Riding with the wind at her back, a cyclist takes an hour less time to cover 80 miles than without any wind. Riding with the wind increases the cyclist's speed by 2 miles per hour. What is her speed when riding with the wind?

Riding With The Wind At Her Back, A Cyclist Takes An Hour Less Time To Cover 80 Miles Than Without Any

Answers

Answer 1

Answer:

41 MPH

Step-by-step explanation:

Let's assume the original speed with or without, is around 82 miles, within 2 hours.

So in this case, it'd be half the miles, half the hours!

Answer 2

Solution:

Let the speed of cyclist without any wind = x miles per hour

   Speed of cyclist when speed of wind increases by 2 miles per hour =              (x + 2 )miles per hour

Also , relation that is given between speed of cyclist without wind and with wind is :Riding with the wind at her back, a cyclist takes an hour less time to cover 80 miles than without any wind.

Converting this statement into terms of equation:

[tex]\frac{80}{x}-\frac{80}{x+2}=1  \\\\ 160 = x^2 + 2x \\\\ x^2 + 2x - 160=0 \\\\ x= \frac{-2\pm\sqrt{4+640}}{2}, {\text {As speed can't be negative, so taking positive value of x}} Gives,  x =11.68[/tex]→→→To solve the Quadratic equation of type : a x² + b x + c=0, I have used discriminant method, to find the roots, which is x= [tex]\frac{-b\pm\sqrt{D=b^2-4ac}}{2a}[/tex]

Speed of cyclist without wind = 11.68 miles per hour

Speed of cyclist when wind is flowing = 11.68 +2 = 13.68 miles per hour





Related Questions

The length of a rectanglewith area 54 square centimeters is 9 centimeters. What is the perimeter of the rectangle, in centimeters?

Answers

So, first we have to find the width.


Area of a rectangle = length * width


54 = 9 * width

width = 6cm


Now we can plug this into the perimeter formula.

2w + 2l = P

P = 2(6) + 2(9)

P = 12 + 18

P = 40

Select the scatterplot that represents the data shown in the table.

Answers

C is the correct answer. It is the third graph.

Answer:

c is the correct answer

Step-by-step explanation:

HELP 20 POINTS AND WILL GIVE BRAINIST!!

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Simplified form: -3/2
Mixed number: -1 1/2
Those are the answers
Just simplify the equation
Make them as an exact form
Then divide.

Tom receive an allowance of 20 Dollars per week if he bought 3 comic books for 2.75 Dollars each and an action figure for 10.99Dollors how much of his allowance did he have left

Answers

20 - (3 * 2.75) - 10.99

20 - 8.25 -  10.99

12.75 - 10.99

1.76

A wall is 26 inches wide. Twelve inches is​ concrete, 9 inches is​ brick, and 5 inches is limestone. What fraction of the wall is​ concrete?

Answers

Final answer:

The fraction of the wall that is concrete is obtained by dividing the width of concrete (12 inches) by the total wall width (26 inches). This gives a fraction of 12/26, which simplifies to 6/13. Therefore, 6/13 of the wall is made of concrete.

Explanation:

To solve this problem, we can express the width of the concrete part of the wall as a fraction of the total wall width. First, we will identify the total width of the wall, which includes the different sections of concrete, brick, and limestone. In this case, that is 26 inches (12 inches of concrete + 9 inches of brick + 5 inches of limestone = 26 inches).

Next, we need to determine the width of the concrete section, which is 12 inches.

To express the width of the concrete wall as a fraction of the total wall width, we divide the width of the concrete part by the total wall width. So, we have: 12 inches / 26 inches. Therefore, the fraction of the wall that is concrete is 12/26, which simplifies to 6/13. Out of every 13 parts of the wall, 6 parts are made up of concrete.

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Is -27 meters deeper than -31 meters

Answers

No -31 would be deeper.

yes that is because they are both negative but when both are absolute valued, 31 is larger than 27

!!GET 43 POINTS!!
!!ASAP!!

After a holiday dinner,
there are 3 1/3 apple pies left and 2 5/6 pumpkin pies left. How much total pie is left?

Answers

To find the total pies left,we can simply add up the amount left.

