A car sharing service offers a membership plan with a $50 per month fee that includes 10 hours of driving each month and charges $9 for each additional hour
(A) Write a piecewise definition of the cost F(x) for a month in which a member uses a car for x hours
(B) Graph F(x) for 0 < x s 15
(C) Find lim x--->10 F(x), lim x--->10F(x), and lim x--->10F(x), which- ever exist.

Answers

Answer 1

Answer and Step-by-step explanation:

Given:

Charges includes 10 hour per month = $50

Charges for additional hour = $9

Piecewise definition of cost F(x) for a month in which a member use a car for  hours.

Find limits?

Find lim x--->10 F(x), lim x--->10F(x), and lim x--->10F(x), which- ever exist.

Lim x → 10- F(x) = 50$

Lim x → 10 [ 9x – 70] = 9( 10) – 70  

                                = 90 – 70

                                = 20 > 10

Limit does not exist.

Lim x → 10+ F(x) = 50$

Lim x → 10+  F(x) = Lim x → 10+   [90x – 70]

                         = 90 – 70

                          = 20 > 10

Limit does not exist.

Lim x → 10 F(x) = 50$

An integer or an decimal.

The limit does not exist.

Answer 2

The piece wise definition of the cost [tex]f(x)[/tex] for a month in which a member uses a car for [tex]x[/tex] hours is given by the equation,[tex]f(x)= 50+9(x-10)[/tex].

Given,

Membership plan is [tex]\$50[/tex] per month.

We have to write a piece wise definition of the cost [tex]f(x)[/tex] for a month in which a member uses a car for [tex]x[/tex] hours.

Here, [tex]\$[/tex][tex]$50[/tex] per month fees includes 10 hours of driving each month, so the cost for a month is given as,

[tex]f(x)= 50+9(x-10)[/tex]

Here [tex]x[/tex] is the no. of additional hours for the month.

Further,

[tex]f(x)= 9x-40[/tex].

Now at,

[tex]lim _{x \to 10^+}f(x) = 9\times 10-40\\[/tex]

Or,

[tex]f(x)= 90-40\\f(x)=50[/tex]

Similarly, at left limit,

[tex]lim _{x \to 10^-}f(x) = 9\times (-10)-40[/tex]

Or,

[tex]f(x)=-90-40[/tex]

[tex]f(x)=-130[/tex]

Finally at [tex]x=10[/tex], [tex]f(x)=9\times10-40[/tex]

[tex]f(x)=90-40\\f(x)=50[/tex]

Since [tex]lim{x \to}10^+[/tex] [tex]\neq limx\to 10^-\neq f(x) (at x= 10)[/tex]

So the required function [tex]f(x)[/tex] is discontinuous at [tex]x=10[/tex]

Hence the piece wise definition of the cost [tex]f(x)[/tex] for a month in which a member uses a car for [tex]x[/tex] hours is given by the equation,[tex]f(x)= 50+9(x-10)[/tex].

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Related Questions

Edgar has 20 dimes and nickels,all together sum up to $1.40.what does each one of them cost?

Answers

Answer:Edgar has 12 nickles and 8 dimes.

Step-by-step explanation:

Write the expression using exponents.

a⋅a⋅c⋅c

Answers

The expression using exponents we can rewrite as [tex]a^2 . c^2[/tex] .

What are exponents ?The number of times a number is multiplied by itself is referred to as its exponent. For instance, 2 to the third (written as [tex]2^3[/tex] ) means: 2 x 2 x 2 = 8. 2 x 3 = 6 does not equal [tex]2^3.[/tex] Keep in mind that a number raised to the power of one is itself.Exponentiation is the process of expressing huge numbers in terms of powers. That is, exponent refers to the number of times a number has been multiplied by itself.The key distinction is that an exponential function has its variable in the exponent, but a power function has its variable in the base.

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Given the domain {-4, 0, 5}, what is the range for the relation 12x + 6y = 24?

