Mathematics Middle School

Marlene rides her bicycle to her friend​ Jon's house and returns home by the same route. Marlene rides her bike at constant speeds of 6 mph on level​ ground, 4 mph when going uphill and 12 mph when going downhill. If her total time riding was 2 ​hours, how far is it to​ Jon's house?

Answers

Answer 1

x = level ground

y = hills

x/6 +y/4 +y/12 + x/6 = 2 hours

 multiply everything by 12 to get rid of the denominators:

 equation becomes 2x +3y +y +2x = 24

 combine like terms:

4x +4y = 24

 divide everything by 4

 f +h = 6 miles to Jon's house

Answer 2

Jon's house is 6 miles further away from Marlene's house.

Given that:

Speed on level ground is 6 mph

Speed on uphills is 4 mph

Speed on downhills is 12 mph

Let there are x miles level ground and y miles hills(either up or low, which while returning to home will serve as low or up respectively) in the route, then the whole route's length is x + y miles.

Since time taken = distance/speed , thus we have:

[tex]2 = \dfrac{x}{6} + \dfrac{y}{4} + \dfrac{x}{6} + \dfrac{y}{12}\\\\\text{Multiplying 12 on both sides}\\\\24 = 4x + 4y\\6 = x + y[/tex]

Since x + y denotes the length of the whole route(one sided), thus, Jon's house is 6 miles further away from Marlene's house.

Learn more here:

https://brainly.com/question/21470320

Related Questions

Joesl's father is 45. He is 15 years older than twice joe's age. How old Is joe?

Answers

Joe father is 45

Joe father is 2x + 15

2x + 15 = 45
2x + 15 (-15) = 45 (-15)
2x = 30
2x/2 = 30/2
x = 15

Joe is 15

hope this helps
So, you make your equation 2x+15=45, because of the given numbers. Now you solve for x.
First, you subtract 15 from both sides, which gives you 2x=30.
Then you divide both sides by 2, which give you x=15.
So, Joe is 15 years old.

Which statement is true

Answers

It is more safe to say that B) Lines ED and HA are parallel.
Since they are "lines" and not "line-segments", they go on forever, and with my eye (which is horrible (not google's google's is great lol)) it seems like it is parallel

hope this helps

Two examples that have a gcf of 8

Answers

12 & 24
16 & 24
4 & 16
16 & 32

hope this helps.
An example would be 24 and 16. Their GCF would be 8.

A recipe calls for 2/3 cup of brown sugar.marilyn is making 5 batches.how many cups of brown sugar should Marilyn use?

Answers

well 2/3 *5 is the answer so 3 1/3 is the answer

10/3 cups of brown sugar, or 1 1/3 cups of brown sugar.

I have a fair six sided dice numbered 4,9,12,16,20 and 24 what is the probability of rolling a multiple of 4

Answers

It would be 5/6 because 4 can go into 4,12,16,20, and 24.

4, 12, 16, 20, and 24 are multiples of four, so there is a 5/6 chance of landing on a multiple of four.

The drama club is selling short-sleeved shirts for $5 each, and long-sleeved shirts for $10 each. They hope to sell all of the shirts they ordered, to earn a total of $1,750. After the first week of the fundraiser, they sold  1/3 of the short-sleeved shirts and  1/2of the long-sleeved shirts, for a total of 100 shirts.
This system of equations models the situation.
   5x + 10y = 1,750
1/3x + 1/2y = 100
Let x represent the number of short-sleeved shirts ordered and let y represent the number of long-sleeved shirts ordered.
How many short-sleeved shirts were ordered?

How many long-sleeved shirts were ordered?

Answers

150 short-sleeved shirts
100 long-sleeved shirts

Answer:

150 short-sleeved shirts and 100 long-sleeved shirts.

Step-by-step explanation:

We will use elimination to solve this system of equations.  We will make the coefficients of x the same in order to eliminate them; to do this, we must multiply the bottom equation by 15 (1/3 of 15 is 5, so 15(1/3) = 5):

[tex]\left \{ {{5x+10y=1750} \atop {15(\frac{1}{3}x+\frac{1}{2}y=100)} \right. \\\\\left \{ {{5x+10y=1750} \atop {5x+7.5y=1500}} \right.[/tex]

Subtract the second equation from the first one:

[tex]\left \{ {{5x+10y=1750} \atop {-(5x+7.5y=1500)}} \right. \\\\2.5y=250[/tex]

Divide both sides by 2.5:

2.5y/2.5 = 250/2.5

y = 100

Substitute 100 in for y in the first equation:

5x+10(100) = 1750

5x+1000 = 1750

Subtract 1000 from both sides:

5x+1000 - 1000 = 1750 - 1000

5x = 750

Divide both sides by 5:

5x/5 = 750/5

x = 150

What is 8(c-9)=6(2c-12)-4c

Answers

Since cc is on the right side of the equation, switch the sides so it is on the left side of the equation.6(2c−12)−4c=8(c−9)6(2c-12)-4c=8(c-9)Simplify the left side.8c−72=8(c−9)8c-72=8(c-9)Simplify the right side.8c−72=8c−728c-72=8c-72Move all terms containing cc to the left side of the equation..−72=−72-72=-72Since −72=−72-72=-72, the equation will always be true.Always true
On the left side of the equal sign, multiply everything in the parenthesis by 8.
On the right side of the equal sign, multiply everything in the parenthesis by 6.

