A car rental company's standard charge includes an initial fee plus an additional fee for each mile driven. The standard charge S (in dollars) is given by the function =S+0.60M18.95, where M is the number of miles driven.

The company also offers an option to insure the car against damage. The insurance charge I (in dollars) is given by the function =I+0.15M3.70
.

Let C be the total charge (in dollars) for a rental that includes insurance. Write an equation relating C to M. Simplify your answer as much as possible.

Answers

Answer 1

Lets see... we have two companies charging two different prices. So, the first thing we need to do if find the equation of both companies. Company A: c= 0.25m+30 m is the number of miles, which costs .25 cents. Hence, .25mCompany B: c= 0.10m+40 it charges 10 cents per mile, which is 0.10 m Now, make the two equations equal to each other. The answer that we get will be the exact number when you pay the same cost for either company A or B. In other words, at that number of miles you don't care which company you choose. However, if you go beyond that number of miles or below that number of miles, it will make a difference. 0.25m+30=0.10m+40 Subtract 30 from both sides -30 -300.25m= 0.10m+10 Subtract 0.10m from both sides -0.10m -0.10m0.15m= 10 Divide both sides by 0.15 m= 66 2/3 Up to that point, company A will be the best choice. After that particular number of miles, company B will be the better choice. Hope this helps you.

~ Natalia

Related Questions

PLEASE HELP ASAP!!!

Answers

the correct answer is A because if you add 200 and 85 together to get the amount of money he has to have, and then divide that by 45, you get 13 weeks

The correct answer is A

Use k as the constant of proportionality to write the equation expressing the relationship: y varies inversely as x. if y = 10 when x = 5, determine k.

Answers

For an inverse relationship of the form
[tex]y= \dfrac{k}{x} [/tex]
you can solve for k, the constant of variation (or proportionality), by multiply both sides of the function to get [tex]xy=k[/tex]. Substituting 5 for x and 10 for y, you see that k = 50.

y = k/x

Step-by-step explanation:

Find the volume of this square pyramid, given that its height is 8 m.

A) 24 m3.

B) 72 m3.

C) 216 m3.

D) 648 m3.

Answers

Answer:

A) [tex]24\text{ m}^3[/tex].

Step-by-step explanation:

We have been given an image of a square pyramid and we are asked to find the volume of our given pyramid.

[tex]\text{Volume of square pyramid}=\frac{a^2*h}{3}[/tex], where,

a = Base length of square,

h = height of pyramid.

Upon substituting our given values in above formula we will get,

[tex]\text{Volume of square pyramid}=\frac{\text{(3 m)}^2*\text{ 8 m}}{3}[/tex]

[tex]\text{Volume of square pyramid}=\frac{9\text{ m}^2*\text{ 8 m}}{3}[/tex]

[tex]\text{Volume of square pyramid}=\frac{72\text{ m}^3}{3}[/tex]

[tex]\text{Volume of square pyramid}=24\text{ m}^3[/tex]

Therefore, the volume of our given square pyramid is 24 cubic meters and option A is the correct choice.

Answer:

A. 24 m3.

Step-by-step explanation:

Using radicals , write an equivalent expression for the expression 2 1/3

Answers

I'm assuming that the 1/3 is an exponent.

If so, then [tex]2^{1/3} = \sqrt[3]{2}[/tex]

Which is the cube root of 2. Raising any value to the 1/3 power is the same as taking the cube root.

I'm assuming that the 1/3 is an exponent.

If so, then

Which is the cube root of 2. Raising any value to the 1/3 power is the same as taking the cube root.

Rene has a coupon for $3.25 off a package of name brand cookies that normally costs $7.89. The store brand cookies coats $5.58. How much will Rene save if she uses her coupon and buys the name brand cookies instead of the store brand cookies? HELP

Answers

she would save 94 cents buying the name brand cookies

Final answer:

Rene will save $0.94 if she uses her coupon and buys the name brand cookies instead of the store brand cookies.

