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3 years ago

3^-2 expanded form

Mathematics

1 answer:

Zanzabum3 years ago

5 0

3^(-2) = 1/(3^2) = 1/(3*3) = 1/9

The rule used here is x^(-y) = 1/(x^y) to make the exponent positive.

3^2 turns into 3*3 because the exponent 2 tells us how many copies of the base '3' to multiply out.

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<h3>The add-on options</h3>

For the purpose of this exercise, the add-on options to select are:

Sunroof
Keyless entry

<h3>Dealership A</h3>

The total amount of the add-on options is:

Total = $500 + $1500

Total = $2000

<u>The inequality</u>

This is represented using:

Base price * (1 + Tax) + Fees + Add-on total ≤ 20000

So, we have:

(1 + 6.75%) * x + 751.56 + 2000 ≤ 20000

<u>Solve for x</u>

We have:

(1 + 6.75%) * x + 751.56 + 2000 ≤ 20000

Evaluate the like terms

(1 + 6.75%) * x ≤ 17248.44

Divide both sides by (1 + 6.75%)

x ≤ 16157.79

The solution means that the base price of the car cannot exceed $16157.78 for dealership A

<u>The graph of the possible base price</u>

See attachment

<h3>Dealership B</h3>

The total amount of the add-on options is:

Total = $750 + $1000

Total = $1750

<u>The inequality</u>

This is represented using:

Base price * (1 + Tax) + Fees + Add-on total ≤ 20000

So, we have:

(1 + 6.75%) * x + 1524.72 + 1750 ≤ 20000

<u>Solve for x</u>

We have:

(1 + 6.75%) * x + 1524.72 + 1750 ≤ 20000

Evaluate the like terms

(1 + 6.75%) * x ≤ 16725.28

Divide both sides by (1 + 6.75%)

x ≤ 15667.71

The solution means that the base price of the car cannot exceed $15667.71 for dealership B

<u>The graph of the possible base price</u>

See attachment

<h3>Where to buy from</h3>

Buy from dealership B because dealership B has a lesser base price