A farmer drives a tractor from one town to another, a distance of 120 kilometers. He drives 10 kilometers per hour fast on the return trip, cutting an hour off the time. How fast does he drive each way?

Answers

Answer 1
120/x - 120/(x+10) = 1
120x + 1200 - 120x = x(x+10)
1200 = x^2+10x
x^2 + 10x - 1200 = 0
(x+40)(x-30) = 0
Positive solution:
x = 30 km/hr (rate on the 1st trip)
x+10 = 40 km/hr (rate on the return trip)

Related Questions

Peter is reading a 193-page book. he has read three pages more than one-fourth of the number of pages he hasn't yet read. how many pages has he not yet read? 147 144 152 141

Answers

Let's call the number of pages we have read [tex]m[/tex]. To find the number of pages we have left to read, we'll need to subtract the number of pages we've read from the total number of pages in the book. Our total page count is 193, and the number of pages we've read is the unknown [tex]m[/tex], so the number of pages we haven't read can be written as [tex]193-m[/tex]. With that knowledge, let's construct the rest of our equation.

"He has read three pages more than one-fourth of the number of pages he hasn't yet read." The first key phrase here is "he has read." What this means is that the number of pages he's read, which we've named [tex]m[/tex], is equal to everything in the rest of the sentence. "Thee pages more than" means that we're going to be adding 3 to whatever the next quantity described is, which, in this case, is "one-fourth of the number of pages he hasn't yet read." We already established earlier that "the number of pages he hasn't yet read" is [tex]193-m[/tex], so one-fourth of that would be [tex] \frac{1}{4} (193-m)[/tex]. Putting everything together, we get the following equation:

[tex]m= \frac{1}{4} (193-m)+3[/tex]

To solve for [tex]m[/tex], we might first want to eliminate the fraction 1/4 by multiplying both sides of the equation by 4, obtaining

[tex]4m=193-m+12[/tex]

Solving for m, we get:

[tex]4m=193+12-m\\5m=205\\m=41[/tex]

Now that we have m, it's a simple matter to solve for [tex]193-m[/tex]:

[tex]193-41=152[/tex]

So, he has not yet read 152 pages.

Find the distance between the given points . find the midpoint of the segment with the given endpoints. round to the nearest tenth, if necessary

Answers

Where are the given points

number divided by -3 is less than 6

Answers

n/-3 < 6
if you need to solve to find the number then
n > -18

The equation below describes a proportional relationship between x and y. What is the constant of​ proportionality? y=2/7x

Answers

hello : 
is the constant of​ proportionality is : 2/7

Identify the hypothesis of the statement below.

If the sum of the measures of two angles is 180°, then the angles are supplementary angles.

Answers

Hello Crylicx, If the sum of the measures of two angles is 180° , then the angles are supplementary angles so if you saying if its true or false you answer is correct.

there are 13 animals in the barn some are ducks and some are pigs there are 42 legs in all how many of each animal are there (ducks have 2 legs and pigs have 4)

Answers

there ar 7 of each animal
1=6(2 legs from the duck, 4 legs from the pig)
2=12(4 legs from the ducks, 8 legs from the pigs)
3=18(6 legs from the ducks, 12 legs from the pigs)
4=24(8 legs from the ducks, 16 legs from the pigs)
5=30(10 legs from the ducks, 20 legs from the pigs)
6=36(12 legs from the ducks, 24 legs from the pigs)
7=42(14 legs from the ducks, 28 legs from the pigs)

Vehicle a averages 14 miles per gallon of gasoline, and vehicle b averages 36 miles per gallon of gasoline. at these rates, how many more gallons of gasoline does vehicle a need than vehicle b to make a 1,008-mile trip?

Answers

Final answer:

Vehicle A requires 72 gallons and vehicle B requires 28 gallons for a 1,008-mile trip. Therefore, vehicle A needs 44 more gallons of gasoline than vehicle B for the trip.

Explanation:

To calculate the number of gallons of gasoline each vehicle needs for the trip, we would divide the total distance of the trip by the miles per gallon (mpg) that each vehicle gets. Then, to find out how many more gallons of gasoline vehicle A needs than vehicle B, we subtract the gallons of gasoline used by vehicle B from the gallons used by vehicle A.

First, we find the gallons needed for vehicle A:

Vehicle A: 1,008 miles ÷ 14 mpg = 72 gallons

Next, we calculate the gallons needed for vehicle B:

Vehicle B: 1,008 miles ÷ 36 mpg = 28 gallons

Finally, we determine how many more gallons vehicle A requires than vehicle B:

Additional gallons needed by vehicle A: 72 gallons - 28 gallons = 44 gallons

The radius of a sphere is 3 inches. Which represents the volume of the sphere?
A) 12π cubic inches
B) 36π cubic inches
C) 64π cubic inches
D) 81π cubic inches

Answers

Hello! The volume of a sphere is 4/3πr³. The radius is 3. 3³ is 27. 27/1 * 4/3 is 108/3 or 36 in simplest form. When you do that, you're left with 36π. The answer is B: 36π cubic inches.

