Taylor and Morgan would like to spend some time on the river while camping with their family. Taylor wants to rent a two-person kayak. There is a $5 setup fee for kayak rentals and then kayaks are rented at $8 per hour. The setup fee for canoes is $9 and they are rented at $6 per hour. Determine the number of hours it takes for canoe rentals and kayak rentals to cost the same amount.

Answers

Answer 1

Answer:

After 2 hrs canoe rentals and kayak rentals cost would be same.

Step-by-step explanation:

Let the number of hours be 'x'.

Given:

Set up fee for Kayak rental = $5

Hourly rate for Kayaks rental = $8

Solution:

First we will find the total cost of Kayak rentals.

total cost of Kayak rentals can be calculated by sum of Set up fee for Kayak rental and Hourly rate for Kayaks rental multiplied by number of hours.

framing in equation form we get;

total cost of Kayak rentals = [tex]5+8x[/tex]

Now Given:

Set up fee for Canoe rental = $9

Hourly rate for Canoe rental = $6

Now we will find the total cost of Canoe rentals.

total cost of Canoe rentals can be calculated by sum of Set up fee for Canoe rental and Hourly rate for Canoe rental multiplied by number of hours.

framing in equation form we get;

total cost of Canoe rentals = [tex]9+6x[/tex]

Now to find the number of hours when both rentals would cost same we will make both the equation equal we get;

[tex]5+8x=9+6x[/tex]

Combining like terms we get;

[tex]8x-6x=9-5\\\\2x=4[/tex]

Now Dividing both side by 2 we get;

[tex]\frac{2x}{2}=\frac{4}2\\\\x=2\ hrs[/tex]

Hence After 2 hrs canoe rentals and kayak rentals cost would be same.

Answer 2

Final answer:

To find when the cost of renting a canoe equals the cost of renting a kayak, we set up an equation for each rental's cost, equalize them, and solve for the number of hours. It takes 2 hours for both to cost the same.

Explanation:

To determine the number of hours it takes for canoe rentals and kayak rentals to cost the same amount, we can set up an equation based on the cost structures provided:

Kayak rental: $5 setup fee + ($8 per hour × number of hours)Canoe rental: $9 setup fee + ($6 per hour × number of hours)

If we let h be the number of hours, the costs for both rentals can be expressed as $5 + 8h (kayak) and $9 + 6h (canoe). To find when they cost the same, we can set these expressions equal to each other:

5 + 8h = 9 + 6h

Now, let's solve for h:

Subtract 6h from both sides to get the terms involving h by themselves:

5 + 8h - 6h = 9 + 6h - 6h

5 + 2h = 9

Next, subtract 5 from both sides to solve for h:

2h = 9 - 5

2h = 4

Finally, divide both sides by 2:

h = 4 / 2

h = 2

The number of hours it takes for the cost of renting a canoe and a kayak to be the same is 2 hours.


Related Questions

Solve the following system of equations graphically.



x = -5

y = -6



What is the solution set?
Ø
{(-5, -6)}
{(-6, -5)}

Answers

Answer: The right answer is [{-5,-6]}

Explanation: I got it right on my test

Answer:

[{-5,-6]}

Step-by-step explanation:

Select the correct answer.
The temperature on Saturday was 2°C. On Sunday, it became 4°C colder. What was the temperature on Sunday?
7O

Answers

Answer:

6C

Step-by-step explanation:

Final answer:

By subtracting the 4°C decrease from the initial temperature of 2°C, it is determined that the temperature on Sunday was -2°C.

Explanation:

The question involves a basic mathematics operation related to temperature changes. The temperature on Saturday was 2°C, and on Sunday, it became 4°C colder. To find the temperature on Sunday, you simply need to subtract 4°C from Saturday's temperature:

Saturday's temperature: 2°C

Temperature decrease: 4°C

Sunday's temperature: 2°C - 4°C = -2°C

Thus, the temperature on Sunday was -2°C.

In a class, 8/9 of the students have blue eyes.
If 32 students have blue eyes, how many students are in the class in total?

Answers

32/8=4
4x9=36
36 students total

Write a word problem that can be solved by dividing 10 by 2/3 include the answer to the problem

Answers

Answer:  

Step-by-step explanation:

you need to divide 10 by 2/3.

Katty has 10/1 tanks of gas fuel in his truck. He uses 2/3 of it each day.

Abigail's car uses 3 2/3 gallons of gas every hour on a long distance trip. How many gallons does the car use in 8 1/2 hours?