A.
{-4, 4, 14}
B.
{2, 4, 9}
C.
{-12, -4, 6}
D.
{12, 4, -6}

Answers

Answer:

The range is {12, 4, -6} ⇒ D

Step-by-step explanation:

The range of the relation is the values of y corresponding to the values given for x which is the domain of the relation

∵ The relation is 12x + 6y = 24

∵ The domain of the function is {-4, 0, 5}

→ That means x = -4, 0, 5, we need to find their corresponding values of y

∴ Substitute the values of x in the relation

x = -4

∴ 12(-4) + 6y = 24

∴ -48 + 6y = 24

→ Add 48 to both sides

∴ -48 + 48 + 6y = 24 + 48

∴ 6y = 72

→ Divide both sides by 6 to find y

∴ [tex]\frac{6y}{6}=\frac{72}{6}[/tex]

y = 12

x = 0

∴ 12(0) + 6y = 24

∴ 0 + 6y = 24

∴ 6y = 24

→ Divide both sides by 6 to find y

∴ [tex]\frac{6y}{6}=\frac{24}{6}[/tex]

y = 4

x = 5

∴ 12(5) + 6y = 24

∴ 60 + 6y = 24

→ Subtract 60 from both sides

∴ 60 - 60 + 6y = 24 - 60

∴ 6y = -36

→ Divide both sides by 6 to find y

∴ [tex]\frac{6y}{6}=\frac{-36}{6}[/tex]

y = -6

∵ The range is the values of y which corresponding to the domain

The range is {12, 4, -6}

The answer is down below have a good day!!!

85 miles on 8 gallons of gas

Answers

Answer:

11.6 miles per gallon

Step-by-step explanation:

Answer:

11.6 miles per gallon

Step-by-step explanation:

just divide

Can you guys help me with this angle problem for Geometry tysm

Answers

Answer:

You need to solve for x

Step-by-step explanation:

3x + 5 + 10x - 7 = 180

13x + 5 - 7 = 180

13x - 7 = 175

13x = 182

x = 14

Plug in x

3(14) + 5 for QRT and 10(14) - 7 for TRS

QRT = 47 and TRS = 133

Answer:

QRT = 47

TRS = 133

Step-by-step explanation:

The two angles form a straight line so they add to 180

3x+5 + 10x-7 = 180

13x-2 =180

Add 2 to each side

13x-2+2 =180+2

13x= 182

Divide by 13

13x/13 = 182/13

x =14

We want QRT = 3x+5 = 3*14+5 = 42+5 = 47

TRS = 10x-7 = 10*14-7 = 140-7 = 133

2 An art studio charges $65 per month for art lessons. There is also an additional supply fee of $25 at the time of registration. Which equation best describes the total cost, c, given the number of months, m?​

Answers

Answer:

The equation should be, 65m+25=c

Answer: it’s going to be c=65m+25

Step-by-step explanation:

z=b+ m/a, solve for a

Answers

You can not solve for a as all of the numbers are unknown

Circle the true number sentences and rewrite the false sentences to make
4= 4
5 + 1 = 6 + 1
3 + 2 = 5 + 0
6+2=4+4
3+3= 6 + 2
9 + 0 = 7 + 2
8-8 +0
6+3=5+4
3+3=6+2

Answers

4=4 is true
5+1=6+1 False try 5+2=6+1
3+2=5+0 is true
6+2=4+4 is true
3+3=6+2 is false try 3+5=6+2
9+0=7+2 is true
8-8+0 not sure what this one is if 8-8=0 true
6+3=5+4 is true
3+3=6+2 again false try 3+3=6-0

The given statements 4=4, 3+2=5+0, 6+2=4+4, 9+0=7+2, 8-8=0 and 6+3=5+4 are the true.

What is an equivalent expression?

Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value for the variable.

Here,

1) 4=4

Statement is true.

2) 5+1=6+1

6≠7

Statement is not true.

3) 3+2=5+0

5=5

Statement is true.

4) 6+2=4+4

8=8

Statement is true.

5) 3+3=6+2

6≠8

Statement is not true.

6) 9+0=7+2

9=9

Statement is true.

7) 8-8=0

0=0

Statement is true.

8) 6+3=5+4

9=9

Statement is true.

9) 3+3=6+2

6≠8

Statement is not true.

