the function y = 3.75 + 1.5(x-1) can be used to determine the cost in dollars for a taxi ride of x miles. what is the rate of change of the cost in dollars with respect to the number of miles?

Answers

Answer 1

Answer:

rate of change of the cost in dollars with respect to the number of miles= 1.5

Step-by-step explanation:

We have been given the function y = 3.75 + 1.5(x-1)

Let us simplify this equation

y = 3.75 + 1.5(x-1)

y= 3.75+1.5x-1.5

y = 1.5x+2.25

On comparing this equation withe the slope intercept form y = mx + b, we get

m = 1.5

b = 2.25

here x represents distance in miles and y represents the cost in dollars. So, the  rate of change of the cost in dollars with respect to the number of miles would be equal to the slope of the line.

Thus, we have

rate of change of the cost in dollars with respect to the number of miles

= slope

= 1.5

Answer 2

The rate of change of a function is the slope of the function.

The rate of change of the function is $1.5 per miles

The function is given as:

[tex]\mathbf{y= 3.75 + 1.5(x - 1)}[/tex]

Open bracket

[tex]\mathbf{y = 3.75 + 1.5x - 1.5}[/tex]

Collect like terms

[tex]\mathbf{y = 1.5x - 1.5 + 3.75}[/tex]

[tex]\mathbf{y = 1.5x +2.25}[/tex]

A linear equation is represented as:

[tex]\mathbf{y = mx +b}[/tex]

Where: m represents the slope

So, by comparison:

[tex]\mathbf{m =1.5}[/tex]

Hence, the rate of change of the function is $1.5 per miles

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Related Questions

You can buy a 2-pound loaf of bread for $2.50 or a 2-pack of 1 1/2 pound loaves for $3.30. Which is the better buy?

Answers

the 2 pound pack would be the better one to buy

A family has $35 to spend on dinner. They spend $18 on entrees. Side dishes are $3 each. What is the greatest number of side dishes they can buy?  4 5 6 7

Answers


I believe the answer is 5.

The greatest number of side dishes they can buy is 5, as per linear equation.

What is a linear equation?

"A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation."

The family has $35 to spend on dinner.

They spend $18 on entrees.

Therefore, they are left with $(35 - 18) = $17.

Side dishes are $3 each.

Therefore, the most number of side dishes they can buy is

($17/$3)

= 5.67

≈ 5

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Explain how to model the multiplication of 3 and ‒4 on a number line

Answers

First, start at zero. Now, because we are multiplying -4 by 3, we will jump over by 4 to the left  ; 3 times on the number line. We should reach -12, and if we check our work, 3 x -4 = -12.                                            

Final answer:

To model the multiplication of 3 and -4 on a number line, start at zero and make three moves to the left by 4 units, ending up at -12. This demonstrates the rule that multiplying numbers with opposite signs results in a negative product.

Explanation:

To model the multiplication of 3 and -4 on a number line, you can follow these steps:

Start at zero on the number line.

Since you are multipling a positive number by a negative number, you will move in the negative direction (to the left).

Make three moves (corresponding to multiplying by 3), each 4 units to the left. This represents adding -4 three times.

Where you end up on the number line is the product of 3 and -4, which is -12.

This method of multiplication on a number line illustrates the rule that when two numbers multiplied have opposite signs, the answer has a negative sign, such as in the example ( -4) x 3 = -12.

The number 75 falls between what two perfect squares?

Answers

64 and 81, which when taken square root of equal 8 and 9 respectively.

The number 75 falls between the two perfect squares of 8 and 9.

What is Algebra?

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

PEMDAS rule means for the Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to solve the equation in a proper and correct manner.

We know that square of the numbers from 5 to 10 will be given below.

5² = 25

6² = 36

7² = 49

8² = 64

9² = 81

10² = 100

From the above, the number 75 falls between the two perfect squares of 8 and 9.

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todays Temperature is 3 degrees warmer than it yesterday. Write an expression for today's temperature

Answers

t =temperature  d = day temp


t+3=d



Gali found that she can drive 140 miles in 3 hours, including rest stops, or interstate highways. How long would it take her to drive the interstates from Cleveland, Ohio to Washington, D.C. which is 350 miles?