Answers

Answer:

31.166 repeating

Step-by-step explanation:


Find the y-intercept of the line: 9x – 8y + 5 = 0

Answers

Answer:

-8y = -9x - 5

y = (9/8)x + 5/8

Step-by-step explanation:

y-int 5/8

Final answer:

The y-intercept of the given line equation 9x – 8y + 5 = 0, is 5/8, which is obtained by rearranging the equation into the slope-intercept form.

Explanation:

The subject pertains to finding the y-intercept of a line from a given equation, which is a topic in Algebra.

The equation given is 9x – 8y + 5 = 0. First, we need to rearrange the equation into the slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.

Arranging the equation, we get: -8y = -9x -5, which simplifies further to y = 9/8x + 5/8. So, the y-intercept of the line is 5/8.

Learn more about y-intercept here:

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--x² + 5x – 8=0
What is the x

Answers

Answer:

x =(-5-√57)/2=-6.275

Step-by-step explanation:

Write as an equation/inequality. x is less than or equal to 38.

Answers

Answer:

x[tex]\leq[/tex]38

Step-by-step explanation:

bring back the x and the 38 with a space between to decide on the symbol put back i the less than sign between both terms then put a line underneath to form the symbol less than or equal to.

The measure of CDA is 113.42°. what is the value of x?

Answers

I need to know x is exactly

Is a 24 square centimeter rectangle larger than a 24 square inch rectangle?

Answers

Answer:

No, a 24 square centimeter rectangle is smaller than a 24 square inch rectangle

Step-by-step explanation:

we know that

[tex]1\ in=2.54\ cm[/tex]

so

Convert in^2 to cm^2

[tex]24\ in^2=24(2.54)^2=154.8\ cm^2[/tex]

so

[tex]24\ cm^2 < 154.8\ cm^2[/tex]

therefore

[tex]24\ cm^2 < 24\ in^2[/tex]

A 24 square inch rectangle is larger than a 24 square centimeter rectangle due to unit conversion.

No, a 24 square inch rectangle is larger than a 24 square centimeter rectangle.

To compare rectangles of different units, we need to convert the units to the same measurement. Since 1 inch is equal to 2.54 centimeters, a square inch is larger than a square centimeter.

Therefore, a 24 square inch rectangle has a greater area than a 24 square centimeter rectangle.

X3-8y3+27+18xy factorise

Answers

Answer:

this expression is not factorable

Step-by-step explanation:

my math problem dealing with fractions ask What is 1/8 of 9?

Answers

Answer:

a

Step-by-step explanation:

Answer:

1 1/8

Step-by-step explanation:

1/8 of 9

Of means multiplication

1/8 x 9

= 9/8

= 1 1/8

Suppose you are choosing between two checking accounts. One account charges you $1.50 ATM
fee every time you withdraw money from a non-sponsored ATM, and the other charges you no
ATM fees and a $15 monthly fee.
How many ATM transactions are equivalent to $15 in monthly fees?

Answers

Answer:

10

Step-by-step explanation:

$15.00 / $1.50 = 10

the equivalent fraction of 2/4​

Answers

Answer:

1/2

Step-by-step explanation:

u could simplify it to 1/2 pls give brainliest answer

Answer: 1/2 and if you mean multiplying 4/8 because 2 ÷ 2 = 1 and 4 ÷ 2 = 2, and if you mean multiplying 2 • 2 = 4 and 4 • 2 = 8 so those are two answers.

I NEED THE ANSWER ASAP PLEASE

Answers

72.5+5.6= 78.1
78.1 degrees

-4x-2y=-12 4x+8y=-24

Answers

Answer:

[tex]x=6\\ \\y=-6[/tex]

Step-by-step explanation:

Given the system of two equations:

[tex]\left\{\begin{array}{l}-4x-2y=-12\\ \\4x+8y=-24\end{array}\right.[/tex]

Add these two equations (left side add to left side and right side add to right side):

[tex]-4x-2y+4x+8y=-12+(-24)\\ \\-2y+8y=-12-24\\ \\6y=-36\\ \\y=-6[/tex]

Substitute [tex]y=-6[/tex] into the first equation:

[tex]-4x-2\cdot (-6)=-12\\ \\-4x+12=-12\\ \\-4x=-12-12\\ \\-4x=-24\\ \\x=6[/tex]

which has gradient -1/2 and cuts the y-axis at 4​

Answers

Answer:

y = - [tex]\frac{1}{2}[/tex] x + 4

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Here m = - [tex]\frac{1}{2}[/tex] and c = 4, thus

y = - [tex]\frac{1}{2}[/tex] x + 4 ← equation of line

Tickets to the garden show cost $6.75 for adults and $3.75 for children. By rounding to the nearest whole dollar, find an estimate of the cost for a family with 2 adults and 3 children to visit the garden show. A. $21 B. $23 C. $24 D. $26

Answers

Answer:

$26

Step-by-step explanation:

$6.75 - $7

$3.75 - $4

2 adults = 7x2= $14

3 children = 4x3= $12

$14 + $12 = $26

The answer is D. $26.


