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weqwewe [10]
3 years ago
14

17. You have $850 to buy new carpet for the game room. The dimensions of the game

Mathematics
1 answer:
gregori [183]3 years ago
3 0

Answer:

Cost of new carpet per square foot should be less than or equal to $3.54.

Step-by-step explanation:

Given:

Money have to buy carpet = \$850

dimension of game room is 20 feet by 12 feet

So we can say length l = 20 feet

and width w = 12 feet

let x be the cost per square foot for new carpet.

Assuming game room to be rectangular in shape we will find the area of it.

Area of room = length \ l \times width \ w = 20 ft\times 12 ft = 240 \ ft^2

Total area \times cost per square feet ≤ Total money we have

Hence,

240 \ ft^2 \times x \leq \$850\\\\x\leq \frac{\$850}{240 \ ft^2}\\\\x\leq \$3.54 \ per \ ft^2

Hence Cost of new carpet per square foot should be less than or equal to $3.54.

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<h3>Answer: Choice B is correct</h3>

========================================================

Explanation:

Use a graphing tool like GeoGebra, Desmos, or your graphing calculator to plot each expression given as a separate y equation. Four parabolas should result.

The x intercept is the same as the root or zero of a function.

You should find that only choice B has a root thats larger than 4. That specific root being x = 7.

----------------------------

A non-graphing approach:

You can use the quadratic formula or the factoring method to find the roots.

For choice A, it factors to (x+5)(x+6) = 0. The roots are x = -5 and x = -6 which aren't greater than 4. So we cross choice A off the list. Choices C and D are similar stories.

On the other hand, choice B factors to (x-7)(x+2) = 0 and it has roots of x = 7  and x = -2. This is another way to see why choice B is the answer.

Here are the steps for the quadratic formula for choice B

x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x = \frac{-(-5)\pm\sqrt{(-5)^2-4(1)(-14)}}{2(1)}\\\\x = \frac{5\pm\sqrt{81}}{2}\\\\x = \frac{5\pm9}{2}\\\\x = \frac{5+9}{2} \ \text{ or } \ x = \frac{5-9}{2}\\\\x = \frac{14}{2} \ \text{ or } \ x = \frac{-4}{2}\\\\x = 7 \ \text{ or } \ x = -2\\\\

The quadratic formula is handy in case factoring is either not possible, or guess-and-check is too lengthy of a process. As you can probably tell, we could use the quadratic formula's results to help construct the factored form.

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