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

PLEASE PLEASE HELP I NEED THE ANSWER SOON

Answers

9514 1404 393

Answer:

  A, C

Step-by-step explanation:

The domain is the list of x-values in the table. Choice A correctly lists the domain values.

The range is the list of y-values in the table. Choice B incorrectly describes the domain.

For x = -1, the table tells you f(x) = 6, so f(-1) = 6.

For x = 5, the table tells you f(x) = 12, so f(5) = 12, not -2.

Choices A and C are correct.

A bag contains 1 blue, 2 green, 3 yellow, and 3 red marbles, as shown.Which best describes the complement of choosing a red marble?

choosing a green or blue marble
choosing any marble
choosing a blue, green, or yellow marble
choosing a yellow marble

Answers

Answer:

C) choosing a blue, green or yellow marble.

Step-by-step explanation:

The Complement of choosing a red marble means choosing any other marble that isn't red.

From the question , it was said that there were a blue , green, yellow and red marble.

So the Complement of choosing a red marble will be choosing any other marble apart from the red so ,that will be choosing a blue yellow or green marble.

Answer:

c

Step-by-step explanation:



Use a scale factor to find the missing side.

A)10
B)12
C)15
D)16

ᴄᴀɴ sᴏᴍᴇᴏɴᴇ ᴘʟᴇᴀsᴇ ʜᴇʟᴘ ᴍᴇ.

Answers

Answer:

15

Step-by-step explanation:

If we accept that the left side of the left triangle corresponds to the left side of the right triangle, then the scale factor is 6/8 = 3/4. By multiplying the scale factor by the bottom side of the first triangle, you'll get the corresponding side of the right triangle: 20 * 3/4 = 15.

Answer:

15

Step-by-step explanation:

I need a quick answer plss

Answers

Answer:

girl u didnt add the question...

Step-by-step explanation:

elias is training for a marathon. The table shows the total number of miles he has run each 0 I
1 I 9 sorry i could not make a line so i use this > I for a line Please what is the rate.
2 I
3 I 21
4 I
5 I 33

Answers

Answer:

rate of 6

Step-by-step explanation:

(–3i) (4i)(–5i)
a
60i3
b
60i
c
60
d
−60i

Answers

Answer: -60i

Step-by-step explanation:

(-3i) (4i) = -12i^2 = 12 because i^2 = -1

then lastly

12 (-5i) = -60i

PLEASE HELP WILL NAME BRAINLEST
determine which lines, if any, must be parallel. Explain your reasoning

Answers

Answer:

All of them are parallel

Step-by-step explanation:

This is due to the all of the 90 degree angle which would make the rest of the line a would be another 90 degree angle Which are found on every line. This would make all of the lines parallel because it is a total of 180 degrees.

Geometry...Please help as soon as possible please and Thank you!!!

Answers

Answer:

I answered the question according to "ASA" Angle, side, angle

.....

Step-by-step explanation:

Note : I'm not a teacher but I'm quite sure about my answer...

Anyway...

If I'm wrong just tell me...

.....

GOOD LUCK... ❤️

Will give brainliest!

Answers

Answer:

Answer is C multiply 5 by every ticket

Step-by-step explanation:

I need Help please #22

Answers

Answer:

A: 7.5

Step-by-step explanation:

If the length is 5 inches longer than the width, we must multiply the width by 4 and add ten to figure out the perimeter. 7.5 x 4 = 30. 30 + 10 = 40.

Answer:

8

Step-by-step explanation:

40/5=8 plz trust me i need it!!!

need help on worksheet

Answers

Answer:

-2, -1, 0, 1, 2

Step-by-step explanation:

the answer will be 0,-2,2,-1,1

I’m a little confused can someone help??

Answers

Answer:

C!

Step-by-step explanation:

83+30=113

Drag the missing statements and reasons to the correct spot to complete the proof

Answers

Answer:

The two column proof can be presented as follows;

1. [tex]\overline{AB}[/tex] ≅ [tex]\overline{CD}[/tex]      [tex]{}[/tex]               Given

2. [tex]\overline{AD}[/tex] ≅ [tex]\overline{CB}[/tex]      [tex]{}[/tex]              Given

3. [tex]\overline{BD}[/tex] ≅

4. ΔABD ≅ ΔBCD      [tex]{}[/tex]     SSS

Step-by-step explanation:

Given that we have;

Segment [tex]\overline{AB}[/tex] of triangle ΔABD being congruent to the corresponding segment [tex]\overline{CD}[/tex] of triangle ΔBCD and segment [tex]\overline{AD}[/tex] of triangle ΔABD being congruent to the corresponding segment [tex]\overline{CB}[/tex] of triangle ΔBCD, and that the common segment [tex]\overline{BD}[/tex] of both triangles are congruent by reflexive property, we have that ΔABD is congruent to ΔBCD by the Side-Side-Side (SSS) rule of congruency.

isac walks 6/10 of a mile in 1/5 of an hour if his rate remains constant what is isac walking rate in miles per hour

Answers

Answer:amazing

Step-by-step explanation:

Lizzy has 6.5 hours to tutor 4 students and spend 1.5 hours in a lab. She plans to
tutor each student the same amount of time. The inequality 4t +1.5 < 6.5 can be
used to find t, the greatest amount of time in hours Lizzy could spend with each
student. a. Solve the inequality and interpret what your solution means. b. Can
Lizzy tutor each student for 1.5 hours? Explain. *

Answers

Answer:

A. t= 4.1

B. No because t = 4.1 and if you do 6.5 divided by 1.5 then you get 4.3 and that won't work.

Step-by-step explanation:

can you help me answer this question

Answers

Answer:

it would be 18 over 5

It’s 18 over 5 ok bye

Help this confusing no matter how any times I do it

Answers

Answer:

The variable 8. Equation is 16 + 12x = 112.