8c - 72 = 12c - 72 - 4c

Combine like terms.

8c - 72 = 8c - 72

Add 72 to both sides.

8c = 8c

Subtract 8c from both sides.

0 = 0

This means that there is an infinite amount of solutions.

Hope this helps!

The The graph of g(x) is the result of translating the graph of f(x) = 3x six units to the right. What is the equation of g(x)?
g(x) = 3x – 6
g(x) = 3x + 6
g(x) = 3x – 6
g(x) = 3x + 6
Mark this and return

Answers

I hope this helps

g(x)=3x-6

Answer:

The graph of g(x) is the result of translating the graph of f(x) = 3x six units to the right

When a graph is shifted 'a' units to the right f(x) becomes f(x-6)

Given f(x)= 3x

When graph is shifted 6 units to the right , then g(x)= f(x-6)

Replace x with x-6

g(x)= 3(x-6)= 3x-12

so g(x)= 3(x-6)

Step-by-step explanation:

slope is -2 and (1,1) is on the line

Answers

-2x+3. X intercept is +3. Moves two steps down and one step to the right to land on the point (1,1)

what is 3 3/5 divided by 6 in simplest form

Answers

This os the answer. Simply make the top fraction improper the multiply by the reciprical of 6. simplify from there.
I must don't know but do you actually understand 33/5 I think you should put 33 over 5 then divide it by 6 over one when you get the answer post it so I can see if you got it right.

Why there must be at least two lines on any given plane

Answers

The answer is that any plane must have a X and a Y. I hope this helped :)

A window has a radius of 12 inches. What is the circumference of the window? Use 3.14 to approximate pi. Round your answer to the nearest whole number.

Answers

75 inch is the circumference
You can use π*R² to work out the area of a circle,
The radius has been given to you so...
π*12² = 452.38

The area is 452.38 inches²

You can use π*2r to work out the circumference;
π*24 = 75.3 inches
Hope this helps! :)

Susan can buy 312312 lb of strawberries for $7.00. How many pounds of strawberries can she buy for $1.00? Express you answer as a fraction in simplest form

Answers

The first step would be to create an equation for this problem. 
[tex] \frac{312,312 lb}{7.00} [/tex]

Now, all you would have to do it solve it. 
[tex] \frac{312,312 lb}{7.00} [/tex] = [tex] \frac{44616 lb}{1.00} [/tex]

You can buy 44616 lb of strawberries for one dollar. 

I hope this helps!

Answer:

are you sure it is that large number and not 3 1/2

Step-by-step explanation:

A card is drawn from a standard deck and a letter is chosen from the word incredible. What is the probability of drawing a king then getting an i?

Answers

There is a 4/52 chance of getting a king, because there are 52 cards in a deck, and 4 kings in each. And there is a 2/10 (1/5) chance of getting an i, because there are 2 i's in the word "incredible", and 10 letters (so simplifying that, you would get 1/5).

Step-by-step explanation:

A card is drawn from a standard deck. A standard deck of cards has 52 cards. Its been asked if it is a king. There are 4 kings in a deck, so probability is = [tex]\frac{4}{52}[/tex] or [tex]\frac{1}{13}[/tex]

Simultaneously, a word is chosen from 'incredible' that has 10 letters. We have been asked if the letter is 'i'. In the given word, we have 2 'i's. So, probability is [tex]\frac{2}{10}[/tex] or [tex]\frac{1}{5}[/tex]

1.) Each time a ball hits the ground, it bounces back to 2/3 of its previous height. On its second bounce, the ball reaches a height of 12 in. What was the balls original height?

2.) A runner jogs on a 1/4-mi track. How many miles does the jogger run in 18 laps?

Thanks!

Answers

this is the answer check it out

Suppose that 12 inches of wire costs 48 cents. At the same rate, how many inches of wire can be bought for 24 cents?

Answers

6in is the answer
jjsjdjdjdjdjdjdjjdjdj





Use the equation of two ratios to solve this:

12 in                x
------------ = -----------      Cross multiplying, 48x = 12(24)        x=6 inches
48 cents       24 in

325 people were in a tour group. Six buses were completely filled and 7 people chose to walk. How many people did the bus hold?

Answers

325 - 7 = 318
(subtracting people that walked since we're not dealing with them)
318/6 = 53
(divided by 6 since there were 6 total buses)
Answer is 53, that's how many people one bus could hold.

What is a FREAKIN ratios

Answers

The quantitative relation between two amounts showing the number of times one value contains or it’s contained within the other.

pretty simple

compares two amounts like 4:5 is a ratio

art supplies in washington DC cost 28 dollars if the sales tax is 6 percent what was the total cost of supplies

Answers

(28 : 100) *6 = 1.68 (tax)

28 + 1.68 = 29.68 (total cost)

You divide a number by 3,add 6 then subtract 7. The result is 4 . What is the number

Answers

the answer is 15, hope this helps
The number and result is 15.

