Gavin likes biking. This week his goal is to bike about 65 total miles over four days. Each day he wants to ride 1.5 times as far as he rode the day before. How far should he ride on each of the four days. Write the expressions for the distance Gavin needs to bike each day. Then relate these expressions to create an equation that represents Gavin's situation.

Answers

Answer 1

Step-by-step explanation:

let the first-day ride be x

Then the second-day ride will be =1.5 x

The third-day ride will be=1.5(1.5x)      

The Fourth-day ride will be=1.5*1.5(1.5x)  

hence for the four days the distance covered is

65=x+1.5x+1.5*1.5x+1.5*1.5*1.5x

65=x+1.5x+2.25x+3.375x

65=8.125x

divide both sides by 8.125 we have

x=65/8.125

x=8mile

the first-day ride be x=8miles

the second-day ride will be =1.5 x =1.5*8= 12miles

The third-day ride will be=1.5(1.5x) = 18miles

The Fourth-day ride will be=1.5*1.5(1.5x) = 27miles


Related Questions

solve 3(x-4)=16+5x show work

Answers

Answer:

hi… I think it's written that way

Marcia has a monthly income of $3,500. She budgets 8% for her cell phone. What amount does she budget for her cell phone, in dollars and cents?

Answers

Answer:

[tex]280 \: dollars[/tex]

Step-by-step explanation:

[tex]3500 \times .08 = 280[/tex]

Simple as that ^^^ Just find 8% of 3500

280,00$

8% of 3500$ equals to

(8/100)*3500=

280,00$=

Why is it that when comparing a squares area with a rectangles area, with the SAME PERIMETER, that the square has a greater area?

Answers

s = side length of square

4s = perimeter of square

L = length of rectangle

W = width of rectangle

P = 2L+2W = perimeter of rectangle

4s = 2L+2W .... since we want the perimeters the same

4s = 2(L+W)

s = 0.5(L+W)

s^2 = (0.5(L+W))^2 ... square both sides

s^2 = 0.25(L+W)^2

The last equation shows the area of the square, s^2, in terms of L and W. This way we can connect the square to the rectangle.

-----------------------------------

The area of the rectangle is LW

Let's subtract this from the area of the square and see what we get

A = area of square = s^2

B = area of rectangle = LW

C = difference in area

C = A - B

C = s^2 - LW

C = 0.25(L+W)^2 - LW

C = 0.25(L^2+2LW+W^2) - LW

C = 0.25L^2+0.5LW+0.25W^2-LW

C = 0.25L^2-0.5LW+0.25W^2

C = 0.25(L^2-2LW+W^2)

C = 0.25(L-W)^2

Regardless of what we pick for L and W, the expression (L-W)^2 is always positive. Squaring a negative number leads to a positive result.

So C is always positive as long as [tex]L \ne W[/tex]

If C > 0, and C = A - B, then

C > 0

A-B > 0 .... replace C with A-B

A > B .... add B to both sides

This shows the square area is always larger than the rectangle.

Again this only works if L and W are different values. If L = W, then the argument falls apart because the rectangle becomes the square.

We make [tex]L \ne W[/tex] to have a nonsquare rectangle.

A line passes through the point (-6,6) and has a slope of 3/2.

Answers

Answer:

y=3/2x+15

Step-by-step explanation:

Answer:

y=3/2+15

Step-by-step explanation:

Suppose at age 22 mort starts investing 200$ at the end of each month into a savings plan with an apr of 2.9% and he continues to do so through the next 43 years ( planning to retire at age 65). How much will be in his savigns plan towards retirement? How much of his balance was from the interested loans

Answers

Answer:

Kindly check explanation

Step-by-step explanation:

Given the following :

Monthly Payment (PMT) = 200 at the end of each period

interest rate = 2.9% = 0.029/12 = 0.0024166

Period (n) = 43 years x 12 = 516

Using the future value(FV) of an ordinary annuity:

FV = PMT[(1 + r)^n - 1] / r

FV = 200[(1 + 0.0024166)^516 - 1] / 0.0024166

FV = 200[(1.0024166)^516 - 1] / 0.0024166

FV = 200(2.4745372) / 0.0024166

FV = 204,794.93

Amount which will be in saving plan towards retirement = $204,794.93

Interest amount :

$204,794.93 - total monthly deposits

$204,794.93 - (200 * 516)

$204,794.93 - $103,200

= $101,594.93

Evaluate the expression for z = 3.

z2

Answers

Answer:

6

Step-by-step explanation:

z=3

z2= 3*2 = 6

Good luck

What is the slope of the line?
I NEED HELPP?!

