Ally's tricycle has two different wheel sizes: one larger wheel and two smaller wheels. As Ally travels the distance between her house and her neighbor's house on the tricycle, the larger wheel revolves 10 times and each of the smaller wheels revolve 25 times. If half the circumference of the larger wheel is 5 inches more than the circumference of one of the smaller wheels, what is the distance, in inches, traveled by the tricycle between Ally's house and her neighbor's house?

Answers

Answer 1

Answer:

500 inches

Step-by-step explanation:

Let C₁ and n₁ be the circumference and the number of rotations of the larger wheel. Also, let C₂ and n₂ be the circumference and the number of rotations of the smaller wheel. Since the distance moved by both wheels from Ally's house to her neighbor's house is the same, n₁C₁ = n₂C₂. (1)

Also it is given that half the circumference of the larger wheel is 5 inches more than the circumference of one of the smaller wheels.

So, C₁/2 = C₂ + 5

C₁ = 2(C₂ + 5)  (2)

Substituting C₁ into (1), we have

n₁C₁ = n₂C₂.

n₁[2(C₂ + 5)] = n₂C₂.

Since n₁ = 10 and n₂ = 25, we have

10[2(C₂ + 5)] = 25C₂

20(C₂ + 5) = 25C₂

expanding the bracket,

20C₂ + 100 = 25C₂

collecting like terms, we have

25C₂ - 20C₂ = 100

5C₂ = 100

dividing both sides by 5, we have

C₂ = 100/5

= 20 inches

So, the distance between Ally's house and her neighbor's house is d = n₂C₂ = 25(20)

= 500 inches

Answer 2

The distance travelled by Ally's tricycle is [tex]500inches[/tex]

Let

[tex]d=\text{the distance between Ally's house and her neighbor's house}\\C_b=\text{the circumference of the larger wheel}\\C_s=\text{the circumference of each of the smaller wheels}[/tex]

Then, from the question

[tex]d=10C_b=25C_s\\\\\frac{C_b}{2}=C_s+5[/tex]

Eliminating [tex]C_s[/tex] from the second statement, we get

[tex]\frac{C_b}{2}=5+\frac{2C_b}{5}[/tex]

Solving for [tex]C_b[/tex],

[tex]C_b=50inches[/tex]

To calculate the distance travelled between her house and her neighbor's house,

[tex]d=10C_b\\\implies d=10\times 50inches=500 inches[/tex]

Therefore, the distance travelled between Ally's house and her neighbor's house is [tex]500inches[/tex]

Learn more about circumferences here: https://brainly.com/question/3131741


Related Questions

Laurie had three $2 off coupons for the mini-golf course, but everybody else had to pay $9 per person, the full price. What was the total cost for their group of 8 to play mini-golf?

A: $51
B:$62
C:$63
D:$66​

Answers

Answer:

D

Step-by-step explanation:

9x8=71

2x3=6

71-6=66

Answer:

D $66

Step-by-step explanation:

So first we need to figure how much money she was able to deduct from the three $2 coupons. Remember the original price is $9

3×2=6 (which means she can get $6 off of the original price $9.)

9-6= 3 (So now she only has to pay $3 while the other seven people in her group pays the original price $9.)

9×7= 63 (So $9 for the 7 other people equals $63. That is how much they are paying. Now let's add Laurie's amount!)

63+3=66 (So altogether everyone including Laurie is paying $66.)

So the final answer is $66

(I hope this helps you! Have a wonderful day everyone!)

:)

|) Mei Li is going orange
picking. She is choosing
between two orange
orchards. The cost of a
basket of oranges at each
orchard is shown.
Which orchard should Mei
Li choose? Explain.

Answers

Answer:

Annie's Orange Grove

Step-by-step explanation:

* you need to find out how much each pound of oranges cost at both orchards.

* to do so you take the total amount of money and divide it by the number of pounds you get.

1) 7.25 ÷ 20 = .36

2) 5 ÷12 = .4

* as you can see .36 is less than .4 and therefore is the better deal.

what is. 60+6000=?? (●'◡'●)

Answers

Answer:

6060

Step-by-step explanation:

ヽ(゚Д゚)ノ

Answer:

6060

Step-by-step explanation:

6000+60

Helpp pleasee it's solving mulit=step equations.