The solving steps would be:

[tex]3 \frac{1}{3} + 2 \frac{5}{6} \\ = \frac{10}{3} + \frac{17}{6} \\ = \frac{10 \times 2}{3 \times 2} + \frac{17}{6} \\ = \frac{37}{6} \\ = 6 \frac{1}{6} [/tex]

Alternatively:

[tex]3 \frac{1}{3} + 2 \frac{5}{6} \\ = 3 \frac{1×2}{3×2} + 2 \frac{5}{6} \\ = 3\frac{2}{6} + 2 \frac{5}{6} \\ = 5 \frac{7}{6} \\ = 6 \frac{1}{6}[/tex]

Therefore the answer is 6 1/6.

Hope it helps!

ineed help with this qusetion plox

Answers

Assist

The answer should be Assist  

Let me know if the answer is wrong and i'll correct it


Answer:

Step-by-step explanation:

assist

What is the sum 4x+1/x+2 + x-1/3x

Answers

Answer:

[tex]\dfrac{4x+1}{x+2}+\dfrac{x-1}{3x}=\dfrac{13x^2+4x-2}{3x^2+6x}[/tex]

Step-by-step explanation:

[tex]Domain:\\x+2\neq0\ \wedge\ 3x\neq0\\\\x\neq-2\ \wedge\ x\neq0[/tex]

[tex]\dfrac{4x+1}{x+2}+\dfrac{x-1}{3x}=\dfrac{(4x+1)(3x)}{(x+2)(3x)}+\dfrac{(x-1)(x+2)}{(3x)(x+2)}\\\\=\dfrac{(4x)(3x)+(1)(3x)+(x)(x)+(x)(2)+(-1)(x)+(-1)(2)}{(3x)(x+2)}\\\\=\dfrac{12x^2+3x+x^2+2x-x-2}{(3x)(x)+(3x)(2)}\\\\=\dfrac{13x^2+4x-2}{3x^2+6x}[/tex]

Mrs.gauthier plans to take her class on 2 field trips this year there are 23 students in her class and each field trip will cost $5 per student use mental math to find the total cost for both field trips

Answers

If there is 2 field trips with 23 students and each student costs $5 dollars. So for the 1st trip it will be 23x$5

1st trip- $115

And on the second trip its the same because there is 23 students that cost 5 dollars so it will be 23x5

2nd trip- $115

To find out the total of both trips youd add 115+115/

In total, for both trips it will cost $230 dollars.

which is a disadvantage of purchasing and owning a home?

Answers

The answer to your question is,

B. Homeowners pay additional property taxes

-Mabel <3

Final answer:

Owning a home can lead to a lack of flexibility, high maintenance costs, and financial risks associated with changes in the housing market.

Explanation:

A significant disadvantage of buying and owning a home is the commitment and reduced flexibility compared to renting. When you purchase a home, it becomes a major part of your portfolio, any change in the housing market can directly affect your financial status. Not to mention, if you need to move for a career opportunity or a change in life circumstances, it can be challenging to sell the house, especially if the market conditions are unfavorable.

Furthermore, home ownership often comes with substantial maintenance costs and responsibilities. Unlike renting, where the landlord typically handles maintenance tasks, as a homeowner, these responsibilities and costs are up to you. This can include routine tasks such as gardening and cleaning, to significant unexpected costs like roof replacement or plumbing issues.

Additionally, despite the potential financial return of selling the house in the future for more than you paid for it, this is not guaranteed. The housing market can fluctuate and you may not always make a profit on the resale of your home.

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Six people can sit at each table.

How many tables are needed for 175 people?

Answers

175/ 6 = 29.1

So you would need at least 30 tables.

Hope this Helps!!

So to figure this out first setup the equation to do so take note of the amount of people and how many can sit at a table.

6 and 175

so now make the equation which will be

175/6=29.1

Round to the most is 30. So 30 tables are needed to seat 175 people.

Is the simplified form of 2 square root of 3 + 3 square root of 3 rational?

Answers

[tex]2\sqrt3+3\sqrt3=(2+3)\sqrt3=5\sqrt3-\text{It's an irrational number}[/tex]

No it is not rational

Given the equation: y=mx+b

m=slope

true

false

Answers

Your answer is true.

[tex]y=mx+b[/tex]

The equation is used to find the equation of a line in slope-intercept form.

m is used to represent the slope.

x is used to represent the x-axis.

y is used to represent the y-axis.

b is used to represent the y-intercept.