Explanation:

To find out how much Rene will save if she uses her coupon and buys the name brand cookies instead of the store brand cookies, we have to first determine how much the name brand cookies will cost after applying the coupon. We subtract the value of the coupon i.e. $3.25 from the original cost of name brand cookies which is $7.89. The result comes out to be $4.64.

To calculate the savings, we now have to subtract the cost of name brand cookies after coupon ($4.64) from the original cost of the store brand cookies ($5.58). Hence, the savings amount to $5.58 - $4.64 which equals $0.94

So, if Rene uses her coupon and buys the name brand cookies instead of the store brand cookies, she will save $0.94.

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If you wanted to predict the value of the y variable when the x variable is 15, you would be _____ the data.

A.) Correlating
B.) Extrapolating
C.) Interpolating

Answers

B) extrapolating ...

Answer:

If you wanted to predict the value of the y variable when the x variable is 15, you would be extrapolating the data.

Step-by-step explanation:

If you wanted to predict the value of the y variable when the x variable is 15, you would be Extrapolating the data.

Extrapolation means, estimating the value of a variable beyond its given range.

what is the approximate distance between the points (1 -2) and (-9 3) on a coordinate grid?

Answers

[tex]d= \sqrt{(-9-1)^2+(3-(-2))^2}= \sqrt{100+25}= \sqrt{125} \approx 11.18 \ \ \text{units}[/tex]

Answer:

11.18

Step-by-step explanation:

Write an equation in point-slope form for the line through the given point with the given slope. (–3, –7); m = -6/5

Answers

Point slope form : y-y₁=m(x-x₁)

Goes through (-3, -7) and the slope = -6/5

Since we are given the slope and the x₁ as well as y₁, we can simply plug everything into the point slope formula.

y - (-7) = -6/5(x - (-3))

Simplify.

y + 7 = -6/5(x + 3)

~Hope I helped!~

Rico travelled from the United States to the United Kingdom. Once Rico arrived, he converted his American dollars into British pounds (the currency in the U.K.). He gave the bank teller $500 and was given back 295 pounds. At the end of his vacation Rico had 75 pounds left over which he converted back into US dollars. How much money (in US dollars ) did Rico have when he got home? Round the answer to the hundredth.

Answers

105 us dollars is 75 pounds

How to calculate linear distance between two points on circle circumference?

Answers

The distance between two points on the circumference of a circle is called the arc. If the arc length subtends an angle θ to the center of the circle and the circle has a radius r, then the length of the arc is calculated by the formula;
θ/360 × 2πr.

Explain why 81 3/4 equals 27

Answers

81 to the 4th root is 3 and 3 cubed is 27.

General Idea:

There are few exponent rules that need to be used to simplify the rational exponent to get to the answer.

Exponent rules:

[tex] Rule\; 1: a \cdot a \cdot a \cdot a =a^4\\ \\ Rule\; 2: (a^m)^n=a^{m \times n} [/tex]

Applying the concept:

Rewriting 81 as a number with an exponent using prime factorization.

[tex] 81=3 \times 3 \times 3 \times 3 = 3^4\\ \\ Applying \; Rule \; 1, \; we\; get\; \\\\81^{\frac{3}{4}}=(3^4)^{\frac{3}{4}} \\ \\ Applying \; Rule \; 2,\; we\; get\\ \\ 3^{4 \times\frac{3}{4} } = 3^{\frac{12}{4} }=3^3=3 \times 3 \times 3 = 27 [/tex]

Conclusion:

The above explanation explains why [tex] 81^{\frac{3}{4}} =27 [/tex]

Which function is a shrink of the exponential growth function shown on the graph?
A.) f(x) = 2(3)x
B.) f(x) = 1/2(3)x
C.) f(x) = 2(1/3)x
D.) f(x) = 1/2(1/3)x

Answers

The exponential function shown in the graph is 3^x, so (1/2)3^x is a shrink of it.

Selection B is appropriate.

Consider the diagram. What is the length of segment AB?

