Linear Functions Unit Portfolio Directions: Complete each of the tasks outlined below. Cab companies often charge a flat fee for picking someone up and then charge an additional fee per mile driven. Pick a U.S. city and research the rates of two different cab companies in that city. Find companies that charge different amounts per mile and have different flat fees. If you have trouble finding this information for two companies, you can make up what you think would be reasonable prices for a cab's flat rate and a cab's rate per mile. Task 1 a. For the first company, express in words the amount the cab company charges per ride and per mile. b. Write an equation in slope-intercept, point-slope, or standard form. Explain why you chose the form you did. C. What do the slope and y-intercept mean in the context of this problem? Hint: What do you pay when you step into the cab? Task 2 For the second company, express in a table the cost of the cab ride given the number of miles provided. A. Write and equation in slope-intercept, point-slope, or standard form. Explain why you chose the form you did. B. What does the slope mean in the context of the problem? Task 3 Cabs use a valuable commodity—gas! Research average gas prices from 2005-2015 for the city you chose. If you can't find this information for your specific city, you can research national gas price averages instead. A. Create a table showing the average gas price each year. B. Create a scatter plot of the data in your table. C. What equation models the data? What are the domain and range of the equation? Do you think your equation is a good fit for the data? Explain how you determined your answers. D. Is there a trend in the data? Does there seem to be a positive correlation, a negative correlation, or neither? How much do you expect gas to cost in 2020? Explain.​

Answer:

See answers below

Step-by-step explanation:

Given the following ratios. We are to express them in their simplest forms

15:12

= 15/12

= (3*5)/(3*4)

= 3/3 * 5/4

= 5/4

b) 42:1

= 42/1

= 42

Given that  2:x :: 4:6​

2/x = 4/6

Cross multiply

4x = 2*6

4x = 12

x = 12/4

x = 3

Hence the value of x is 3

Answer:

Step-by-step explanation:

It is hard to guess the coordinates of any points, because the graph doesn't go through any intersections of the grid.

Fortunately, I can tell that the axis of symmetry is x=2.

Put the equation into vertex form by completing the square.

axis of symmetry = b/2

b/2 = 2

b = 4

Answer:

150

Step-by-step explanation:

Collected bills: 18 * 10= 180

1/6 of 180 = 30

180-30=150

Answer:

15 ten dollar bills, 150 dollars

Step-by-step explanation:

1/6 of 18 is 3, so he gave 3 bills to the theater and kept the other 15 for himself

Answer:

$2.50

Step-by-step explanation:

if 3 books=0.75 lbs.

then...

1 book= 0.25

so...

0.25x10=...

10 books= $2.50

Answer:

Step-by-step explanation:

Answer: $179.70

Step-by-step explanation:

The simple interest will be:

= (Principal × Rate × Time) / 100

= ($6000 × 5.99% × 5) / 10

= ($6000 × 0.0599 × 5) / 10

= $1797 / 10

= $179.70

Therefore, the total interest on the loan is $179.70

Answer:

c. 0 and 7

Step-by-step explanation:

Answer:

300

Step-by-step explanation:

Answer:

the missing side of the rectangle should be twelve

Step-by-step explanation:

Answer: the other side is 7 units right ?i do not know but that is my answer

Step-by-step explanation:

Answer:

340 in^2

Step-by-step explanation:

1. First square

A = l*w = 12^2 OR 12*12 = 144

2. Second square

A = l*w = 14^2 OR 14*14 = 196

3. Combined Area

144+196=340

The area of a square is found by squaring the side length, which is the same as multiplying two of the sides together.

Square 1: 12 x 12 = 144 square inches.

Square 2: 14 x 14 = 196 square inches.

Total area = 144 + 196 = 340 square inches.

