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2 years ago

Kayleigh has 3 1/2 gallons of water. She wants to fill up 1/3 cups. How many cups can she fill and how much is left over?

Mathematics

2 answers:

Fantom [35]2 years ago

5 0

Answer:

168 and nothing left over.

Step-by-step explanation:

There are 4 quarts in a gallon and 4 cups in a quart, so 16 cups in a gallon. So 3.5 gallons is 16 times 3.5, or 56 cups total. That 56 cups is what needs to poured into the 1/3 cup measure as many times as possible. So 56 divided by 1/3 is 168, with zero left over.

erastovalidia [21]2 years ago

3 0

3 1/2 gallons into cups:

56 cups / 1/3:

169.69697 US cups

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3 years ago

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<u>Factoring:</u>

This equation cannot be factored because its roots are irrational (as shown by solving with the quadratic formula). Also, to factor a quadratic equation, you need to find a pair of numbers whose product is equal to the c term (-5) and whose sum is equal to the b term (-6). There is no pair of numbers which satisfies this, further showing that the equation cannot be factored.

<u>Quadratic Formula:</u>

The quadratic formula is x= $\frac{-b ± \sqrt{b^{2}-4ac } }{2a}$ .

First, you need to find the a, b and c terms of your equation. They are 1, -6, and -5 respectively.

Now, you must plug in to the equation and solve for x. You must do so twice, once with a plus sign in the numerator and once with a minus.

$\frac{6 ± \sqrt{(-6)^{2}-4(1)(-5) } }{2(1)} \\\frac{6 ± \sqrt{36+20} }{2} \\\frac{6 ± \sqrt{56} }{2} \\\ \frac{6 ± 2\sqrt{14} }{2} \\3+\sqrt{14} \\3-\sqrt{14}$

The answers are 3+√14 and 3-√14.

Hope this helps!!

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