Answers

B. 9 I think because it looks like it is bisected in the middle to cut into two equal parts. Please correct me if I am wrong. Thanks.

we know that

A median of a triangle is a line segment joining a vertex to the midpoint of the opposing side, bisecting it.

In this problem the line DB is a median of triangle ADC

The line DB is also the altitude of a triangle ADC, because is perpendicular to the side AC

AB=BC

we have that

[tex]BC=9\ units[/tex]

therefore

[tex]AB=9\ units[/tex]

the answer is the option

[tex]9[/tex]

The area of a triangle is 1440 cm^2. the base of the triangle is 5 times the height. what is the height of the triangle?

Answers

height = "h"
Triangle Area = .5 * base * height
1,440 = .5 * 5h * h
1,440 = 2.5 h^2
576 = h ^2
height = 24 centimeters
and the base is therefore 120 centimeters

Double Check
base = 120 cm
height 24 cm
area = .5 * 120 * 24
area = 1,440

A farmer has a collection of chickens and dogs. all together there are 120 legs and 43 heads. how many of each animal does he have? answer

Answers

Using trial and error method,

(26*2)+(17*4)=120 legs
26 chickens and 17 dogs

Number of chicken = 26

And, Number of dogs = 17

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

A farmer has a collection of chickens and dogs.

And, all together there are 120 legs and 43 heads.

Hence, Number of chicken = x

And, Number of dogs = y

Thus, We get;

⇒ x + y = 43

⇒ x = 43 - y .. (i)

⇒ 2x + 4y = 120

⇒ x + 2y = 60 .. (ii)

Substitute value of x from (i) to (ii);

⇒ x + 2y = 60

⇒ 43 - y + 2y = 60

⇒ y = 60 - 43

⇒ y = 17

And, From (i);

⇒ x = 43 - y

⇒ x = 43 - 17

⇒ x = 26

Thus, Number of chicken = 26

And, Number of dogs = 17

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If three tangents to a circle form an equilateral triangle, prove that the tangent points form an equilateral triangle inscribed in the circle

Answers

I added a figure so you can guide yourself throughout the proof I'm about to write, so I recommend that you download the picture beforehand and have this window and the picture's window open. Alright, let's get started!
Assuming that [tex]FED[/tex] is an equilateral triangle according to the wording of the problem, we have that the angles [tex]\widehat{AFB}=\widehat{BEC}=\widehat{CDA}=60[/tex].
We also know that the circle in green is Inscribed in [tex]FED[/tex].

The following applies to every inscribed circle inside a triangle:
The center of the inscribed circle of a triangle is the intercept of all three angle bisectors of the triangle.

The above theorem implies that the line [tex](FO) [/tex] is an angle bisector because it goes through the vertex F and the center of the inscribed circle.

The previous statement implies that the angle [tex]\widehat{OFB}=30[/tex].

Now let's work on the [tex]OFB[/tex] triangle.
Knowing that [tex]\widehat{OBF}=90[/tex] (because [tex](EF)[/tex] is tangent to the circle at B and [tex]OB[/tex] is a radius of the circle. If you're lost here, remember that a tangent to a circle is always perpendicular to the radius of the circle.) we can then derive that [tex]\widehat{FOB}=180-90-30=60[/tex] (because the sum of the measures of all angles in a triangle is always equal to 180 degrees).

In the same way, we can prove also that:
[tex]\widehat{BOE}=\widehat{EOC}=\widehat{COD}=\widehat{DOA}=\widehat{AOF}=60 degrees[/tex].
Knowing the above we notice that [tex]\widehat{BOC}=\widehat{COA}=\widehat{AOB}=120degrees[/tex].

We're at the last part of our proof here:
Now notice that [tex]\widehat{BOA}[/tex] subtends the same arc on the circle that [tex]\widehat{BCA}[/tex].
According to the inscribed angle theorem, an angle [tex]\theta[/tex] inscribed in a circle is half of the central angle [tex]2\theta[/tex] that subtends the same arc on the circle.
Therefore [tex]\widehat{BCA}=\frac{\widehat{BOA}}{2}=60degrees[/tex]

We can prove in a similar fashion that: [tex]\widehat{CAB}=\widehat{ABC}=60degrees[/tex]
Therefore all the angles of the [tex]ABC[/tex] triangle have a measure of 60 degrees, we conclude then that [tex]ABC[/tex] is equilateral.