If you have any questions, feel free to ask! :)

blake thinks the solution to the equation 4=6-2x is -5 is he corect? explain

Answers

He isn't correct. Blake added 6 to both sides instead of subtracting 6 from both sides which gave him 10=-2x ---> x=-5 isn't correct. Instead, he should have subtracted 6 from both sides and then divide. the answer would turn out to be x= -2


5 1/5 in simplest form

Answers

That is the simplest for the number can be in

If you mean 5 and 1/5 then that is the simplest form.

jeffrey purchased a card for $180 that gives him 20 visits to a new gym and includes a one-time fee for unlimited use of the sauna. After 5 visits, Jeff has $123.75 left on the card, and after 11 visits, he has $74.25 left on the card. Write an equation that Jeffrey can use to determine the cost of each visit and the fee for the sauna use.

Answers

There is many ways to do this but i did it this way.

180-123.75= 56.25

56.25/5=11.25

=11.25

The value of the sauna fee is $ 15, while each visit to the gym is worth $ 8.25.

Since Jeffrey purchased a card for $ 180 that gives him 20 visits to a new gym and includes a one-time fee for unlimited use of the sauna, and after 5 visits, Jeff has $ 123.75 left on the card, and after 11 visits, he has $ 74.25 left on the card, to determine an equation that Jeffrey can use to determine the cost of each visit and the fee for the sauna use the following calculation must be performed:

The difference between the remaining sum after 5 visits and 11 visits should be obtained, and then divided by 6 to obtain the value of a visit to the gym. Then, you must multiply this result by 20, and subtract the result from the initial value of 180 to know the value of the sauna fee.

(123.75 - 74.25) / 6 = X 49.5 / 6 = X 8.25 = X 180 - (8.25 x 20) = X 180 - 165 = X 15 = X

Therefore, the value of the sauna fee is $ 15, while each visit to the gym is worth $ 8.25.

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Jodi is cutting out pieces of paper that measures 8 1/2 inches by 11 inches from a larger sheet of paper that has an area of 1,000 square inches. What is the area of each piece of paper that Jodi is cutting out

Answers

Answer:

the area of each piece of paper that Jodi is cutting it is 93.5.

the width of a rectangle is 12 cm less than the length the perimeter is 156 cm. Find the length and width

Answers

We can write this question as an equation to solve it. Using L for length and W for width we know that

L+L+W+W=perimeter
2L+2W=perimeter

We can put the value of the perimeter into this

2L+2W=156cm

Next, we have to make sure all the terms (letters) are the same so we can solve it. This means we have to rewrite either the length or width in terms of the other.

We know the width is 12cm less than the length, which is the same as saying L-12
Then we substitute this into the equation and solve L

2L+2(L-12)=156
2L+2L-24=156
4L-24=156
4L=180
L=45cm

Next we use this value to find W.
45-12=33
W=33cm

|x|=13 Can someone please help me fin the solution? Pleaseeeeeeeee ASAP, and can you explain it to?

Answers

The absolute value of 13 is 13. The absolute value of a number is always positive.

What is 1 2/3 times 2 5/8

Answers

4 3/8 because 1 2/3 and 2 5/8 multiplied together is that.

change each to an improper fraction

1 2/3 = (3*1+2)/3 = 5/3

2 5/8 = (8*2+5)/8 = 21/8

5/3 * 21/8  = 105/24

divide by 3

35/8

4*8 = 32  35-32 = 3

4 3/8

theoretical probability and experimental probability are the same true or false?

Answers

Answer:

FALSE

Step-by-step explanation:

Final answer:

The statement 'theoretical probability and experimental probability are the same' is generally false. Theoretical probability is what we expect to happen, while experimental probability is based on actual results from experiments. With more trials, these two probabilities tend to get closer, thanks to the Law of Large Numbers.

Explanation:The statement 'theoretical probability and experimental probability are the same' is generally false. Theoretical probability is defined as the number of desired outcomes divided by the number of possible outcomes, assuming that all outcomes are equally likely. It is what we expect to happen in an experiment.On the other hand, experimental probability is the proportion of times an outcome occurs based on actual experimental results. In other words, it is the data observed from repeated trials of an experiment. It's worth noting that with an increasing number of trials, experimental probability tends to get closer to theoretical probability, in accordance with the Law of Large Numbers.