Therefore, the statements 4=4, 3+2=5+0, 6+2=4+4, 9+0=7+2, 8-8=0 and 6+3=5+4 are the true.

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Please help me solve both of them

Answers

Answer:

first one: a,d,e

second one: d

Step-by-step explanation:

pemdas

Answer:

1.- A

2.- A

Step-by-step explanation:

Can y’all help plzzzzz

1.
m
In the figure below, m||n. Match the angle pairs with the
correct label for the pairs.
A. 24 and 26
a.
Corresponding Angles
HA
B. 25 and 28
b.
?
Same-Side Interior Angles
C. Z2 and 26
c.
?
Alternate Interior Angles
D. 24 and 25
d. ?
Vertical Angles

Answers

Answers
A- B
B-D
C-A
D-C

The matching is as follows:

1. <4 and <6 ------> same- side interior angle

2. <5 and <6 ------> vertical angles

3. <2 and <6  ------> corresponding angle.

4. <4 and <5  ------> alternate interior angle

What are properties of parallel lines?

Properties of Parallel Lines

The pairs of corresponding angles are equal.The pairs of vertically opposite angles are equal.The pairs of alternate interior angles are equal.The pairs of alternate exterior angles are equal.

Now, from the figure

1. <4 and <6 shows the relationship of same- side interior angle

2. <5 and <6 shows the relation of vertical angles

3. <2 and <6 shows the relation of corresponding angle.

4. <4 and <5 shows the relation of alternate interior angle

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PLZ HELP FAST
A cruise ship is currently 15 kilometers away from its port and is traveling away from the port at 15
kilometers per hour. The function y = 15x + 15 relates the number of kilometers y the ship will be from
its port x hours from now. How far will the cruise ship be from its port 3 hours from now?

The cruise ship will be______ kilometers away from port in 3 hours.​

Answers

Answer:

45

Step-by-step explanation:

Answer: 60 kilometers

Step-by-step explanation:

Plug in your hours:

y = 15(3) + 15

y = 45 + 15

y = 60 kilometers

Hope this helps!

What is the circumference of a circle that has a radius of 7 m?

Answers

Step-by-step explanation:

you you can use two formulas here either pi d or 2 pi r so when you use pie d which change the radius to diameter by multiplying by two so in this case we will multiply 7 by 2 to get 14 then use the formula so is 22/7 * 14 to get 44

PLSSSSSS 15 POINTS

create a discount booklet using
actual advertisements available right
now. Use newspaper or flyers. Must
have actual ads for the work. You
must show your calculations for each
ad.

Answers

Actually it's 8
It's supposed to represent half of what the people who answer are getting but in total you ow 15 or 16 so it takes that amount

Answer:

You cant make this..

Step-by-step explanation:

I WILL MARK BRAINLIEST BUT PLEASE ANSWER FAST

Answers

Answer:

B

Step-by-step explanation:

It had this question on my test. I already answered it. I put c and got it wrong. The answer is B.

There is 3 questions help asap

Answers

The answer is A. C. D.

can someone help me i don’t get this at all !!!! OLEASEEE

Answers

Answer:

A

Step-by-step explanation:

not enough info

3. An almirah is sold at 5,225 after allowing a discount of 5%. Find its marked price.

Answers

Answer:

4,963.85

Step-by-step explanation:

Please help me ..................

Answers

1)
a)E
b)D
c)A

2)Between 3 and 4
decimal estimate is 3.6

3)Between -12 and -13
Decimal estimate is -12.25

4)5.48 or 5.5inches

5)32 feet

6)B

7)C

The answers are shown below:

What is square root?

The square root of a number is that factor of a number which when multiplied by itself gives the original number. Squares and square roots are special exponents.

Consider the number 9. When 3 is multiplied by itself, it gives 9 as the product. This can be written as 3 × 3 or 32. Here, the exponent is 2, and we call it a square. Now when the exponent is 1/2, it refers to the square root of the number. For example, √n = n^1/2, where n is a positive integer.

a) point E represent √47 ( 6.855)

b) point D represent √27 ( 5.19)

c) point A represent √11 ( 3.316)

√13(3.6050 lies between 3 and 4.