The perimeter of an equilateral triangle with a side of 6 inches is
12 in.
18 in.
36 in.

Answers

equilateral means all sides are equal. perimeter is all sides added up. 6+6+6 = 18

Five is a solution of (Y < -3)

A.True

B.False

Answers

This is false.

The integer '5' has a higher value than -3 as it leans on the right side of a number scale, while -3 sits on the left side.

I hope this helps!

Someone please help, with a cherry on top?

View attached graph and find the approx. slope

THANK YOU SOOO MUCH!!!

Answers

your answer is 4.8. hope this helps

WILL GIVE A BRAINLEST!!!!!!

Solve and check : c-4/c-2=c-2/c+2 - 1/2-c

The solution is c =

How many extraneous solutions are there?

Answers

[tex]c=14[/tex]

There is no extraneous solution because as we put the value of c in equation (1), it does not make the equation (1) not define.

Step-by-step explanation:

Given :

[tex]\dfrac {c-4}{c-2} = \dfrac {c-2}{c+2} - \dfrac{1}{2-c}[/tex] --------- (1)

Calculation :

[tex]\dfrac {c-4}{c-2} = \dfrac {(c-2)^2+(c+2)}{(c+2)(c-2)}[/tex]

[tex]c-4 = \dfrac {(c^2-4c+4)+(c+2)}{(c+2)}[/tex]

[tex](c-4)(c+2) = (c^2-3c+6)[/tex]

[tex](c^2-2c-8) = (c^2-3c+6)[/tex]

[tex]c=14[/tex]

There is no extraneous solution because as we put the value of c in equation (1), it does not make the equation (1) not define.

For more information, refer the link given below

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Answer:

14 and Zero

Step-by-step explanation:

Is the transformation a rotation about point j?

Answers

yes, if you rotated one of the figures at point B it would overlap the 2nd figure exactly.

Yes, it seems to have rotated about 90 degrees

The band is selling wrapping paper for a fundraiser. Customers can buy rolls of plain wrapping paper and rolls of shiny wrapping paper. The band sold a total of 55 rolls and made $950. If a roll of plain wrapping paper cost $14 and a roll of shiny cost $20, how many rolls of each did they sell ?

Answers

x= # plain rolls
y= # shiny rolls

QUANTITY EQUATION:
x+y=55

COST EQUATION:
$14x + $20y= $950

SOLVE:
Solve for one variable in quantity equation. Substitute that answer in cost equation.

STEP 1:
x+y=55
subtract y from both sides
x= 55-y

STEP 2:
$14x + $20y= $950
14(55-y) + 20y= 950

multiply 14 by all in parentheses
(14*55)+(14*-y) + 20y= 950
770-14y+20y= 950

combine like terms
770+6y= 950

subtract 770 from both sides
6y= 180

divide both sides by 6
y= 30 shiny rolls

STEP 3:
Substitute y answer in either equation to solve for x.

x+y=55
x+30=55
subtract 30 from both sides
x= 25 plain rolls

Hope this helps! :)

The roll of plain wrapping paper sold is 25.

The roll of shiny wrapping paper sold is 30.

What are the linear equations that represent the question?

a + b = 55 equation 1

14a + 20b = 950 equation 2

Where:

a = roll of plain wrapping paper sold

b = roll of shiny wrapping paper sold

What is the roll of shiny wrapping paper sold?

Multiply equation 1 by 14

14a + 14b = 770 equation 3

Subtreact equation 3 from equation 2

6b = 180

Divide both sides by 6

b = 30

What is the roll of plain wrapping paper sold?

