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andrey2020 [161]
3 years ago
8

A taxicab service charges a flat fee of $7 plus an additional $1.25 per mile driven. Show the relationship between the total cos

t and the number of miles driven. Which variable is independent, and which is dependent? Write an equation to model the relationship, and make a table to show the cost of 4 to 10 miles.
Mathematics
1 answer:
Zarrin [17]3 years ago
5 0

Answer with Step-by-step explanation:

We are given that

Flat fee of taxicab=$7

Cost of one mile=$1.25

1.We have to show that relationship between total cost and the number of miles driven.

2.We have to find independent variable and dependent variable

3.We have to write an equation to model the relationship and make a  table to show the cost of 4 to 10 miles.

1.Let x be the number of miles driven by taxicab and total cost y of taxicab.

According to question

y=1.25x+7

This is a relation between number of miles drive and total cost.

2. Independent variable : It is that variable which does not depend on value of another variable .

Dependent variable : it is that variable which depend on value of  another variable.

We can see that y depend on x and value of x does not depend on  any value.

Therefore, y is dependent variable and x is independent variable.

Substitute x=4 then we get

y=1.25(4)+7=$12

Substitute x=5 then  get

y=1.25(5)+7=$13.25

y=1.25(6)+7=\$14.5

y=1.25(7)+7=$15.75

y=1.25(8)+7=$17

y=1.25(9)+7=$18.25

y=1.25(10)+7=$19.5

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The answer is, x = 4,  \frac{3}{2}, -7

I'm about to basically type up a report on explaining this answer so bear with me :P

<em>Step 1.)</em> Factor 2x^{3}+  3x^{2}  +65x+84 using Polynomial Division.

Just a basic rundown of what polynomial division is. When using polynomial division for this problem we find all the factors of our constant, 84, and then see which one, when substituted for x, makes the expression equal zero. After we find our variable that makes the problem equal zero, we divide it into our original expression. Here's how it's done:

These are our factors of 84: 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84

strating from one and plugging in these numbers, the first one we come upon that works is 4. So, now we will divide. below is a picture of what it should look like.

After we divide, we get an answer of ( 2x^{2} +11x-21)(x-4)

<em>Step 2.)</em> split ( 2x^{2} +11x-21)(x-4) into two terms

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Now we ask "which two numbers add up to equal 11, but multiply to equal -42". Those two numbers are 14 and -3.

Now we basically split 11x as the sum of 14 and -3. So now our problem should look like this: (2x^{2}+14x-3x-21) (x-4)
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From this: (2x^{2}+14x-3x-21) (x-4)

To this: (2x(x+7)-3(x+7))(x-4)

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The last thing we do is set each parenthesis equal to zero and work it out to find our zeros.

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That gives us our answer of our zeros being x = 4, \frac{3}{2}, -7

Thank you for our question! I hope this helped! Have an amazing day! :D

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