Factor the expression. 36y2 – 84y – 147


(2y + 7)(6y – 7)

3(2y + 7)(6y + 7)

3(2y – 7)(6y + 7)

(2y – 7)(18y + 21)

Answers

Answer:

1) 3 (6y+7) (2y−7)

2) 12y2+28y−49

3) 36y2+168y+147

4) 36y2−84y−147

5) 3(6y+7)(2y−7)

A math teacher graded 45 problems in 3/5 of an hour. At that rate, how many problems can she grade in one hour

Answers

Answer:

75

Step-by-step explanation:

45*1/3=15

15*5=75

Answer: 75 problems

Step-by-step explanation:

3/5 of an hour is the same as 3/5 x one hour.

one hour is the same as 60 minutes , this means that 3/5 of an hour is the same as :

3/5 x 60 = 36 minutes

This means that , the teacher graded 45 problems in 36 minutes. then in 1 minutes ;

The teacher will grade 45/36 problems

so in 60 minutes ;

the teacher will grade 45/36 x 60 = 75 problems

if a car is 200 inches long, and the truck is 75% longer, how long is the truck

Answers

Your answer will be 350 inches long

What identity can be used to rewrite the expression 27x^3-64?


Answers

Option A:

Difference of cubes

Solution:

Given expression is [tex]27 x^{3}-64[/tex].

27 can be written as [tex]3^3[/tex].

64 can be written as [tex]4^3[/tex].

[tex]27 x^{3}-64=3^3x^3-4^3[/tex]

[tex]27 x^{3}-64=(3x)^3-4^3[/tex]

To find the identity to rewrite the given expression:

Option A: Difference of cubes

[tex]27 x^{3}-64[/tex] can be rewritten as [tex](3x)^3-4^3[/tex].

That means the difference of two cubes.

So, it is true.

Option B: Difference of squares

[tex]27 x^{3}-64[/tex] cannot be written as square terms.

So, it is false.

Option C: Sum of cubes

[tex]27 x^{3}-64[/tex] cannot be written as sum of cubes.

So, it is false.

Option D: Pythagorean Triples

[tex]27 x^{3}-64[/tex] cannot be written as Pythagorean Triples.

So, it is false.

Hence difference of cubes if the correct answer.

9. Martika says factors and multiples are

related. Use the equation 6 X 7 = 42

to describe the relationship between

factors and multiples.

BBOUD SOTTO

Answers

Answer:

So the factors and multiples of 42 are 1, 2, 3, 6, 7, 14, 21, 42

Step-by-step explanation:

Factors are what you can multiply to get a number and a multiples are what you get after multiplication. We can determine the factors of 42. The multiples of 42 are:

[tex]1 x 42= 42[/tex]

[tex]2 x 21= 42[/tex]

[tex]3x 14 = 42[/tex]

[tex]6 x 7 = 42[/tex]

So the factors of 42 are 1, 2, 3, 6, 7, 14, 21, 42

The multiples of 42 are 1,2,3,4,5,6 etc

So common multiples and factors are 1, 2, 3, 6, 7, 14, 21, 42

Final answer:

In the equation 6 X 7 = 42, 6 and 7 are factors and 42 is the multiple. Factors are numbers that can be exactly multiplied to get another number, while a multiple is a number that can be divided evenly by another number. Hence, the relationship between factors and multiples is inherently interconnected.

Explanation:

In the equation 6 X 7 = 42, 6 and 7 are the factors, and 42 is the multiple. Factors are numbers you can exactly multiply together to get a another number, in this case 6 and 7 are factors of 42 because when multiplied together, they equal 42. On the other hand, a multiple is a number that can be divided by another number without leaving a remainder, so 42 can be evenly divided by 6 or 7, making it a multiple of those numbers. The relationship between factors and multiples can be seen as two sides of the same coin - factors are what you multiply together to get a multiple.