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what is the line equation of the line parallel to the y-axis and 3 units to the right of the y-axis?
A. X=-3
B. X=3
C. Y=-3
D. Y=3

Answers

B x = 3

the equation of a line parallel to the y- axis is x = c

where c is the value of the x-coordinate the line goes through

here the line is 3 units to the right of the y-axis, that is x = 3

thus equation is x = 3


The line option is option  B x = 3

The following information should be considered:

The equation of a line parallel to the y- axis is x = c Here c is the value of the x-coordinate the line goes through Here the line is 3 units to the right of the y-axis, that is x = 3

Therefore,  equation is x = 3

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maria ran 12 miles las week phoebe ran 60 miles last week how many times as far did phoebe run compared to the

Answers

5 times as far take 60 and divide by 12 and you get 5

X+90 = 4x
What does x equal?

Answers

From what I remember it should be 30

Standard form:  −3X + 90 = 0


you do 90/4 I think I'm not the best at math but I'm trying to help

The system of equations shown below is graphed on a coordinate grid:

3y + x = 4
2y − x = 6

Which statement is true about the coordinates of the point that is the solution to the system of equations?

a. It is (−2, 2) and lies on both lines.
b. It is (−5, 3) and lies on both lines.
c. It is (−5, 3) and does not lie on either line.
d. It is (−2, 2) and does not lie on either line.

Answers

(−2, 2)

3(2) + (-2) = 4

6 - 2 =4

4 = 4 .............TRUE

2(2) − (-2) = 6

4 + 2 = 6

6 = 6 ..............TRUE

Answer:

a. It is (−2, 2) and lies on both lines.

Answer:

The answer is A. It is (−2, 2) and lies on both lines.

Hope This Helps!

the masses of four cars loaded on a car transporter are 2.1 tonnes 3.7 tonnes 2.8 tonnes and 1700kg what is the total mass in tonnes

Answers

First you turn the the kg to tonnes so it’ll be 1.7 tonnes, then you simply add them as follow:

2.1 + 3.7 + 2.8 + 1.7

So the answer will be 10.3 tonnes
Final answer:

To find the total mass of the four cars, first convert the mass given in kilograms to tonnes, and then sum all the masses. The total mass of the cars on the car transporter is 10.3 tonnes.

Explanation:

The total mass of the four cars loaded on a car transporter can be calculated by first ensuring all the masses are in the same unit. The masses are given as 2.1 tonnes, 3.7 tonnes, 2.8 tonnes, and 1700 kg. We must convert the mass given in kilograms to tonnes before we add them together, as there are 1000 kg in a tonne.

To convert 1700 kg to tonnes:

1700 kg ÷ 1000 = 1.7 tonnes

Now that all masses are in tonnes, we sum them up:

2.1 tonnes3.7 tonnes2.8 tonnes1.7 tonnes

Total mass in tonnes = 2.1 + 3.7 + 2.8 + 1.7 = 10.3 tonnes.

Therefore, the total mass of the four cars on the car transporter is 10.3 tonnes.

How do I factor trig functions?
I am stuck on how to factor out equations like 1+sinX-cos2x=0
I am confused on where to go from here to solve the equation. Pls help.

Answers

Use cos2x =1-2sin^2x

1+sinx- (1-2sin^2x) = 1+ sinx -1+2sin^2x

=sinx+2sin^2x=sinx(1+2sinx)

Therefore

Either sinx=0 or 1+ sin2x =0

X=npi or sin2x=-1

Sin2x=sin 3pi/2

2x= npi +(-1)^n3pi/2

x=npi/2 + (-1)^n 3pi/4

On a piece of paper, graph y> -2x -2 . Then determine which answer choice matches the graph you drew.

Answers

Answer:

C) Graph B

Step-by-step explanation:

All of these equations have the line y = -2x - 2 graphed.

In the inequality, we have the symbol greater than or equal to.  This tells us the line drawn must be solid, not dashed.  This means the correct graph is either B or D.

Since it is greater than or equal to, the shaded area must be above the line.  This is graph B.

We need to therefore plot the graph passing through the coordinate point (0, -2) and (-1, 0). Option B is correct

Graph of inequality functions

Inequality are expression not separated y an equal sign. For an inequality, the upper graph is shaded for greater than and the lower part shaded for less than sign.

Since the sign is greater than and equal to, hence the line will be a solid line as shown in the graph.

Given the inequality y≥ -2x -2. Find the intercepts

If x = 0

y = -2(0) - 2

y = -2

The y-intercept is at (0,-2

If y = 0

0 = -2x - 2

2x = -2

x = -1

The x-intercept is at (-1,0)

We need to therefore plot the graph passing through the coordinate point (0, -2) and (-1, 0) as shown

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what's 3 and 1 in a half

Answers

the answer to the question is 4 1/2
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