Answer: B) [tex]36\pi \text{cubic inches}[/tex]

Step-by-step explanation:

We know that the volume of a sphere is given by :-

[tex]\text{Volume}=\dfrac{4}{3}\pi r^3[/tex], where r is radius of the sphere.

Given : The radius of the sphere = 3 inches

Then , the volume of the sphere will be :-

[tex]\text{Volume}=\dfrac{4}{3}\pi (3)^3\\\\\Rightarrow\ \text{Volume}=36\pi \text{ cubic inches}[/tex]

Hence, the volume of the sphere = [tex]36\pi \text{ cubic inches}[/tex]

m/x = k - 6 Solve for m

Answers

You just multiply the x and the answer would be m = k-6/x
Not sure if this is 100% correct but it's m=kx-6x

If b= the number of boys, which algabraic expression represents the phase?

Answers

The answer is c because you are looking for the SUM so you would add 15 plus the number of boys (b).

can you help me round 3,418,913 to the nearest thousand

Answers

3,419,000 because the 913 rounds the number up
3,418,913 to the nearest thousand is 3,419

How do you write 650 as a fraction or mixed number in simplest form?

Answers

how do u write 650 as a fraction......650/1

** if u have a whole number, and u want to make it a fraction, just put it over 1

Which answer is equal to i58 ?

−i
i
−1
1

Answers

As per complex number, the value of [tex]i^{58}[/tex] is (- 1).

What is a complex number?

"Complex number is the number that is expressed in the form of [tex](a + ib)[/tex]where, 'a', 'b' are real numbers and 'i' is an imaginary number."

Therefore, the simplified value is

[tex]i^{58} \\= (\sqrt{-1})^{58} \\= (-1)^{29} \\= -1[/tex]

Learn more about a complex number here: https://brainly.com/question/10251853

#SPJ2

Need some geometry help

Answers

check the picture below.

that means

angle AFB is 27 + 2 = 29

angle BFC is 2(27) + 12 = 66

and angle CFD is 2(27) or 54

so hmmmm, you'd know which one isn't there.


Xavier is a salesperson who is paid a fixed amount of $455 per week. He also earns a commission of 3% on the sales he makes. If Xavier wants to earn more than $575 in one week, how many dollars (x) in sales must he make?

Answers

He needs to make $4,000 in sales in order to hit $575 so if he earns more than $4,000 in sales then he will exceed his goal. I did 575-455=120 to see how much he needs. Then I did 0.03×4=0.12. Well if you add 0's you will get 120 because the decimal will move so then I added 3 0's to get 0.03×4,000=120. Hope this helped.

The answer is c reason I now this is cause I had this on my test



If 17 is increased to 23, the increase is what percent of the original number? (this is known as the percent of change.)

Answers

23-17=6
The percentage of increase:
(6/17)*100=35.2942%

The value increase= 23-17
                              = 6
The percentage is for 100%
Thus, the increase divided by the original value, gives you the answer.
So, 6/23 x 100% is equal to 26.08%
If we round that answer up we get, 26.1

Hope this helps :))

Jon makes $78 in 12 hours of work for his mom. how much would jon make in 20 hours of work

Answers

$ 78 in 12 hrs....78/12 = 6.50 per hr

for 20 hrs...
6.50 * 20 = $ 130 <==

Answer:

$130

Step-by-step explanation:

This is a direct proportionality between the amount he makes and the time worked. As the time increases, so does the amount he makes and vice versa.

Let the amount made be A and the time T

A ∝ T,

A = KT where K is the constant of proportionality

where Jon makes $78 in 12 hours of work, A = 78, T = 12

78 = 12K

K = 6.5

A = 6.5T

In 20 hours of work, T =  20

A = 6.5 × 20

A = $130

will give award to whoever answers! 

justify each step in solving 4x - 3 = 9

4x - 3 + 3 = 9 + 3
4x = 12
4x/4 = 12/4
x = 3

Answers

4x - 3 = 9

4x = 9 + 3

4x = 12

x = 3

hope that helps, God bless!
4x−3+3=9+3Step 1: Simplify both sides of the equation.4x−3+3=9+34x+−3+3=9+3(4x)+(−3+3)=(9+3)(Combine Like Terms)4x=124x=12Step 2: Divide both sides by 4.4x/4=12/4
x=3is this right?

