Answer:
7x
Step-by-step explanation:
4x ( linear function) + 3x ( linear function) = 7x
Answer: x^3 - 1 = (x - 1)(x^2 + x + 1)
Explanation:
This is a type of factorizing called the sum or difference of 2 cubes:
a^3 - b^3 = (a - b)(a^2 + ab + b^2)
The sum of the cubes is factored as:
a^3 + b^3 = (a + b)(a^2 - ab + b^2)
In this case, we have: x^3 - 1 so follow the rule above.
x^3 - 1 = (x - 1)(x^2 + x + 1)
Answer:
The volume of the concentrated 80 gallons mixture is 20 gallons
The volume of water in the 80 gallons mixture is 60 gallons
Step-by-step explanation:
The given parameters are;
The content of Container A = The cleaner
The concentration of the cleaner = 20% solution
The content of Container B = Pure water
The concentration of the desired solution = 5%
The volume of the required solution = 80 gallons
Let x represent the volume of the concentrated solution and y represent the volume of water in the 80 gallons mixture
Therefore, we have;
20/100 × x + y×0 = 5/100×80
x + y = 80
y = 80 - x
20/100 × x + (80 - x)×0 = 5/100×80
0.2·x = 4
x = 4/0.2 = 20
x = 20 gallons
y = 80 - x = 80 - 20 = 60
y = 60 gallons
The volume of the concentrated solution (80 gallons mixture) = x = 20 gallons
The volume of water in the 80 gallons mixture = y = 60 gallons.
Answer:
y = -3x + 9
Step-by-step explanation:
y = mx + b where m is the slope and b is the y intercept
The hypotenuse is on the same line as BC but twice as long. So extend that line up and it will cross the y axis at (0,9). 9 will be your y intercept.
To find the slope start at C and count up 9 and to the left 3 to get to B.
So the slope is rise/run or 9/(-3) = -3.
Final equation would be y = -3x + 9