Step-by-step explanation:

We know that she spent $16 dollars on magazines, so we can put it in the equation (16 + x= ?). We also know that the total is $112, so we can also add that (16+ x= 112). We don't know how many books she got, but we do know how much they cost (16 + 12x=112. So that makes  the books the variable (X).

To find the variable we need to take out the magazines from the price. 112-16=96. Now we're left with 12x=96. Now all we have to do is divide 96 by 12, which equals 8.

Sorry everything is so long, I tried to make it short as possible

Kendra knits hats. She starts with 334 yd of yarn. After knitting for 514 h, there is 118 yd of yarn left. At what rate does the amount of yarn change? Show your work.

Answers

Answer:

Step-by-step explanation:

Total yarn = 334 yards

Amount remaining = 118 yards

Amount knitted = 512

amount per hat =x

amount used = y

amount used = 334 - 118 = 514*x

y= 216= 514x

216 = 514 x         Divide by 514

216/514 = x

.42 yards/hat = x

when is it best to use the graphing method to solve a system of equations????

Answers

Answer:

graphing by hand it probably can help or you could do it your way if u want

Which of the following is NOT a rational number?
-4/7
3/5
(the symbol for pie)
2/3

Answers

Answer: (the symbol of pi)

Step-by-step explanation: Because if you divide each of those fractions only pi keeps in going without repeating itself.

please help me like i really don't understand this and i really need help​

Answers

Answer:

Therefore, the coordinates of the vertices of ΔA'B'C' after the dilation with a scale factor of 2.5.

A'(-5, -2.5)B'(2.5, 5)C'(5, -10)

Step-by-step explanation:

Given the vertices of ΔABC

A(-2, -1)B(1, 2)C(2, -4)

Given that ΔA'B'C' is a dilation of ΔABC with a scale factor of 2.5 and the center of dilation (0, 0).

We know that when the scale factor > 1, then the image is enlarged.

The formula to determine the dilation with a scale factor of 2.5.

P(x, y) → P'(2.5x, 2.5y)

Here, P' is the image of P, and the vertices of the image is dilated by a scale factor of 2.5.

In other words, the vertices of the image can be obtained by multiplying the vertices of the original triangle with 2.5.

Thus,

P(x, y) → P'(2.5x, 2.5y)

A(-2, -1) → P'(2.5(-2), 2.5(-1)) = A'(-5, -2.5)

B(1, 2) → B'(2.5(1), 2.5(2)) = B'(2.5, 5)

C(2, -4) → C'(2.5(2), 2.5(-4)) = C'(5, -10)

Therefore, the coordinates of the vertices of ΔA'B'C' after the dilation with a scale factor of 2.5.

A'(-5, -2.5)B'(2.5, 5)C'(5, -10)

Can you please help? I’m tired and I have to work on this

Answers

1. 1/3 2. 1/2 3. 4:1 4. 3:4

Answer:

1) 1/3

2) 1/2

3) 4/1

4) 3/4

5) 2/5, 4/10, 4:10, 4 to 10

6) 3:4, 6/12, 6:12, 6 to 12

7) 3 to 1, 9/3, 9:3, 9 to 3

8) 7/9, 14/18, 14:18, 14 to 18

9)

a) 3/2

b) 3/5

c) 27:18

10) 96 birds visited the feeder

11)

a) nuts row: 3, 6, 9, 12

   raisins row: 4, 8, 12, 16

b) 7.5 cups

12)

a) This ratio means that for every 9 boys in the school there are 10 girls

b) 570 students

What is the distance from L to M?

Answers

Answer:

B or A

But i would go with B

Step-by-step explanation:

Answer:

A. 14 units

Step-by-step explanation:

You can just count blocks down and right. (vertical and horizontal)

f(x) =∛2x g(x)=2x+1 Find (f/g) (x) Include any restrictions on the domain

Answers

Answer: ∛2x / 2x+1

x cannot equal -1/2

Step-by-step explanation: f/g means we divide the f function by the g function

so that’s all we do!

then, remember, we can’t divide by 0. so 2x+1 can’t be 0. if we solve that out, we get that x can’t be -1/2, because that would make it 0. there’s our domain restriction!

After a 5% discount, a car is on sale for $11,400. What was the price of the car before the discount?