-√150 (12.247) lies between (-12 and -13)

side = √area= √30 = 5.477 inch

√90=9.48 ( option b)

The incorrect statement is √12 lies between 4 and 5

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Maddy made $22.50 for babysitting for 5 hours for her aunt. Maddy was paid $21.00 for 3.5 hours of babysitting for her neighbor. How much more per hour does Maddy’s neighbor pay than her aunt?
A. $1.00/hr
B. $1.50/hr
C. $2.00/hr
D. $2.50/hr

Answers

B. $1.50/hr
Hope this helps!!!!!

Answer: B.1.50

Step-by-step explanation:

22.50 divided by 5 = 4.5

21.00 divided by 3.5 = 6.0

           6 - 4.5 = 1.50

This will tell us the differences in

  how much money they made.

Use a triple integral to find the volume of the given solid. The solid bounded by the parabolic cylinder y = x2 and the planes z = 0, z = 4, y = 16.

Answers

Answer:

The answer is "[tex]\bold{\frac{1024}{3}}[/tex]".

Step-by-step explanation:

[tex]= \int\limits^{4}_{-4} \int\limits^{4}_{0} \int\limits^{16}_{x^2} dy\ dx \ dz \\\\= 2 \int\limits^{4}_{0} \int\limits^{4}_{0} \int\limits^{16}_{x^2} dy\ dx \ dz \\\\ = 2 \int\limits^{4}_{0} \int\limits^{4}_{0} (16-x^2) dx \ dz \\\\= 2 \int\limits^{4}_{0} \int\limits^{4}_{0} 16x -\frac{x^3}{3} dx \ dz \\\\= 2 (16x -\frac{x^3}{3})^4_{0} \ dz \\\\= 2 (4) (16x -\frac{64}{3}) \\\\=8(\frac{2}{3} \times 64) \\\\=(\frac{16\times 64}{3} ) \\\\= \frac{1024}{3}[/tex]

The volume of the given solid is [tex]\frac{1024}{3}[/tex] cubic units.

In this question we must use the triple integral formula in rectangular coordinates to determine the volume of the solid ([tex]V[/tex]):

[tex]V = \iiint dy\,dx\,dz[/tex] (1)

The solid is constrained by the following intervals:

[tex]y \in [x^{2}, 16][/tex], [tex]x \in [-4, 4][/tex], [tex]z\in [0, 4][/tex]

Then, the triple integral is now described:

[tex]V = \int\limits_{0}^{4}\int\limits_{-4}^{4}\int\limits_{x^{2}}^{16} dy\,dx\,dz[/tex]

Now we proceed to integrate thrice to obtain the volume:

[tex]V = \int \limits_{0}^{4}\int \limits_{-4}^{4} (16-x^{2})\,dx\,dz[/tex]

[tex]V = \int\limits_{0}^{4} \left(16\cdot x - \frac{x^{3}}{3}\right)\left|\limits_{-4}^{4} dz[/tex]

[tex]V = \frac{256}{3} \int\limits_{0}^{4} dz = \frac{1024}{3}[/tex]

The volume of the given solid is [tex]\frac{1024}{3}[/tex] cubic units.

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PLEASE HELP FAST!!!! THIS IS URGENT!!!


For the following set of triangles, fill in the blanks with the correct measure. Enter your answers as number only.

1) m∠A = _____˚

2) m∠B = _____˚

3) m∠C = _____˚

4) m∠X = _____˚

5) m∠Y = _____˚

6) m∠Z = _____˚

7) Segment AB = ___ units

8) Segment BC = ___ units

9) Segment AC = ___ units

10) Segment XY = ___ units

11) Segment YZ = ___ units

12) Segment XZ = ___ units​

Answers

Answer:

1. 53°

2. 90°

3. 37°

4. 57°

5. 90°

6. 37°

7. 3

8. 4

9. 5

10. 3

11. 4

12. 5

Step-by-step explanation:

it's alot to explain, if you need an explanation for a certain one, just ask me lol

Paula caught a tarpon with a weight that was 11 times as great as the weight of a permit fish she caught. The total weight of the two fish was 168 pounds

Answers

Answer:

Permit fish=14 pounds if thats the question

Tarpon=154

Step-by-step explanation:

Miguel works for a company that installs and repairs dishwashers. Last week he installed 3 and repaired 4 dishwashers. What is the ratio of Miguel’s total jobs to dishwashers that he repaired?