Learn more about Factors and Multiples here:

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If side A is twice as long as B and C is 25 using the Pythagorean Theorem,What are the lengths of side A and B? Round to the nearest tenth if necessary

Answers

Answer:

The lengths of side A is 22.4 and B is 11.9.

Step-by-step explanation:

Given:

If side A is twice as long as B and C is 25 using the Pythagorean Theorem.

Now, to find the lengths of side A and B.

Let the side B be [tex]x.[/tex]

So, the side A be [tex]2x.[/tex]

Side C = 25.

Now, to solve by using Pythagorean Theorem:

A² + B² = C²

[tex](2x)^2+(x)^2=(25)^2[/tex]

[tex]4x^2+x^2=625[/tex]

[tex]5x^2=625[/tex]

Dividing both sides by 5 we get:

[tex]x^2=125[/tex]

Using square root on both sides we get:

[tex]x=11.18.[/tex]

B rounding to the nearest tenth =  11.9.

Now, to get A by substituting the value of [tex]x[/tex]:

[tex]2x\\=2\times 11.18\\=22.36.[/tex]

A rounding to the nearest tenth =  22.4.

Therefore, the lengths of side A is 22.4 and B is 11.9.

What would be 49.38 rounded to tenthes

Answers

Answer:

49.4

Step-by-step explanation:

Round up, since the 8 [tex]\geq[/tex] 5

Oh the other side of the balance is 4 oz and another 4 oz and on the other side is 8 oz. <— To help you find out the answer. Please I’d like some help?

Answers

Answer:
11

Explanation:
4+7 = 11
And we are trying to make it 0.
So we need to add 11 more on the other side to make it even.

Answer this question please. I need help!!☺️

Answers

Step-by-step explanation:

From the looks of it, it seems that you're factoring out the greatest common factor. I gotcha covered.

The square boxes are the biggest common factors in those equations. Hopefully, this helps!

28v^3+16v^2-21v-12 factor by group please

Answers

The factor of [tex]28v^3+16v^2-21v-12[/tex] = [tex](7v+4)(2v+\sqrt{3})(2v+\sqrt{3})[/tex] or [tex](7v+4)(4v^2-3)[/tex]

Step-by-step explanation:

The given equation:

[tex]28v^3+16v^2-21v-12[/tex]

To find, the factors of [tex]28v^3+16v^2-21v-12[/tex] = ?

∴ [tex]28v^3+16v^2-21v-12[/tex]

[tex]=(4\times 7)v^3+(4\times 4)v^2-(3\times 7)v-(3\times 4)[/tex]

= [tex]4v^2(7v+4)-3(7v+4)[/tex]

= [tex](7v+4)(4v^2-3)[/tex]

= [tex](7v+4)[(2v)^2-\sqrt{3}^2][/tex]

Using the algebraic identity,

[tex]a^{2}-b^{2}=(a+b)(a-b)[/tex]

= [tex](7v+4)(2v+\sqrt{3})(2v+\sqrt{3})[/tex]

∴ The factor of [tex]28v^3+16v^2-21v-12[/tex] = [tex](7v+4)(2v+\sqrt{3})(2v+\sqrt{3})[/tex] or [tex](7v+4)(4v^2-3)[/tex]

A school plans the weekly reading activities. They have 18 storys books, which is 4 books more than 2 times that of science books. What is the number of science books?

Answers

Answer:

[tex]Number\ of\ science\ books=7[/tex]

Step-by-step explanation:

[tex]Let\ number\ of\ science\ books=x\\\\Story\ books=18\\\\2\times science\ books+4=Story\ books\\\\2x+4=18\\\\Subtract\ 4\ from\ both\ the\ sides\\\\2x+4-4=18-4\\\\2x=14\\\\Divide\ both\ sides\ by\ 2\\\\\frac{2x}{2}=\frac{14}{2}\\\\x=7\\\\Number\ of\ science\ books=7[/tex]

Where would you put 2 1/8th on a number line?

Answers

Answer:

See diagram and explanation

Step-by-step explanation:

A number on the right is greater than a number on the left on the number line.

Mark numbers 2 and 3 on number line (number 3 is to the right from number 2, because 3 > 2).

Divide the unit segment  between numbers 2 and 3 into 8 equal parts (this segment is the unit segment because the distance between 3 and 2 is 1).

Each such part represents [tex]\frac{1}{8}[/tex] of the segment.

Mark the number [tex]2\dfrac{1}{8}[/tex] next to the right from 2 (you have to take 2 and 1/8).

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