Answers

3 hours and 30 minutes

It would take Gali approximately 7.5 hours to drive from Cleveland, Ohio, to Washington, D.C. on the interstate highways.

To find Gali's average driving speed, we can divide the distance she can travel by the time it takes her:

140 miles / 3 hours = 46.67 miles per hour (approx).

Now that we know her average driving speed, we can calculate the time it would take her to drive 350 miles from Cleveland to Washington, D.C.

Time = Distance / Speed

Time = 350 miles / 46.67 miles per hour

Time ≈ 7.5 hours

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find a number such that 8 times the number is 36 greater than the opposite of the number. Explain also please. ♥

Answers

Let's turn this sentence into an equation:

8n = -n + 36

Then solve:

9n = 36 => n=4
8x=36-x
+x +x
16x=36
---- -----
16 16

X= 36/16 by solving for x in an equation

What is the slope of this line?



A.5

B.1/5

C.−1/5

D.−5

Answers

I think is C. I did that i remember
B. 1/5 this is the answer

a certain medicine is given an amount proportional to a patient's body weight. suppose a patient weight 132 pounds requires 143 milligrams of medicine. what is the amount of medicine required by a patient weighing 156 pounds?

Answers

Final answer:

To solve this problem, we set up a proportion based on the provided information: 132 pounds correlates to 143 milligrams. We then use cross multiplication to find the required dosage for the patient with the weight of 156 pounds, which results to about 169.3 milligrams.

Explanation:

The method to solve this issue is to use the concept of proportionality. First, we set up a proportion based on the given information: 132 pounds (patient weight) correlates to 143 milligrams (medicine dosage). Secondly, we could use cross multiplication to find the unknown medicine dosage for the patient weighting 156 pounds. Here's the mathematical process:

Set up the proportion: 132/143 = 156/x Cross multiply: 132*x = 143*156 Solve the equation: x = (143*156)/132

Carrying out the multiplication and division should result in x ≈ 169.3 milligrams. So a patient weighing 156 pounds would require approximately 169.3 milligrams of the medicine.

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Josh has eight pairs of white socks, two pairs of black socks, and one pair of blue socks. Write a fraction to represent the part of his socks that are white.

Use / for the fraction line.

thankyou so much for helping please do it correctly and dont just guess

Answers

8/11  is the answer. I hope it helped
Answer is 8/11 because there are 11 socks in total and 8 out of 11 are white

What was the purpose of the coordinate graphing system described by Descartes in his book Discourse on Method?

Answers

To use algebraic methods to solve geometric problems.

Answer:

A

Step-by-step explanation:

A cell phone provider offers a plan that costs ​$30 per month plus ​$0.20 per text message sent or received. A comparable plan costs ​$60 per month but offers unlimited text messaging. Complete parts a. and b. below.
a. How many text messages would have to be sent or received in order for the plans to cost the same each​ month?
In order for the plans to cost the​ same,? nothing text messages would have to be sent or received. ​(Simplify your answer. Type an integer or a​ decimal.)

Answers

5 times 30 = 150 text messages

Fewer - lower Equal to - same More - higher
The first plan has a fixed cost, $30, and a cost per text message of $0.20.
If you sent t number of text messages, the cost per message is $0.20t.
The total cost of the first plan is

0.2t + 30

The second plan simply costs $60 no matter how many texts you used.
The second plan costs

60

Set the two costs equal to each other to find out how many messages you need to send with the first plan to cost the same as the second plan.

0.2t + 30 = 60

0.2t = 30

t = 150

If you use exactly 150 text messages, the plans cost the same.
If you use fewer than 150 text messages, the first plan costs less.
If you use more than 150 text messages, the firs plan costs more.

A pool is filling with water at a constant rate.after 10 minuets the height of the water level is 6 inches.after 15 minuets the water level is now at 9 inches when will the pool be completely filled if the entire pool is 30 inches deep?

Answers

the answer would be 18 minutes.

15/9 = 30/x

cross multiply

15x=270

then divide

x=18

What is the order of 75%, 1/3, 3/8, and 0.625 from least to greatest? Also, please please explain how to do it...I’m having trouble. Thanks!

