The square roo it 7.07106781 i
Answer:
x = 5, y = 2
Step-by-step explanation:
First, find the value of x in respect to y:
2x + 3y = 16
2x = 16 - 3y
x = 8 - 3/2y
Then, substitute this expression into the second equation (Since we've established x is equal to 8 - 3/2y, we can put that in place of x):
4(8 - 3/2y) + 10y = 40
Then, distribute and solve for y:
32 - 6y + 10y = 40
32 + 4y = 40
4y = 8
<u>y = 2</u>
Now that we know what y equals, we can substitute the value of y in the equation to find x:
2x + 3(2) = 16
2x + 6 = 16
2x = 10
<u>x = 5</u>
6x² + 24x - 72
Divide all the terms by the greatest common of factor of 6. Makes factoring easier. We will need to put this 6 on at the end so keep it in mind.
(6x² + 24x - 72) / 6 = x² + 4x - 12
Your simplified equation is x² + 4x - 12
Now to factor we must find out what two factors of - 12 can be added together to equal 4. The factors are 6 and -2:
x² - 2x + 6x - 12
Now we must group and factor.
(x² - 2x) + (6x - 12)
We can pull an x out of the first binomial because both terms have that in common:
x(x - 2) + (6x - 12)
We can pull a 6 out of the second binomial for the same reason:
x(x - 2) + 6(x - 2)
The terms inside the parentheses match each other, this means (x- 2) is one of the factors of the original trinomial. The other comes from the terms on the outside x and + 6. Put them together, (x + 6)
So your factors are (x - 2)(x + 6); this isn't it though. We need the 6 from the top, the one we divided out to make factoring easier. We will put it on the outside of whichever factor you list first so that your final answer reflects that to get back to the original trinomial, you would have to multiply the whole thing by 6.
Your final answer is:
6(x - 2)(x +6)
If you have 7 candles lit and 2 go out, the number of candles left is given by
7 - 2 = 5
Therefore, 5 candles are left lit.