Answers

Answer:

Slope of a line = rise/run

Your answer:

m = 8/5

Sharonda uses a blend of dark chocolate and milk chocolate to make the ice cream topping at her restaurant. She needs to buy 120\,\text{kg}120kg120, start text, k, g, end text of chocolate in total for her next order, and her recipe calls for twice the amount of dark chocolate as milk chocolate. Let ddd be the number of kilograms of dark chocolate she buys and mmm be the number of kilograms of milk chocolate she buys.

Answers

Step-by-step explanation:

ATQ,

Let d be the number of kilograms of dark chocolate she buys and m be the number of kilograms of milk chocolate she buys.

She needs to buy 120 kg of chocolate in total for her next order, and her recipe calls for twice the amount of dark chocolate as milk chocolate.

So,

m = 2d .....(1)

m + d = 120 ...(2)

We can also solve the above equations,

Put m = 2d in equation (2)

2d + d = 120

3d=120

d = 40

Put d = 40 in equation (1)

m = 2(40)

m = 80

Hence, she will need 40 kg of dark chocolate and 80 kg of milk chocolate.

Answer:

d+m=120

d=2m

Step-by-step explanation:

Which equation represents a line parallel to the line shown on the graph. I need this for a test so pls be quick. Last answer choice is y=-1/3x+12

Answers

The first answer choice should be parallel. This is due to opposite reciprocal slopes being parallel.

Barnes and noble needs to ship 14 mystery books, 12 science-fiction books, and 8 historical-fiction books. The store can only pack one genre of book in each box, and they must pack the same number of books in each box. What is the greatest number of books Barnes and Noble can pack in each box?

Answers

Answer: 2

Step-by-step explanation:

Given:  14 mystery books, 12 science-fiction books, and 8 historical-fiction books needs to b shipped.

If they want to pack one genre of book in each box such that they pack same number of books in each box.

Then, the greatest number of books Barnes and Noble can pack in each box

= GCD(14,12,8)

Since, 14 = 2 x 7

12 = 2 x 2 x 3

8 = 2 x 2 x 2

GCD(14,12,8)=2

Hence, the greatest number of books Barnes and Noble can pack in each box = 2

rrange the numbers in decreasing order.



a.

8.508

8.58

7.5

7.058

Answers

Answer:

8.58

8.508

7.5

7.058

Step-by-step explanation:

Answer:

8.58, 8.508, 7.5, 7.058

Step-by-step explanation:

Um, I think this means greatest to least.

8.58, 8.508, 7.5, 7.058

Look at the place values.

Two integers have a difference of 18 and a sum of 2. What is the product of the two integers?

Answers

Answer:

the product of the two integers is -80

Answer:

-80

Explanation:

it was on a mathcounts competition

someone help with this ASAP I HAVE FEW MINS !!!

Answers

Answer:

Symmetric

Step-by-step explanation:

help pls ?? anyone ?? :(

Answers

7.  yes

8. yes

9. no

10. no

b because it just is i took this

Haddle wrote a check to the grocery store for $156.00. However, when she looks at her check register later that night, she sees she only has

$122.66 In her checking account. Haddle has opted in to the standard overdraft practices at her bank. How many fees is Haddle likely to pay for

writing the check?

Answers

Answer:

she will have one fee for standard overdraft practices and that will prevent a fee from the grocery. store

Step-by-step explanation:

We are told she wrote a check to the grocery store for $156.00.

And that when she looked at her check register later that day, she had only $122.66.

This means she doesn't have sufficient balance for the grocery.

It means the bank will pay the overdraft and it attracts charges which may vary for different banks.

Thus, she will have one fee for standard overdraft practices and that will prevent a fee from the grocery store

Find the x-intercept of the graph of y = -10x - 36


The x-intercept is_____

Answers

The answer is 10 I think maybe

2÷5 × -4 what Is the answer please? ​

Answers

Answer:

-1 3/5

Step-by-step explanation:

2÷5 × -4

Work from left to right

2/5 * -4

-8/5

-1 3/5

Line AB is 14 inches long. What is the approximate area of the circle?






615.44 inches
21.98 inches
153.86 inches
43.96 inches

Answers

Answer:

The third one is closest

Step-by-step explanation:

half of the diameter=the radius 14/2 = 7 and the formula for the area of a circle is r^2π so 49 × π is 153.93804

Based on a graph below which sequence of transformation is needed to carry ABCD onto its image A’B’C’D?

Answers

Given:

The vertices of ABCD are A(2,3), B(5,6), C(8,6) and D(8,3).

The vertices of A'B'C'D' are A'(-2,6), B'(-5,3), C'(-8,3) and D'(-8,6).

To find:

The sequence of transformation is needed to carry ABCD onto its image A’B’C’D.

Solution:

The vertices of ABCD are A(2,3), B(5,6), C(8,6) and D(8,3).