Solve the inequality. -2/3x – 10 < 1/3

Answers

x > -31/2

Hope this helps
x>-31/2, -15.5, or -15 1/2

-2/3x-10<1/3
add 10 to both sides
-2/3x<10 1/3
divide -2/3 (which means to flip the numbers and multiply!)
since you divide by a negative, you flip the sign!
x> -31/2, -15.5, -15 1/2

In a closing-down sale a shop reduces all its prices by 20%.
Find the sale price of a coat which previously cost $44

Answers

i honestly do not know but if you put it in the calculator I am pretty sure it will tell you
Hello! I can help you with this! There will be a 20% discount of all items, which means that there will be 80% of the original price left to pay. 100 - 20 = 80. To find the sale price of the coat, multiply 44 * 0.8. When you do that, you get 35.2. The new sale price of the coat is $35.20.

are the lines the same if the right line is a translation of the left line 4 units to the right

Answers

Yes, the lines are the same even though the right line is translation the the left line 4 units to the right. The function moves the line a certain distance. The line is not altered in any way so thus the lines are the same.


A population of rabbits is growing exponentially. The function f(x) = 5(2)t models the number of rabbits after t months.

Based on the model, what is the growth factor for the population of rabbits?

Answers

13 months

Tell me if its right...

Answer:

The growth factor is '2'

Step-by-step explanation:

Here, the given function that represents the population of the rabbits that is increasing exponentially,

[tex]f(x)=5(2)^t----(1)[/tex]

Since, the growth factor is a multiplier that increases the value per period,

Also, in an exponential growth function,

[tex]y=ab^x[/tex]

b is called the growth factor where x is a variable,

Since, in function (1) t is a variable ( time in months )

By comparing, b = 2,

Hence, the growth factor is 2 for the given function.

Your business borrowed 10 bitcoins on May 1, when 1 bitcoin was worth $1,418.86. On June 1, 1 bitcoin was worth $2,441.29. Not counting the 1 month of interest, what is the total amount, including the principal, your business owed on June 1, in dollars?

Answers

Final answer:

The business owed a total of $24,464.43, including the principal, on June 1.

Explanation:

To calculate the total amount your business owed on June 1, we need to find the value of the borrowed bitcoins in dollars on that date.

Step 1: Convert the number of borrowed bitcoins to dollars on May 1 by multiplying it by the value of 1 bitcoin in dollars: 10 bitcoins * $1,418.86/bitcoin = $14,188.6.

Step 2: Convert the value on May 1 to the value on June 1 by multiplying it by the change in the value of 1 bitcoin:

$14,188.6 * ($2,441.29/$1,418.86)

= $24,464.43.

Therefore, your business owed a total of $24,464.43, including the principal, on June 1.

The total amount owed on June 1, not counting the 1 month of interest, is $24,412.90.

To calculate the total amount owed on June 1, we need to multiply the number of bitcoins borrowed by the value of one bitcoin on that date.

On May 1, the business borrowed 10 bitcoins, and the value of one bitcoin on June 1 was $2,441.29. Therefore, the total amount owed on June 1, excluding interest, is calculated as follows:

Number of bitcoins borrowed = 10

Value of one bitcoin on June 1 = $2,441.29

Total amount owed on June 1 (in dollars) = Total amount owed on June 1 (in dollars) = [tex]10 \times $2,441.29[/tex]

Total amount owed on June 1 (in dollars) = $24,412.90

Thus, the total amount owed on June 1, not counting the 1 month of interest, is $24,412.90.

A farmer has 6 1/2 of land for growing crops. If she plants corn on 3/5 of land, how many acres of corn will she have?

Answers

you mus first find common denominator by multiplying bottom number to equal each other. 2*5=10 and 5*2=10. You must also multiply top number by same number used to find common denominator. Resulting in 6 & 5/10 and 6/10. next convert the 6 into a fraction, by multiplying by denominator. 6x10=60. 60+5 = 65. 65/10 and 6/10. Finally subtract and get 59/10. Also known as 5 & 9/10

1/6d + 2/3 = 1/4(d-2)

Answers

Yo, you seem like a cool dude. Could you post another answer on this; https://brainly.com/question/5960230 for me please. I spent 30 minutes answering it but I cannot get brainliest answer unless there is another person. 

1/6d + 2/3  = 1/4(d-2)
1/6d + 2/3 = 1/(4d-8)
Multiplying both sides by 1/(4d-8)
(4d-8/6d) + 2/3 = 1
Multiplying both sides by 6d
(4d - 8) + 2/3 = 6d
4d - 24/3 + 2/3 = 6d
4d - 22/3 = 6d
-2d = 22/3
2d = -22/3
d = -11/3

-0.785714286 as a fraction

Answers

- 392857143/500000000

Find the prime factorization of 210.