Subtract 30 from 55

55 - 33 = 25

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Which expression can you simplify by combining like terms? Clear Check 6 d 2 +5cd−3dc+8 6d2+5cd-3dc+8 12 c 2 −8 d 2 c+3dc+4 12c2-8d2c+3dc+4 7 d 2 −3 c 2 +6d−c 7d2-3c2+6d-c 16 c 2 +8cd+7c−8d 16c2+8cd+7c-8d

Answers

Final answer:

The expression that can be simplified by combining like terms is 16 c^2 + 8cd + 7c - 8d, where 8cd and -3dc are like terms and can be combined to simplify the expression to 16c^2 + 5cd + 7c - 8d.

Explanation:

The expression 16 c2 + 8cd + 7c - 8d can be simplified by combining like terms. Like terms in an algebraic expression are terms that have the same variable raised to the same power. Here, the terms 8cd and -3dc are like terms and can be combined.

Here's the step-by-step simplification:

First, identify like terms in the expression. In 8cd and -3dc, since multiplication is commutative (meaning ab = ba), cd and dc are essentially the same term. So, 8cd and -3dc can be combined.Combine the like terms by adding their coefficients. For 8cd and -3dc, we have 8 - 3 to get 5cd.Now, the simplified expression is 16c2 + 5cd + 7c - 8d.

This process of combining like terms helps in simplifying algebraic expressions, making them easier to work with.

After combining like terms, it's important to always check the answer to see if the simplification is reasonable and if there are any other like terms that can be combined.

So, the simplified expressions are:

1. [tex]$6d^2 + (5c - 3d)d + 8$[/tex]

2. [tex]$12c^2 - (c(8d - 3)) + 4$[/tex]

3. [tex]$7d^2 - 3c^2 + 6d - c$[/tex]

4. [tex]$16c^2 + c(8d + 7) - 8d$[/tex]

Let's simplify each expression by combining like terms:

1. [tex]$6d^2 + 5cd - 3dc + 8$[/tex]

Combine like terms:

[tex]$6d^2 + (5cd - 3dc) + 8$[/tex]

[tex]$6d^2 + (5c - 3d)d + 8$[/tex]

2. [tex]$12c^2 - 8d^2c + 3dc + 4$[/tex]

Combine like terms:

[tex]$12c^2 - (8d^2c - 3dc) + 4$[/tex]

[tex]$12c^2 - (c(8d - 3)) + 4$[/tex]

3. [tex]$7d^2 - 3c^2 + 6d - c$[/tex]

No like terms to combine.

4. [tex]$16c^2 + 8cd + 7c - 8d$[/tex]

Combine like terms:

[tex]$16c^2 + (8cd + 7c) - 8d$[/tex]

[tex]$16c^2 + c(8d + 7) - 8d$[/tex]

“How many times did you ride the Ferris wheel today?” Is the question a statistical question? Explain why or why not.

Answers

Well in a way...im not sure. lets see if we are dealing with statistical and last time i checked thats a part of math soo she/he is wondering how many TIMES the other person so...some part of be is saying Yes But then again no...you choose its your question xD (hope i helped somewhat)

"A statistical question is one that can be answered by collecting data and where there will be variability in that data. This is different from a question that anticipates a deterministic answer. For example, "How many minutes do 6th grade students typically spend on homework each week?" is a statistical question." the first google result. not my work

Which of the following values is closest to the mean for the set of data shown below?
23, 32, 20, 43, 41, 66, 63, 59, 54, 36, 45, 61, 55, 44, 47
A.45.9 B.50 C.58 D.54.3

Answers

the answer b

hoped it helped!!!

ok so to find the mean u need to add all the numbers (689)
then divide by how much numbers there are (49.9)
so your answer is b

please mark brainliest!

WORTH 20 POINTS!!
The endpoints of one diagonal of a rhombus are (0, -8) and (8, -4). If the coordinates of the 3rd vertex are (1, 0), what are the coordinates of the 4th vertex? (7, -12)
(7, -8)
(-8, -4)
(-4, -12)

Answers

Think about this problem as follows:

The rhombus consists of two lines which connecting the endpoints which are intersecting each other. If you have the slopes of these, you can create a relation which says that
[tex]k_1 \cdot k_2 = -1[/tex]
where [tex]k_i[/tex] are the slopes of the lines.

