7/3x+1/3x=3x+6/3+5/3x
8/3x-5/3x=3x+6/3
3/3x=3x+6/3
x=3x+6/3
x-3x=6/3
-2x=2
-x=2/2
-x=1
x=-1
Answer:
- 10 liters of orange juice
- 5 liters of champagne
Step-by-step explanation:
Let c represent the number of liters of champagne Lauren uses. Then (15-c) will be the number of liters of orange juice. The total cost of the mix will be ...
12c +1.50(15-c) = 5.00(15)
10.5c = 52.50 . . . . . subtract 22.50, simplify
52.50/10.5 = c = 5 . . . . divide by the coefficient of c
Then the amount of orange juice is ...
15 -c = 15 -5 = 10 . . . . liters
Lauren should use 5 liters of champagne and 10 liters of orange juice.
Answer: Any real number x as long as
and 
In other words, anything but 0 or -2/3 is valid.
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Explanation:
Set the denominator equal to zero and solve for x
2(3x^2 + 2x) = 0
3x^2 + 2x = 0
x(3x + 2) = 0
x = 0 or 3x+2 = 0 .... zero product property
x = 0 or 3x = -2
x = 0 or x = -2/3
If either x = 0 or x = -2/3, then the denominator 2(3x^2 + 2x) will be zero. But recall that we cannot have zero in the denominator. Dividing by zero is not allowed. The expression is undefined when we divide by zero.
Therefore, we must exclude x = 0 and x = -2/3 from the domain. Any other real number is valid as an x input.
The solution to a system of equations is the point where the 2 lines of a graph cross each other.
On the pictured graph, the lines cross each other at x = -6 and Y = -2.
The answer would be (-6,-2)
The answer is <span>a number that can be written as a ratio of two integers.
I hope this helps!</span>