Answers

Answer:

10,830

Step-by-step explanation:


A bag contains 5 cherry, 8 orange, 2 grape, 7 bubblegum, and 3 apple
lollipops. What is the probability of choosing grape for your first lollipop
and orange for your second? (if you ARE replacing it) *
1/75
2/75
10/625
16/625

Answers

Answer:

16/625

Step-by-step explanation:

Step one:

sample space

A bag contains

5 cherry,

8 orange,

2 grape,

7 bubblegum, and

3 apple  lollipops.

sample size= 5+8+2+7+3= 25

Required:

The probability of choosing grape for your first lollipop

and orange for your second?

1. The probability of choosing the grapes lollipops

=2/25

2. the probability of choosing the orange  lollipops----Note in the second choice the sample size will reduce because the first choice was done with out a replacement

=8/24

The total is

2/25*8/25= 16/625

SOLVE THIS PROOF PLEASE

Answers

Answer:

wait what are you trying to find i-

Step-by-step explanation:

Frieda paid $132 for groceries for her family. This was 1 1/8 as much as she paid for the previous time she shopped. How much did Freda pay on her previous shopping trip

Answers

Answer:

$117.33

Step-by-step explanation:

1 1/8 = 1 + 1/8 = 8/8 + 1/8 = 9/8

She paid 9/8 what she paid the last time.

Let the amount she paid last time equal x.

$132 is 9/8 of x.

9/8 x = 132

8/9 * 9/8 x = 132 * 8/9

x = 117.33

She paid $117.33

what is the expression in radical form? (5x^3 y^2) 2/8

Answers

Answer: (y^{2}x^{3}⋅5)/4

Step-by-step explanation:

Convert to Radical Form

    [tex](5x^3y^2)\frac{2}{8}[/tex]

Reduce the expression [tex]\frac{2}{8}[/tex] by cancelling the common factors.

Factor 2 out of 2.

    [tex]5x^3y^2\frac{2(1)}{8}[/tex]

Factor 2 out of 8.

     [tex]5x^3y^2 \frac{2(1)}{2(4)}[/tex]

Cancel the common factor.

     [tex]5x^3y^2 \frac{1}{4}[/tex]

Combine 5 and [tex]\frac{1}{4}[/tex].

     [tex]x^3y^2\frac{5}{4}[/tex]

Combine [tex]x^{3}[/tex] and [tex]\frac{5}{4}[/tex] .

     [tex]y^2\frac{x^3(5)}{4}[/tex]

Combine [tex]y^{2}[/tex] and [tex]\frac{x^3*5}{4}[/tex]

     [tex]\frac{y^2x^3*5}{4}[/tex]

ill give you brainliest for the correct answer

Answers

Answer:

An equation is 2.50x + 30 = 45

You purchased 6 movies

Other Questions
What idea is the poster trying to convey? the first third and sixth terms of an arithmetic sequence are shown. what is the common difference between consecutive terms in the arithmetic sequence 2,_,8,_,_,17, Evaluate f(x) = - 3x - 4 for x = 1 . Why did Andrew Jackson support laissez-faire economics? quiz 4-1 : classifying and solving for sides/angles in triangles gina wilson (all things algebra) URGENT Ms. Walch works as a car salesperson. She earns a monthly base salary of $ 4,000 Plus $ 500 commission for each car she sells. How many cars does Ms. Walsh need to sell in a given month to earn a total salary of $ 10,000 for that month? Plato, who wrote Republic, believed that: I need help again lol In the 1500s, the Council of Trent was led by a group ofLutheran ministers who wanted to spread their ideas.Catholic cardinals who wanted to reform the Church.German princes who wanted to end a peasants rebellion.Calvinists who wanted to make laws that followed their beliefs. Hey everyone! I have one question for ya'll, who does John Groff voice in frozen. I know the answer, and so should you! First gets brainiest! Good luck! How do you write like ur running out of time....... I have no more points left please I need it Earthquakes release seismic waves, which are waves of .... *soilenergysoil and energysoil, energy, and motion Aye can one of yall help me break this answer down (btw the total is 120) Sketch a polynomial that has: -odd degree negative leading coefficient f(2) = -3 f(-3) = 0 4 is a zero with multiplicity of 2 At which type of boundary do rocks react to tectonic stress and pull away leading to the formation of new crust? Look at pic and answer ASAP The Earth is broken into pieces called plates that are different sizes and shapes. true or false Gabriela has dinner at a cafe and the cost of her meal is \$45.00$45.00dollar sign, 45, point, 00. Because of the service, she wants to leave a 15\%15%15, percent tip.What is her total bill including tip? "Slavery hung over the Philadelphia Convention, threatening to divide northern and southerndelegates. Even though slavery existed by law in some of the northern states in 1787, mostpeople there favored its end. Southerners were more unsure about whether to end slavery, bothbecause they had significantly greater numbers of slaves to deal with and because an end to(slavery) had important economic implications. The result was compromise. The FoundingFathers were more determined to fashion a new nation than they were to bring an end to slavery."- Kermit Hall, historian, The Law of American Slavery, 19876. What compromise is being discussed in the excerpt above?1 pointThe Virginia PlanThe New Jersey PlanThe Three-Fifths CompromiseThe Great Compromise 38. All the bald eagles in an area is an example of a(n):A. species.B. individual.C. populationD. fossil.