Now you have one slope, which is [tex]k_1 = \frac{-8 - (-4)}{0-8} = \frac{1}{2}[/tex] which means that the slope of the other one has to be

[tex]k_2 = -1 \cdot 2 = -2[/tex]

Given that you have the point (1,0) its trivial to see that this is satisfied by the point (7,-12)[tex]k_2 = \frac{-12-0}{7-1}=\frac{-12}{6} = -2[/tex]

Its worth noting that you want to draw the points, that you have the correct order when you calculate the slope.

Lisa made $286 for 13 hours of work. at the same rate, how many hours would she have to work to make $242 ?

Answers

Lisa wpuld have to work 11 hours to make $242

Determine the volume of the pencil

Answers

we have that
[Volume of the pencil]=[Volume of cylinder]+[volume of cone]
[Volume of cylinder]=pi*(0.5²)*15=11.78 cm³
[volume of cone]=pi*(0.5²)*2/3=0.52 cm³
[Volume of the pencil]=[11.78]+[0.52]=12.30 cm³

the answer is 12.30 cm³

The volume of the pencil is approximately 4.05 cm³.

To determine the volume of the pencil, we need to calculate the volumes of the cylindrical body and the conical tip separately and then add them together.

Volume of the cylindrical body:

The formula for the volume of a cylinder is [tex]V = \pi r^2h[/tex], where r is the radius and h is the height.

[tex]V_{cylinder} = \pi (0.5 cm)^2 * 15 cm[/tex]

Volume of the conical tip:

The formula for the volume of a cone is [tex]V = (1/3)\pi r^2h[/tex], where r is the radius and h is the height.

[tex]V_{cone} = (1/3) * \pi (0.5 cm)^2 * 2 cm[/tex]

Now, we can calculate the volumes:

[tex]V_{cylinder} = \pi * (0.5 cm)^2 * 15 cm = 3.53 cm^3\\\\V_{cone} = (1/3) * \pi * (0.5 cm)^2 * 2 cm = 0.52 cm^3[/tex]

Finally, we can add the volumes of the cylindrical body and the conical tip to get the total volume of the pencil:

[tex]Total\ volume = V_{cylinder} + V_{cone} = 3.53 cm^3 + 0.52 cm^3 = 4.05 cm^3[/tex]

Therefore, the volume of the pencil is approximately 4.05 cubic centimeters ([tex]cm^3[/tex]).

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An initial investment of $200 is now valued at $350. The annual interest rate is 8% compounded continuously. The equation mc022-1.jpg represents the situation, where t is the number of years the money has been invested. About how long has the money been invested? Use a calculator and round your answer to the nearest whole number.

Answers

Answer:

7 years

Step-by-step explanation:

An initial investment of $200 is now valued at $350.

The annual interest rate is 8% compounded continuously.

Formula:

[tex]A=Pe^{rt}[/tex]

Where,

A is amount, A=350

P is principle, P=200

R is rate of interest, r=0.08

t is time, t=?

Substitute the value into formula

[tex]350=200e^{0.08\cdot t}[/tex]

[tex]e^{0.8t}=1.75[/tex]

Taking ln both sides

[tex]0.08t = ln(1.75)[/tex]

[tex]t=6.99\approx 7[/tex]

Hence, 7 years ago money was invested.

Answer:

Its 7 years

Step-by-step explanation:

helppppppppppppppppppppppppppppp

Answers

Answer:
x = 4

Explanation:
For the right hand side:
log base 9 of 8 + log base 9 of (x-2) = log base 9 (8*(x-2))
= log base 9 of (8x-16)
For the left hand side:
2*log base 9 of x = log base 9 of x^2

Now, equating the two sides and solving for x:
log base 9 of (8x-16) = log base 9 of x^2
This means that:
x^2 = 8x - 16
x^2 - 8x + 16 = 0
(x-4)^2 = 0
Therefore:
x = 4

Hope this helps :)

Other Questions

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