2 X 3 X 5 X 7
2 X 3 X 35
2 X 7 X 15

Answers

The answer is:  [A]:  " 2 × 3 × 5 × 7 " .
________________________________________________________

210 = 70 * 3 ;

70 * 3 = 35 * 2 * 3 ;

35* 2* 3 = 7 * 5 * 2 * 3 ; which corresponds to "Answer choice:  [A]." .
________________________________________________________

Answer: 2 X 3 X 5 X 7

Step-by-step explanation:

The given number to find the prime factorization =210

We know that 210 can be written as [tex]21\times10[/tex]

Also , 21 can be written as [tex]3\times7[/tex].

And 10 can be written as [tex]2\times5[/tex]

Then , the  prime factorization of 210 is given by :-

[tex]210=21\times10\\\\=3\times7\times2\times5[/tex]

Hence, the prime factorization of 210= 2 X 3 X 5 X 7

Molly bought a case of bottled water at the store. The case contains 48 bottles. Molly knows that she will drink 3 bottles of water each day and plans to restock her supply of water once she has fewer than 10 bottles left. Determine which inequality is used to find the number of days, x, before Molly will need to restock her supply of bottled water

Answers

Let x = number of days before Molly will need to restock
48 - 3x < 10 we use is less than because "has fewer than" 

If you solve this inequality by subtracting 48, then dividing by -3 (switch inequality sign), you get x > 12[tex] \frac{2}{3} [/tex]

48 - 3x < 10, x=13

13 days


?????????????????????

Answers

1) Option A

F = m*a This is the second Law of Newton

2) option J

d = √ [a^2 + b^2 ]

That is the application of Pythagorean theorem, which applys for right triangles.

3) Use sine ratio

sin (30°) = opposite-leg / hypotenuse

=> opposite-leg = hypotenuse * sin(30°)

opposite-leg = f(h)

hypotenuse = h

sin(30°) = 1/2

=> f(h) = h * 1/2

=> option c. f(h) = (1/2)h

4) The formula for the volume of a cylinder is V = area of the base * height

Here area of the base = π(r^2)

height = 2r

=> V (r) = 2π(f^3) <----- option G.

5) The slope - y -intercept function of the line is y = mx + b where m is the slope and b is the y-intercept.

In this problem m = c and b = d

So, the answer is y = cx + d <------ option B.

6) Use the formula speed = distance / time => time = distance / speed

=> f(x) = x / m < ------ option J

7) Use the equation of the distance

distance^2 = (x - x1)^2 + (y - y1)^2

given y = 2x + 7 and (x1,y1) = (3,0)

=> distance^2 = (x - 3)^2 + ( 2x + 7 - 0)^2

=> distance^2 = (x - 3)^2 + (2x + 7)^2

=> f(x) = √ [ (x - 3)2 + (2x + 7)^2 ] <------- option D

How many hours did Miriam stop to rest

Answers

What are you basing this on?
There’s nothing there to help u with all ur saying is the question there’s nothing to solve for u..
Other Questions
Find x value for the point that splits segment CD in half if point C is located at (2, 4) and point D is located at (3, 7). Hall may be the best representative of the earliest roots of modern psychology in that his education included ____. What did William Seward want in the 1860's? What are some common text features and visual cues "what is the difference between a physical change and a chemical change? give an example of both and explain your answer. what are the three physical states of matter?" Durkheim's research on _____ formed the foundation for the functionalist perspective of deviance. the use the epic simile in this excerpt helps readers understand that Critics ofb. f. skinner were concerned that: Te gusta pintar? S. Me gusta _____. A. tampoco B. patinar C. mucho D. a ti Which element does the electron configuration 1s22s22p2 represent ? There are 110 calories per 177.4 grams of Cereal X. Find how many calories are in 252.5 grams of this cereal. Oxygen starvation in a cell will most likely lead to The influence of our physical gestures on our psychological preferences is said to be an indication of A letter often breaks down the barrier between the reader and writer, and allows the author to set a personal tone. Which sentence from Lake's letter best demonstrates this effect?A. I would like to introduce you to my son, Wind-Wolf.B. He has black hair, dark brown eyes, olive complexion.C. He was born and raised on a reservation.D. And like so many Indian children his age, he is shy and quiet in the classroom. Almost all counselors can expect to be increasingly involved with the assessment of clients with: How do you say "Happy Bithday" in Spanish? What role do rocks have within the carbon cycle? Where at in the courtroom do the children sit to watch the trial? El tomate est ___________ vaso con jugo A. Encima delB. Debajo delC. Al lado delD. Entre The mutagens that result in cancer damage DNA by (a) destroying the cells p53 gene directly thereby increasing cell production (b) weakening the DNA strand or interfering with base pairing (c) altering the cells pH and allowing increased cell productions (d) becoming a virus that attacks DNA directly l, impairing duplication Steam Workshop Downloader