Corey has 16 cups of flour to make cookies. one batch of cookies takes 2.5 cups of flour. if he must save 6 cups of flour for other baking, write and solve and solve an inequality to determine how many batches of cookies he can make. Interpret the solution.

Answers

Final answer:

Corey can make at most 4 batches of cookies with the 10 cups of flour available for cookie making, after reserving 6 cups for other purposes.

Explanation:

To determine how many batches of cookies Corey can make, we need to write and solve an inequality. Corey has 16 cups of flour and needs to save 6 cups for other baking, leaving him with 16 - 6 = 10 cups of flour to use for cookies. Each batch of cookies requires 2.5 cups of flour. Let the number of batches be represented by b. The inequality will then be:

2.5b ≤ 10

To solve for b, we divide both sides of the inequality by 2.5:

b ≤ 10 / 2.5

b ≤ 4

This means Corey can make at most 4 batches of cookies with the flour he has, after setting aside 6 cups for other baking purposes.

Use long division to find the quotient of 405 and 27

Answers


27|405 27*1=27
- 27 27*5=135
-------
135
-135
--------
0

Answer is 6 :v

23.791 round to nearest tenth

Answers

24

23.791 is closer 24 than 23



You are setting up a zip line in your yard. You map out your yard in a coordinate plane. An equation of the line representing the zip line is y=2x+4y=2x+4. There is a tree in your yard at the point (−4, 11)(−4, 11). Each unit in the coordinate plane represents 1 foot. Approximately how far away is the tree from the zip line? Round your answer to the nearest tenth.

Answers

Solving this problem needs the distance formula of point to a line.

The formula is:

distance = | a x + b y + c | / √  (a^2 + b^2)

 
So we are given the equation: y = 2 x + 4

Rewriting this would be: y – 2 x – 4 = 0 ->  a = -2, b = 1, c = -4

 We are also given the points:

(-4, 11) = (x, y)

 Plugging it in the distance formula at points (x, y):

distance = | -2 * -4 + 1 * 11 + -4 | / √ [(- 2)^2 + (1)^2]

= 15 / √ (5)

= 6.7

 So the tree is approximately 6.7 feet away from the zip line.

Answer:

on what

Step-by-step explanation:

Which value for x makes the sentence true?

5(9x-6) + 15 = 210

A. 8
B. 10
C. 2 11/17
D. 5

Best full explanation gets brainiest, rating and thx.
PLEASE DONT ANSWER IF YOU CANT EXPLAIN!

Answers

I hope this helps you out
The answer is 5,x =5
5 (9x-6)+15=210
5×9×5=225
5×6=30
225-30=195
195+15=210
see,simple enough to understand
And it is explained step by step

Belinda wants to buy 5 pictures to hang in her family room . If each picture costs $30.90 how much will it cost her to buy 5? Justify your answer by using distributive property

Answers

ur answr would be 154.50 because if u do 30.90 5 times or times 30.90 by 5 its 154.50

Yolanda purchased a prepaid phone card for $25 . Long distance calls cost 23 cents a minute using this card. Yolanda used her card only once to make a long distance call. If the remaining credit on her card is $22.24 , how many minutes did her call last?

Answers

for 12 minutes because 23 x 12 is 2.76 and 25 minus 22.24 is 2.76

How many solutions does the equation have 5(n-2)=5n-10

Answers

5(n-2) = 5n -10

5n - 10 = 5n-10

ALL REAL NUMBERS
I’m pretty sure that’s considered Infinite because they both equal out to 5n-10=5n-10

PLZ TELL HOW U GOT THE ANSWER AND IT'S THE CIRCLED ONE PLLLLLZZZZZ

Answers

California:   22205.26
Kentucky:   19800.41
Ohio:   12102.75

40 pounds of sugar are repackaged of 1/16 pounds each. how many packet of sugar are there?

Answers

We know to each pound of such, there is 16 packets produced per?

So, 16 x 40 = 640.

Final answer:

To find the number of sugar packets from 40 pounds, divide by the weight per packet (1/16 pound). The calculation is 40 divided by 1/16, resulting in 640 packets.

Explanation:

To determine how many packets of sugar you can make from 40 pounds of sugar when each packet is 1/16 pounds, you would divide the total amount of sugar by the amount each packet contains. This is a basic math problem involving division.

Here's the calculation:

First, we establish that there are 40 pounds of sugar that need to be divided into packets.

Next, since each packet will contain 1/16 of a pound of sugar, we divide the total pounds of sugar by the weight of each packet.

The calculation is 40 pounds \/ (1/16) pounds per packet, which simplifies to 40 × 16 packets.

After performing the multiplication, the result is 640 packets of sugar.

Therefore, you would have a total of 640 packets of sugar if you repackage 40 pounds of sugar into 1/16 pound packets.

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