches of oats.

please help it's the SLOPE

Answers

Answer:

3/2

Step-by-step explanation:

do rise over run

rise is 3

run is 2

3/2

hope this helps <3

Answer:

slope is 1.5

Step-by-step explanation:

slope=rise over run

3/2=1.5

look at point

(1,-3) then go up 3 and right 2

lands in point

(3,0)

I will will give brainliest to whoever answers correct
(Please I need this ASAP )

Answers

Answer:

1=3.5 2=10/3

Step-by-step explanation:

they pass each other at the point (3.5,3).

if you find the exact form for both equations you get 10/3 for both

rewrite as as whole number 40/5

Answers

Answer:

8

Step-by-step explanation:

Just do 40 divided by 5.

Joshua borrows $300 from his older sister to buy a bike. He promises to pay the total amount plus 5% simple interest in one year. How much will Joshua
pay back in all?

Answers

Answer:

315

Step-by-step explanation:

will give brainliest

Answers

Answer:

D

Step-by-step explanation:

Protect economic freedom, so that a strong central government couldn't stop them from doing what they wanted to earn money.

***I hope this answer's correct. Plz lmk!!!

Answer:

C I think because it makes most sence sorry if wrong answer

Step-by-step explanation:

( I think this would be a diferent subject just saying)

hope this helps

the length of a rectangle is 4 meters less than twice its width. The area of the rectangle is 70. Find the dimensions of the rectangle

Answers

Answer:  The width is 7 meters. The length is 10 meters.

Step-by-step explanation:   Area = Length × width

Length is 2w - 4  

Substitute that value for length, then solve for w.

70 = w(2w - 4)

70 = 2w² - 4w  reorganize to quadratic equation form

2w² - 4w -70 = 0   These are All even numbers; factor out 2 (divide all by 2)

w² - 2w - 35 = 0  factor this

(w - 7)(w + 5)    set each factor = 0 and calculate the value of w.

w+5=0  w= -5  (disregard this one because dimensions of real rectangles can't be negative)

w - 7 = 0  w = 7   The width is 7

Substitute into the original expressions to get the value of Length.

2(7) -4 = L    14 - 4 = L  The Length is 10.

Check by substituting into the original equation:

w × 2w -4 = 70

7 × 2(7) -4 = 70

7 × 10 = 70    TRUE!

w

Dimensions of the rectangle are length=10 meter and width= 7 meter

What is Rectangle?

A rectangle is a quadrilateral with four right angles.

Given,

The length of a rectangle is 4 meter less than twice its width

Consider,

l is the length of the rectangle

w is the width of the rectangle

l=2w-4

Area of the rectangle = Length × Width

70=l × w

Substitute the value of l is the second equation

70=(2w-4)×w

[tex]2w^{2} -4w=70\\2w^{2} -4w-70=0[/tex]

Take 2 outside

[tex]2(w^{2}-2w-35)=0\\ w^{2} -2w-35=0\\(w+5)(w-7)=0[/tex]

w=7,-5

Hence w wont be negative value

Therefore w=7 meter

Then,

l×w=70

[tex]l=\frac{70}{7}\\[/tex]

l=10 meter

Hence, the dimensions of the rectangle are length=10 meter and width= 7 meter

Learn more about rectangle here

https://brainly.com/question/16167300

#SPJ2

HELP!!!!!
A quadratic function passes through the points (0,5), (2,3), and (3,5). Which function represents the same relationship?

Answers

Answer:

h(x)=x^2-3x+5

Step-by-step explanation:

what is f=483,323+947,6584-84784

Answers

Answer:

9,875,123

Step-by-step explanation:

Please help, thanks for understanding

Answers

Answer:

-5 1/4

Step-by-step explanation:

the answer to the question is a

why does math have to be so hard

Answers

I felt this, I’m currently failing even tho I’m trying but that could also be because my teacher doesn’t like me

Answer:

Math seems difficult because it takes time and energy. Many people don't experience sufficient time to "get" math lessons, and they fall behind as the teacher moves on. Many move on to study more complex concepts with a shaky foundation. We often end up with a weak structure that is doomed to collapse at some point.

Math is hard because it is a non-intuitive, non-natural activity. Math don't happen by chance only, it only happens with deliberate, focused work. For this you expend a lot of energy and cause a lot of mental strain, you put yourself on an uncomfortable condition for hours, days, sometimes weeks to solve a problem.

But some people love math, like me, because they study math more than others. If you study more and learn more about math, then you’ll start to feel more comfortable because you’ll be ahead of the class when your teacher teaches you something.

The most important thing is to keep trying and never give up.

Hope this helps! :)

9. Which graph can be used to find the solution to the system of equations?
y = x-1
9y = 6x – 15

Answers

I used desmos and plotted the equations in. I would find which graphs cross one another at (-2,-3)

1) As you know, the area of a square is A = x , where for this problem, A is area in feet and x is the length of a side, in feet. If the length of a side is changing at a rate of 6 feet/minute when the length of a side is 4 feet, at what rate is the area changing?

Answers

The answer is 2 feet

Please help everyone trolling me​

Answers

Answer:

3

Step-by-step explanation:

6.) Find all zeros (real and complex) of the same function
f(x) = x4 – x3 - 5x2 - x - 6

Answers

Is this even a real question

Ellie and Jamie like to bake cookies. Ellie baked 24 chocolate chip cookies, and Jamie baked p peanut butter cookies. Together they baked a total of 56 cookies. Write an equation that can be solved for p to find the number of cookies Jamie baked?