Answers

Answer:

The answers are

x=-2

m=23

a=-24

x=6

Answer:

Step-by-step explanation:

1. x+5=3

x= 3-5=-2

2. m-4=19

m= 19+4=23

3. a÷6=-4

Multiply by 6 on both sides we get

a = -4×6=-24

4. -6x =-36

Divide by -6 on both sides

x =6

Olivia picked 482 apples from the orchard’s largest apple tree. She divided the apples evenly into 4 baskets. How many apples are in each basket? How many are left over?

Answers

Answer:

there are 120 apples in each basket and 5 are left over

Step-by-step explanation:

What's the value of 6.7×0.54

Answers

Answer:

What's the value of 6.7×0.54

=

3.618

Step-by-step explanation:

Answer:

3.618

Step-by-step explanation:

3.618

What number will complete the point-slope equation that models this scenario?

y−50,000=[_______](x−10)

Answers

Answer:

-3000

Step-by-step explanation:

edge2021

Answer: -3000

Step-by-step explanation: Did it on Edge and got it right!

Find the equation of the linear function represented by the table below in slope-intercept form.

x y

-2 -9

1 3

4 15

7 27

Answers

Answer:

[tex]y = 4x-1[/tex]

Step-by-step explanation:

Required:

Determine the equation of the linear function

First, we need to determine the slope (m) as follows:

[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

Where

[tex](x_1,y_1) = (-2,-9)[/tex]

[tex](x_2,y_2) = (4,15)[/tex]

Substitute these values in [tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

[tex]m = \frac{15- (-9)}{4 - (-2)}[/tex]

[tex]m = \frac{24}{6}[/tex]

[tex]m =4[/tex]

The equation is then calculated using:

[tex]y - y_1 = m(x - x_1)[/tex]

This gives:

[tex]y -(-9) = 4(x - (-2))[/tex]

[tex]y + 9 = 4(x + 2)[/tex]

[tex]y + 9 = 4x + 8[/tex]

Make y the subject

[tex]y = 4x + 8 - 9[/tex]

[tex]y = 4x-1[/tex]

In AFGH, the measure of ZH=90°, the measure of ZF=18°, and GH = 9.4 feet. Find
the length of HF to the nearest tenth of a foot.

Answers

Answer:

20.9 feet

Step-by-step explanation:

i really hope this helps and have a good day

Find the quotient: 6/2 divided by 3/4.

Answers

Answer: the quotient is 4

Answer:

4

Step-by-step explanation:

6

2

÷

3

4

=  

6/4

×

2/3

=  

6 × 4

2 × 3

=  

24/6

=  

24 ÷ 6

6 ÷ 6

=  4

Evaluate 4b – a when a = 12 and b=7.
4b - a= 0

Answers

Answer: 4b - a = 15

Step-by-step explanation: if you replace the variables with their equivalent counterparts you get the equation 4(7) - 12 = __ when you do the math make sure to do the parentheses first then subtract, just like in elementary school remember pemdas parentheses, exponents, multiplication, division, addition, subtraction. I hope this helps.

4b - a
4(7) - (12)
28 - 12
16

The cost of 9 scarves is $87.75. What is the unit price?

Answers

Answer:

the answer is 9.75 for one

Step-by-step explanation:

divide 87.75/9

hope this helped

FERRIS WHEEL Suppose a Ferris wheel is 160 feet high and casts a shadow that is 64 feet long. At the same time, a ticket booth next to the Ferris wheel casts a shadow that is 2.8 feet long. What is the height of the ticket booth?

Answers

Answer:

7 feet

Step-by-step explanation:

Suppose a Ferris wheel is 160 feet high and casts a shadow that is 64 feet long. At the same time, a ticket booth next to the Ferris wheel casts a shadow that is 2.8 feet long. What is the height of the ticket booth?

We solve this question

Length of shadow/Height

Ferris wheel = Ticket booth

64 feet/160 feet = 2.8 feet/x

Cross Multiply

64x = 160 × 2.8

x = 160 × 2.8/64

x = 7 feet

The height of the ticket booth is 7 feet

What is it? I don't understand it or know it.​

Answers

Answer:

3+6n=

Step-by-step explanation:

Suppose a ice cream cone cost lies and $.80 each how many ice cream cone put the couch buy with $42?