Answers

3/8 , 1/3 , 75% , 0.625

To arrange the given numbers from least to greatest we convert the numbers to decimal form.

75% =0.75

(Percent means out of 100.The decimal is shifted two places left to                               convert percent to decimal)

[tex]\frac{1}{3} =0.33[/tex]

[tex]\frac{3}{8}=0.375[/tex]

0.625

The  decimals from least to greatest are:

0.33,0.375,0.625,0.75.

The numbers arranged from least to greatest are:

[tex]\frac{1}{3},\frac{3}{8},0.625,75%[/tex]

   

(6d+5)−(2−3d) find the difference

Answers

(6d + 5) - (2 - 3d)

Remove the parenthesis. This will help the question look more clear

6d + 5 - 2 + 3d

Add like terms.

(6d + 3d) + (5 - 2)

Simplify.

9d + 3

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Final answer:

To find the difference between (6d+5) and (2-3d), distribute the negative sign and combine like terms to get 9d + 3.

Explanation:

To find the difference between (6d+5) and (2-3d), we first distribute the negative sign to the terms inside the second parentheses. This gives us:



(6d+5) - (2-3d) = 6d+5 - 2 + 3d



Next, we combine like terms by adding the coefficients of d:



(6d + 3d) + (5 - 2) = 9d + 3



So, the difference between (6d+5) and (2-3d) is 9d + 3.

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Round off 43,876,503 to the nearest thousand

Answers

Answer: 43,877,000
Hoped that helped♡♡

A group of friends are ordering food. The total amount that they can spend on their food bill is $41, including the delivery charge of $6. The equation below represents the situation, where x is the cost of each friend's meal.



The cost of each friend's meal in terms of a is
.

The cost of each friend's meal when the number of friends is 5 is $

Answers

The cost of each friend's meal in terms of a is 35/a.  

The cost of each friend's meal when the number of friends is 5 is $7.

The cost of each friend's meal in terms of a is 35/a and the cost of each friend's meal when the number of friends is 5 is $7.

How to form an equation?

Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.

In other words, an equation is a set of variables that are constrained through a situation or case.

Given the equation,

6 + ax = 41

Where a is the number of people and x is the cost of each friend's meal.

Now,

ax = 41 - 6

ax = 35

x = 35/a

So it will be the cost of each friend's meal in terms of a.

Now,

If the number of friends = 5

Then,

a = 5

So,

x = 35/5 = 7

Hence "The cost of each friend's meal in terms of a is 35/a and the cost of each friend's meal when the number of friends is 5 is $7".

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Which transformations will produce similar, but not congruent, figures?

Select each correct answer.

Square ABCD is dilated by a scale factor of 4/5 and then translated 1 unit right to form square A"B"C"D".

Square ABCD is rotated 270° clockwise and then dilated by a scale factor of 1/3 to form square A"B"C"D".

Square ABCD is translated 8 units right and 8 units up and then reflected across the y-axis to form square A"B"C"D".

Square ABCD is reflected across the x-axis and then dilated by a scale factor of 2 to form square A"B"C"D".

Answers

The one with a dilation because a dilation is does not result in congruent figures....but rather similar figures

Answer:

A, B and D

Step-by-step explanation:

Any Geometric figure whether translated (slid), rotated  or reflected (flipped) maintains its size since those geometric transformations just dislocate, so they remain congruents. But when a square is dilated, the following outcome is a similar one.

So, in A, B, D we have similar figures, not congruent. In A, B we have smaller squares and in D we have a bigger one.

HELP ME PLEASE, ILL GIVE BRAINLIEST TO YOU Each year, the Department of Water Works measures the chloride concentration level in the water. The first year, they found the chloride concentration changed by −1 3/5 mg/L . It is estimated that the chloride concentration will change −2 1/15 mg/L the next year.

What is the total change that will likely occur in 2 years?

Enter your answer as a simplified mixed number in the box.

Answers

- 1 1/3 - 2  1/5

= -4/3 - 11/5

= -20/15 - 33/15

= -53/15 

= -3 8/15 mg/L


Answer:

- 3 8/15

Step-by-step explanation:

What would this be as an equation “You earn $0.85 for every cup Of hot chocolate you sell. How many cups do you need to sell to earn $55.25?” Please help

Answers

I think you would need 65 cups to get $55.25.


