First, you find out how much can be filled in 1 minute. Then you divide that into 120 to get your answer.

To find out how much can be filled in 1 minute, take the time and divide it into the volume. We'll use the second row (2 minutes and 8 gallons.)

8/2=4. So it takes 1 minute to fill 4 gallons. Now, you just divide 4 into 120.

120/4=30

It takes 30 minutes to fill the pool up to 120 gallons.

3 0

3 years ago

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Solve for x: 2 over quantity x plus 2 plus 1 over 5 equals 6 over quantity x plus 5. x = 0 x = −13 x = 13 x = 0 and x = 13

grandymaker [24]

To solve this problem you must apply the proccedure shown below:

1. You have the following expression given in the problem above:

$\frac{2}{x+2}+\frac{1}{5}=\frac{6}{x+5}$

2. You need to sum the fractions located on the left member, as following:

$\frac{10+(x+2)}{5(x+2)}=\frac{6}{x+5}$

$x=(12+x)(x+5)=6(5x+10)$

3. Simplify it and you will obtain a quadratic equation. Solve it by factor out $x$ :

$x^{2} -13x=0\\ x(x-13)=0\\ x=0; x=13$

Therefore, the answer is: $x=0; x=13$

4 0

4 years ago

Why can't you factor 2cosx^2+sinx-1=0 ?

Masja [62]

$2cos^2x+sinx-1=0\\\\2(1-sin^2x)+sinx-1=0\\\\2-2sin^2x+sinx-1=0\\\\-2sin^2x+sinx+1=0\\\\-2sin^2x+2sinx-sinx+1=0\\\\-2sinx(sinx-1)-1(sinx-1)=0\\\\(sinx-1)(-2sinx-1)=0\iff sinx-1=0\ or\ -2sinx-1=0\\\\sinx=1\ or\ -2sinx=1\\\\sinx=1\ or\ sinx=-\frac{1}{2}\\\\x=\frac{\pi}{2}+2k\pi\ or\ x=-\frac{\pi}{6}+2k\pi\ or\ x=\frac{7\pi}{6}+2k\pi\ where\ k\in\mathbb{Z}$

6 0

4 years ago

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