If figure ABCD translated by the rule, [tex](x,y)\to (x,y-9)[/tex], then

[tex]A(2,3)\to A_1(2,-6)[/tex]

[tex]B(5,6)\to B_1(5,-3)[/tex]

[tex]C(8,6)\to C_1(8,-3)[/tex]

[tex]D(8,3)\to D_1(8,-6)[/tex]

Then the figure rotated 180 degrees clockwise about the origin. So,

[tex](x,y)\to (-x,-y)[/tex]

[tex]A_1(2,-6)\to A'(-2,6)[/tex]

[tex]B_1(5,-3)\to B'(-5,3)[/tex]

[tex]C_1(8,-3)\to C'(-8,3)[/tex]

[tex]D_1(8,-6)\to D'(-8,6)[/tex]

So, the required sequence of transformation that is needed to carry ABCD onto its image A’B’C’D is " A translation by the rule [tex](x,y)\to (x,y-9)[/tex] and then a 180° clockwise rotation about the origin".

Therefore, the correct option is D.

Can someone tell this word please. Identify the vocabulary word that matches the picture. ​

Answers

Answer:

proably and acute angle

Step-by-step explanation:

acute angles are angles that are less than 90 degrees and the picture obviouly shows an angle that is less than 90

need points sorry. hope you get the help you need

What Is 2+4? I need to know.

Answers

Answer:

the answer is 6

Step-by-step explanation:

Answer:

6! Hope this helps have a great night!!!!

Step-by-step explanation:

May I plz have brainliest?

Find the slope of the line
(1,-5),(-4,0)

Answers

Slope formula =

Y^2-Y^1/X^2-X^1

0-(-5)/-4-1
5/-5
-1

Answer:

-1

Step-by-step explanation:

slope = ΔY  / ΔX  = 5/(-5)=-1

Which expression is equivalent to 5 (h + 9)?

Answers

Answer:

5(m+9) = 5m+25

Answer:

5(m+9) = 5m+25

Step-by-step explanation:

durrrrrrrrrrrrrrr

Consider the equation and its solution. 8 (x minus 2) = 64. 8 x minus 16 = 64. 8 x = 80. X = 10. Which property is used in the last step to find that x = 10? Distributive property addition property of equality subtraction property of equality division property of equality

Answers

Answer:

Division property of equality

Step-by-step explanation:

Consider the equation and its solution. 8 (x minus 2) = 64.

8 x minus 16 = 64.

8 x = 80.

x = 10.

Which property is used in the last step to find that x = 10

The property used in the last step to find that x = 10 is called the DIVISION PROPERTY OF EQUALITY

The Division property of equality states that , when two sides of a quadratic equation are divide by the same integer that is greater than zero, both sides will be equal to one another

Let c be the integer greater than zero

ac = bc

Divide both sides by c

a = b

From the above question

8 x = 80

This is also written as:

8x = 8 × 10

Division property of equality

Divide both sides by 8

Hence,

x = 10

Answer:

division property of equality

Step-by-step explanation:

since the equation before our answer was a multiplication equation, you must counteract that with the division property of equality.

The sum of triple a number d and 5
(it’s translating expressions)

Answers

Answer:

3d+5

Step-by-step explanation:


(a)
Stephen and Karen are getting the floor redone in their house. Company A charges $215 and $0.50 per square foot to install carpet. Company B charges $100 and $0.75 per square foot to install carpet.

Determine which company would be a better choice if Stephen and Karen were having 400 square feet of carpet installed. Justify your answer using
math

Answers

Answer:

Company B

Step-by-step explanation:

Given. That :

Company A:

Initial charge = $215

Charge per square foot = 0.50

Company B:

Initial charge = $100

Charge per square foot = 0.75

Which company if installing 400 square feet of carpet :

Company A:

Total bill:

$215 + 0.50(400) =$415

Company B:

Total bill:

$100 + 0.75(400) = $400

Hence, Company B will be a better option as the total cost is cheaper than company As cost.

PLEASE HELP MEEEEEEEEEEEEEEEEEEEEEEEEe

Answers

Answer:

-140 = x

Step-by-step explanation:

Answer:

-140 =x

Step-by-step explanation:

yo, i need some help :/
What is the domain of the function represented by the table?
A). all real numbers
B). x greater-than-or-equal-to 0
C). all integers greater than or equal to zero
D). {5, 10, 15, 20, 25}

Answers

Where the picture? Don’t answer this but I guessing is C

what is value of x , 1x + 2x = 30​

Answers

Answer:

x = 10

Step-by-step explanation:

1x + 2x = 30​

3x = 30

x = 10

Which of the following is an example of the atmosphere interacting with the biosphere?

Answers

I’d say option 4

However, one may think option 3 might be possible as well. But that it is not interacting, it’s affecting.

So I’d stick with option 4.

Good luck!

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