Answer:

A. G'(5) = 20

B. G'(5) = -1

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Calculus

Derivatives

Derivative Notation

Derivative Rule [Product Rule]:                                                                              [tex]\displaystyle \frac{d}{dx} [f(x)g(x)]=f'(x)g(x) + g'(x)f(x)[/tex]

Derivative Rule [Quotient Rule]:                                                                             [tex]\displaystyle \frac{d}{dx} [\frac{f(x)}{g(x)} ]=\frac{g(x)f'(x)-g'(x)f(x)}{g^2(x)}[/tex]

Step-by-step explanation:

Step 1: Define

[Given] F(5) = 4, F'(5) = 4, H(5) = 2, H'(5) = 3

[Given] A. G(z) = F(z) · H(z)

[Given] B. G(w) = F(w) / H(w)

[Find] G'(5)

Step 2: Differentiate

A. G(z) = F(z) · H(z)

B. G(w) = F(w) / H(w)

Step 3: Evaluate

A. G'(5)

B. G'(5)

Topic: AP Calculus AB/BC (Calculus I/II)

Unit: Derivatives

Book: College Calculus 10e

Answer:

14) equilateral triangle

15) right triangle

16) equilateral triangle

Step-by-step explanation:

14) equilateral triangle

15) right triangle

16) equilateral triangle

9514 1404 393

Answer:

  C)  Peta, because she invests the most

Step-by-step explanation:

The additional $70 that Peta invests is equivalent to more than 2 years' interest at either of the other rates. Not only does Peta invest more money, she does so at a higher interest rate.

Peta will have the most money in her account when she closes it.

__

The balances will be ...

  Joan $490.02

  Peta $548.21

  Linda $420.00

Answer:

(2,-9)

Step-by-step explanation:

Answer:

The second ball

Step-by-step explanation:

If you cared to do simple math the percent comes to ...

75%

64%

60%

50%

Answer:Answer: $7.50

Step-by-step explanation:

$55-$10=$45  45/6=7.5

Step-by-step explanation:

1 kilogram of baking soda costs $4.5

Step-by-step explanation:

To solve this problem, we will follow the steps bellow:

Using proportion;

Let x be the cost of 1 kg of baking soda

kilogram = $ 2

1 kilogram  = x

Cross - multiply

 ×  x  = $2  ×   1

 ×  x    = $2

= $2

Multiply both-side of the equation by 9

× 9= $2 × 9

At the left-hand side of the equation 9 will cancel-out 9, hence our equation becomes

4x = $18

Divide both-side of the equation by 4

 = $

x   = $4.5

1 kilogram of baking soda costs $4.5

Step-by-step explanation:

Answer:

6 x 1/3 = 2

Step-by-step explanation:

Answer:

q= 45/14 (or) 3 3/14

Step-by-step explanation:

7/9=5/2/q

cross multiply

7q=45/2

q=45/2÷7

q= 45/14 (or) 3 3/14

Answer:

D

Step-by-step explanation:

Answer:

x=147°

Step-by-step explanation:

1. Analyze: The angle opposite to the 33 degree angle is 33 degrees because they are vertical angles.

2. Make an equation: The sum of all four angles (x, the angle opposite of x, the 33 degree angle, and the angle opposite of the 33 degree angle) is 360°. Therefore the equation would be (33°x2)+2x= 360°.

3. Solve for x:

      a. Multiply 33 by 2

               66+2x=360

      b. Subtract 66 from both sides

               66+2x=360

               -66       -66

               2x=294

      c. Divide both sides by 2

                  [tex]\frac{2x}{2} =\frac{294}{2}[/tex]

                   x=147

4. Remember to add your label- the degree sign (°)

                  x=147°

Answer:

9/24 for the first and 8/24

Answer:

Step-by-step explanation:

f(x)=g(x)

x²-13x+40=x-5

x²-14x+45=0

Answer:

the answer is a

Step-by-step explanation:

division equation is 1÷14

Answer:

186

Step-by-step explanation:

Tyler: 223 less than Kiran

Kiran: 409

409 - 223 = 186

Answer:

Step-by-step explanation:

a > 0 for an up-opening parabola, so a = 0.25 for the third graph.

The greater the magnitude of a, the skinnier the parabola.

|-1| < |-4|, so a = -4 for the first graph.

Answer:

cost of materials - the value of all things needed to create the good or service

opportunity cost - the value of a product given up to produce or obtain another product

fixed cost - costs that are not affected by the level of production

sunk cost - past costs that cannot be recovered

marginal cost - change in total cost that arises when the quantity produced changes by one unit

Step-by-step explanation:

Answer:

cost of materials: the value of all things needed to create the good or service

opportunity cost: the value of a product given up to produce or obtain another product

fixed cost: costs that are not affected by the level of production

sunk cost: past costs that cannot be recovered

marginal cost: change in total cost that arises when the quantity produced changes by one unit