You should divide 55.25/0.85
divide the total ($55.25) by the price per cup ($0.85) then you should get the answer your looking for.

Julio's father is 4 times as old as Julio. The sum of their ages is no less than 55.

What is the youngest age Julio can be?


Enter your answer in the box.

Answers

11? Because, 4 times 11 is 44, plus 11 is 54. 12 would be too much.

Answer:

11

Step-by-step explanation:

Find the sum of the partial products to evaluate each expression.

Answers

It's whatever you want it to be
You just make up your own answer or model



Hope this helps! 
Have a Good Day!

If h = 18 inches, l = 30 inches, and w = 14 inches, what is the area of the figure shown above?
A. 960 square inches
B. 690 square inches
C. 314 square inches
D. 666 square inches

Answers

pretty sure the answer is b do the math
A is the answer. L x H + L x W

Use mental math to solve the problem 8.02 − 5.98

Part B
Explain the method of mental math that you used to find the answer. Be specific with each step you took.

Answers

Round off 8.02 to 8 and 5.98 to 6.  Then subtract:  8 - 6 = 2 (approximately)

Answer:

2.04

Step-by-step explanation:

1. I make an estimate

2. I regroup some of the numbers.

3. then subtract it all and you get...

                     

                       2.04

what is 200 divided by 19.30 rounded ti nearest ten

Answers

the answer probably is 10.4
10.36 would be it I think

a weight of 15 ounces stretches a spring 10 inches. A weight of 24 ounces stretches the same spring 16 inches.
How many inches does the spring stretch per ounce of additional weight?

Answers

Each ounce stretches the spring 1.5 inches

16-10 = 6 inches

24-15  = 9 ounces

it stretches 6 inches when 9 ounces are added

 divide 6 inches by 9 ounces

6 / 9 = 0.67 inches per ounce

A candy manufacturer says on its web site that it wants to reach a 60 : 40 consumer taste preference for new products.What do you think it means

Answers

Final answer:

A candy manufacturer wants to achieve a 60:40 consumer taste preference for new products, meaning they want 60% of consumers to prefer their new products and 40% to prefer other products.

Explanation:

When the candy manufacturer says that it wants to reach a 60:40 consumer taste preference for new products, it means that they aim to have 60% of consumers prefer their new products, while 40% of consumers prefer other products.

For example, if they conducted a taste test and found that out of 100 consumers, 60 preferred their new products and 40 preferred other products, then they have achieved their desired consumer taste preference.

This ratio indicates the target market share the candy manufacturer hopes to capture for its new products.

Final answer:

The candy manufacturer wants 60% of consumers to prefer their new products over others.

Explanation:

The candy manufacturer's statement about wanting to reach a 60:40 consumer taste preference for new products means that they aim to have 60% of consumers prefer their new products over other options, while 40% may still prefer other brands or flavors.

For example, if the company launches a new chocolate bar, their goal is to have 60% of consumers say that they like the new chocolate bar, while 40% may still prefer other chocolate bars or candies.

This ratio indicates the company's desired market share and the level of acceptance they are aiming for in order to consider their new products successful.

the ratio of boys to girls in a class is 4:3 are 35 students in the class how many students are boys

Answers

The number of boys in class
=35÷(4+3)(total ratio)×4(ratio of boys)
=20

I am not very good at explaining but I hope it helps ^^
35 : (4 + 3) = 5
5 * 4 = 20 (Boys)
5 * 3 = 15 (Girls)
-----------------
20 + 15 = 35

The temperature at noon on a winter day was 8°C. At midnight, the temperature had dropped 15°C. What was the temperature at midnight?

Answers

All you have to look at is the word "dropped" and you know it's a subtraction problem. In this case, it would be 8 - 15.

8 - 15 = -7

It would be -7°C at midnight. I hoped this helped! :)

Answer:

-7

Step-by-step explanation:

You had $22 to spend on four raffle tickets. After buying them you had $6. How much did each raffle ticket cost?

Answers

each is ticket is 4 dollars
Each raffle ticket costed $4.
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