Answers

Answer:

ewhyfreu62

Step-by-step explanation:

I need to turn this in by tomorrow!!!!! PLEASE HELP ME.

Answers

Step-by-step explanation:

Alternate interior angles :- 1 , 4

corresponding angles :- 3

same side interior angles :- 2 , 5 , 6

A bag holds 5 pounds of pet food. If Paul uses the 5 pounds of food to fill 6 plastic containers equally how much pet food will each container hold

Answers

Answer: 13 1/3 ounces

Explanation:
1 pound equals 16 ounces
5 x 16=80
80 ounces divided by 6 containers is equal to 13 1/3 ounces of pet food.

Answer:

answer is 0.85 repeat (a line over 5)

Step-by-step explanation:

all you have to do is divide 6 from (5 ÷ 6) wich gives you 0.85 continous (a line over 5) so 0.85 with a line over it is your answer

A water-salt mixture calls for 3/4 cup if salt to be placed in 5 1/2 cups of water if i use 1 cup if salt how much water should i use to preserve the proper water to salt ratio

Answers

Answer:

7⅓ cups of water

Step-by-step explanation:

Water-salt mixture ratio = ¾ cup of salt to 5½ cups of water (¾ : 5½)

To maintain this water to salt ratio, if you intend to use 1 cup of salt, the number of water you need to add can be calculated as follows:

¾ cup of salt : 5½ cups of water = 1 cup of salt : x cups of water

¾ : 5½ = 1 : x

[tex] \frac{\frac{3}{4}}{5\frac{1}{2}}. = \frac{1}{x} [/tex]

[tex] \frac{\frac{3}{4}}{\frac{11}{2}} = \frac{1}{x} [/tex]

[tex] \frac{3}{4}*{\frac{2}{11} = \frac{1}{x} [/tex]

[tex] \frac{3}{2}*{\frac{1}{11} = \frac{1}{x} [/tex]

[tex] \frac{3*1}{2*11} = \frac{1}{x} [/tex]

[tex] \frac{3}{22} = \frac{1}{x} [/tex]

Cross multiply

[tex] 3x = 22 [/tex]

Divide both sides by 3

[tex] \frac{3x}{3} = \frac{22}{3} [/tex]

[tex] x = 7\frac{1}{3} [/tex]

Number of cups of water to add to 1 cup if salt is 7⅓ cups.

Evaluate and reduce:
3
4
35 - -
F
Enter the number that belongs in the
green box.

Answers

Answer:

28

Step-by-step explanation:

35/5 ÷ -3/4

=7÷ (-3/4)

=7× (4/-3)

=(7×4)/-3

=- 28/3

the minus is already placed in the question, that makes the answer 28 without the minus

how to construct cuboid net? what should be the measurement (around 1-5)?

Answers

the measurement should be 4

Solve for x: 3(x + 1) = -2 (x-1) - 4

Answers

Answer: x = -1

Remove parentheses

Calculate

Move the terms

collect like terms, calculate.

divide both sides.

Answer: x = -1

3(x + 1) = -2(x-1) - 4 (Expand by distributing)

3x + 3 = -2x + 2 - 4 (Rearrange the terms so that the terms with a variable of x are on one side)

3x + 2x = 2 - 4 - 3 (Collect like terms)

5x = -5 (Divide both sides by 5 to isolate for x)

x = -1

∴ x = -1.

IM NOT GOOD AT MATH PLEASE HELP WITH THESE FEW QUESTIONS ASAP

Answers

Answer:

for the first question

solve for t:t= square root of 2da/a (2da over a)

Solve for a : a= 2d/t squared

Solver for d: d=t squared /2(over 2)

Step-by-step explanation:

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