Answers

p would equal total cookies minus the total chocolate chip cookies:

p = 56 -24

p = 32

There were 32 peanut butter cookies made.

will mark brainliest to whoever can answer

Answers

Answer:

A. 7

Step-by-step explanation:

h(x)=2x + 4

2(7)=14

14+4=18

I will make you brainliest if correct. please explain how you got it if you can

Answers

They are parallel and if you have more questions like this a good website to help you answer desmos graphing calculator

The Kellam Booster Club made $1,638 selling tickets to the football games this season. A child's ticket costs $3 and they sold 120 of them. An adult ticket costs $9. How many adult tickets did they sell?

Answers

Answer:

They sold 142 adult tickets.

Step-by-step explanation:

120x3=360

142x9=1278

1278+360=1638

Amanda planned to run 5 kilometers. Instead, she ran 170% of the planned distance,
1 kilometer - 1000 meters
How many meters did Amanda run?

Answers

Answer:

8500 meters

Step-by-step explanation:

5 100

   170

please help i’ll give brainliest please tysm :))

Answers

Answer:

7

Step-by-step explanation:

Multiply the first collum by 7. It's basically unit rates

Answer:

7

Step-by-step explanation:

let the left column be x

let the right column be y

x is being multiplied by 7

so the ratio would be 7x=y

Help asap please!! I will mark you as brainliest :)

Answers

Answer:

52

Step-by-step explanation:

bro imma be honest with you the way i figured this out doesnt even make sense so im not even gonna try and explain ths lol

The first choice is the right answer - 52
4 bags for two batches so for one batch it’s 2 bags and for 26 batches you multiply that by 2 so you get 52

Solve 3(x-4)=12x ......

Answers

Answer:

The answer is x= -4/3

Step-by-step explanation:

3(x-4)=12x

=3x-12=12x

=3x-3x-12=12x-3x

-12=9x

To find x divide both sides by 9.

-12÷9=9x÷9

-4/3=x

I will make you brainliest if correct. explain how you got it please

Answers

Answer:

Perpendicular

Step-by-step explanation:

Slope of l1=6\9 = 2\3

Slope of l2 =-3\2

perpendicular lines

Answer:

perpendicular

Step-by-step explanation:

l1 slope= 2/3

l2 slope= 3/2

Other Questions
Write the plurals of (notice some have definite articles and other indefinite):1. el lpiz2. el calendario3. una profesora4. una escuela5. el borrador6. un relojPLEASE HELP ASAP I GIVE YOU 100 BRAINLY POINTS!!!! PLEASE HELP NOBODY EVER ANSWERS MY QUESTIONS Rip van Winkle has fallen asleep for a very long time.The length of his beard (in millimeters) as a function of time (in weeks) is graphed.How long was Rip van Winkle's beard when he fell asleep? SOMEONE PLS ANSWER FAST!!!How will the scientists determine whether or not the Boston Massacre really happened as we are told it did? What is the literary device in this sentence .The overcrowded town square buzzed like a busy beehive Triangle ABC has coordinates A(-2, -3), B(1, 1), and C(2, -1). If the triangle is translated 4 units up, what are the coordinates of A'? In a board game, the player who makes the last move receives an 11-point bonus for ending the game. Let s represent the score before the endgame bonus and f represent the final score. Find the valu of f when s = 1 How can you tell, without multiplying, if the product of three or more integers will be positive or negative? Why is the Declaration of the Rights of Man significant? A red 120 kg bumper car moving at 4 m/s collides with a green 100 kg bumper car moving at 3 m/s. The red bumper car bounces off at 2 m/s. What is the green car's final velocity? QUE VERBO FALTA?1. El mecnico ____ el coche de pap2. Yo ____ zumo de naranja y tostadas 3. Despus de comer ____ los dientes 4. El beb ____ su bibern5. Luisa ____ en la casa de al lado6. Los nios ____ en el parque con su pelota7. El abuelo ____ el peridico por las maanas8. Mara ____ la radio mientras hace los deberes How many humans like beans? tell me where u live(not a stalker just want to know if i live by u) A bag has 5 yellow marbles 3 red marbles and 2 blue marbles.Quinn randomly picks a marble from bag and returns it before another is picked. How many times would quinn expect to pick a blue marble if he picks a marble 200 times Rewrite each sentence and use a comma to separate a city name and a state name where necessary.1) Does your aunt live in Houston Texas still?2) If I could live anywhere in the United States, I would pick Honolulu Hawaii.3) My friend Ava just moved to Boise Idaho.4) My dad is traveling to New York New York for work this week.5) Sarah's mom is originally from Cleveland Ohio.6) I moved here from Las Vegas Nevada when I was six.7) My cousins are traveling to Orlando Florida in May.8) In June, my family will be visiting Atlanta Georgia.9) My oldest brother and his family live in Charlotte North Carolina.My new neighbors are from Austin Texas. The medulla _____.interprets signals from the sense organscontrols heartbeat and breathingcontrols balance and digestioncoordinates muscle movement How do Gracie and Daisy feel when Molly tells them they are going home? A block is released from rest at the top of a hill of height h. If there is negligible friction between the block and the hill, the block arrives at the bottom of the hill with speed v. What do you call the meetings of two planets/objects as seen from the earth? hurrry ASAP!!!!! -10x + 10x + 5x + 5 = 5solve for x helpppThe diagrams below illustrate two systems of government.FederalParliamnentarySelectLegislativeExecutiveExecutiveCitizensLegislativeCitizensAccording to the diagrams, what is the difference in citizen participation when choosing a leader?O In both systems, the citizens vote for an executive.O In the federal system, the citizens vote for an executive.O In the federal system, the citizens do not vote for the legislature.O In the parliamentary system, the citizens do not vote for the legislature.