Answers

So you want to go to your calculator type 42 divided by zero, and you should get a 52.5.

Passing through
(1,2) and (5,10)

Answers

Step-by-step explanation:

equation of the line is

y =mX + C

to calculate m(slope) :

m= 10-2/5-1 = 2

to find C ....Substitute in eq. by one point

2= 2×1+C

C. = 0

So the eq. is

y=2X

Find the lengths of all 3 sides of each triangle.

Answers

Answer:

GH=45

HJ=81.6

GJ=53.4

Step-by-step explanation:

hope i helped <3

Which equation represents the axis of symmetry
for the function y =-4(X+6)* +4?
A X=6
B X=4
C X=-6
X=-4

Answers

the axis of symmetry is -6 because the x always lies.

A customer at a store paid $42 for 4 pairs of pants and 3 shirts. At the same store, a second customer paid $2 more for 1 pair of pants and 7 shirts. The price of each pair of pants is the same, and the price of each shirt is the same. Which system of equations can be used to find the price in dollars of each pair of pants, x, and each shirt, y?

Answers

Answer:

The system of Equations:

4x + 3y = 42

x + 7y = 44

Step-by-step explanation:

Let the price in dollars of

each pair of pants = x

each shirt = y

A customer at a store paid $42 for 4 pairs of pants and 3 shirts.

Hence:

4 × x + 3 × y = $42

4x + 3y = 42

At the same store, a second customer paid $2 more for 1 pair of pants and 7 shirts.

This means he, paid $42 +$2 = $44

Hence:

1 × x + 7 × y = 44

x + 7y = 44

The system of equations can be used to find the price in dollars of each pair of pants, x, and each shirt, y is

4x + 3y = 42.... Equation 1

x + 7y = 44..... Equation 2

solving a compound inequality. check all that apply.

Answers

Answer:

The solutions are:

-28.25, -14.5, -2.25

Step-by-step explanation:

Given compound inequality is:

[tex]-17.5\leq \frac{2x+4}{3} <17.5[/tex]

The compound inequalities are broken down into two inequalities to find the solution

The two inequalities will be:

[tex]\frac{2x+4}{3} \geq -17.5[/tex]   AND   [tex]\frac{2x+4}{3}<{17.5}[/tex]

Solving both inequalities one by one

[tex]\frac{2x+4}{3} \geq -17.5\\2x+4 \geq -52.5\\2x \geq -52.5-4\\2x \geq -56.5\\\frac{2x}{2} \geq \frac{-56.5}{2}\\x \geq -28.25\\\frac{2x+4}{3} < 17.5\\2x+4 < 52.5\\2x < 52.5-4\\2x \geq 48.5\\\frac{2x}{2} \geq \frac{48.5}{2}\\x < 24.25[/tex]

The solution is:

-28.25 ≤ x < 24.25

We have to see which options lie in the solution range.

The solutions are:

-28.25, -14.5, -2.25

A group of 31 students is going to visit the museum. The total cost for the tickets is $145.15. About how much money will each student need to pay for a ticket?

Answers

Answer:

$4.65

Step-by-step explanation:

each student will need about 5.00$

145.15 divided by 31 = 4.68 but since it says about just round up to the closest dollar so you’ll essentially get 5 dollars

Find the x- and y-intercept of the line.

–3x + 5y = 75
a
x-intercept is 5; y-intercept is –3
b
x-intercept is –3; y-intercept is 5
c
x-intercept is –25; y-intercept is 15
d
x-intercept is 15; y-intercept is –25

Answers

Answer:

x intercept-25; y intercept is 15

20 POINTS IF YOU ANSWER! NEED HELP ASAP
The two kids next to your locker are arguing over who got the better deal on the new cell phone plan billy pay $30 for his new phone and only pays $12.50 each month with free texting Annie got her new phone for free in only pays $20 a month how many months will both billy Annie have paid the same amount for the new cell phone plans you must write and solve an equation

Answers

Answer:

They will both have paid the same amount after 4 months

Step-by-step explanation:

Assume that they will pay the same amount after x months

∵ Billy pays $30 for his new phone

∵ He only pays $12.50 each month

→ Find how much he will pay in x month

He will pay → 30 + 12.50x

∵ Annie got her new phone for free

∵ She only pays $20 a month

→ Find how much she will pay in x month

She will pay → 20x

∵ They will pay the same amount

→ Equate their expressions above

20x = 30 + 12.50x

→ Subtract 12.50x from both sides

∵ 20x - 12.50x = 30 + 12.50x - 12.50x

∴ 7.50x = 30

→ Divide both sides by 7.50

x = 4

They will both have paid the same amount after 4 months

How many solutions does 1.25x+4=1.00x+6 have

Answers

Answer:

One solution which is 8

Step-by-step explanation:

Hope this helps. Pls give brainliest.

The directions on a sewing pattern say to cut an extra 15% of fabric to account for error.
Chloe needs 0.75 yard of fabric to make a skirt, and she cuts 0.1125 yard.
Did Chloe cut the correct amount of fabric? Why or why not?



Chloe cut enough fabric because she cut the amount of fabric for the skirt.



Chloe cut enough fabric because she cut enough fabric for the skirt and the amount of extra fabric.



Chloe did not cut enough fabric because she only cut the amount of fabric for the skirt.



Chloe did not cut enough fabric because she only cut the amount of extra fabric.

Answers

Answer:

D

Step-by-step explanation:

She only cut the 15% extra and no the other 75%

Chloe cut enough fabric because she cut enough fabric for the skirt and the amount of extra fabric. The correct option is B.

What is the percentage?

The percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.

Given that The directions on a sewing pattern say to cut an extra 15% of fabric to account for errors. Chloe needs 0.75 yards of fabric to make a skirt, and she cuts 0.1125 yards.

Calculate the percentage of the fabric from the given data,

Percentage = 0.1125 / 0.75

Percentage = 0.15 x 100

Percentage = 15%

Chloe cut enough fabric because she cut enough fabric for the skirt and the amount of extra fabric.

To know more about percentages follow

https://brainly.com/question/24304697

#SPJ2

barney has 14 dimes and quarters worth $2.15. write the system of equations

Answers

Answer: 14 dimes and 3 quarters

Step-by-step explanation:

14x10=140+25=165+25=190+25=215 aka $2.15 meaning that there is 14 dimes and 3 quarters

GAIQNFKDKER HELP PLZ

Answers

Answer:

it's the first answer

Step-by-step explanation:

literally every other answer is ruled out because D is the greatest variable and can't be smaller than anything else

1. Angelina received 10% off a $50 pair of shoes. How much did she save?

Answers

Answer:

$5

Step-by-step explanation:

Multiply 0.10 by $50

5

So Angelina saved $5

Hope this helped :)

Solve cos x + √2 = -cos x for x over the interval [0, 2Π)

Answers

Answer:

[tex]x=\frac{3\pi}{4}\\\\x=\frac{5\pi}{4}[/tex]

Step-by-step explanation:

Trigonometric Equations

It's required to solve:

[tex]\cos x+\sqrt{2}=-\cos x[/tex]

for [tex]x\in [0,2\pi)[/tex]

Adding cos x:

[tex]2\cos x+\sqrt{2}=0[/tex]

Subtracting [tex]\sqrt{2}[/tex]

[tex]2\cos x=-\sqrt{2}[/tex]

Dividing by 2:

[tex]\displaystyle \cos x=-\frac{\sqrt{2}}{2}[/tex]

Solving for x:

[tex]\displaystyle x=\arccos\left(-\frac{\sqrt{2}}{2}\right)[/tex]

We need to find the angles whose cosine is [tex]-\frac{\sqrt{2}}{2}[/tex] over the given interval.

These angles lie on the quadrants III and IV respectively and they are:

x=135°, x=225°

Converting to radians:

135 * π / 180 = 3π/4

225 * π / 180 = 5π/4

The two solutions are:

[tex]\mathbf{x=\frac{3\pi}{4}}[/tex]

[tex]\mathbf{x=\frac{5\pi}{4}}[/tex]

Answer:

The correct answer is option C

Step-by-step explanation:

first to answer gets brainlest <33

Answers

Awww man the other person answered before me :(
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