A 10-gallon water cooler in an office provides water for the whole department. Each hour, 30 ounces of water are removed from the cooler and drunk by office workers. Write an equation to show how long the water in the cooler will last. (10 gallons is 1,280 ounces.)
A. 1,280 + 30h = 0
B. 30h = 10
C. 1,280 - 30h = 0
D. 10 - 30h = 0
The equation that shows how long the water in the cooler will last is:
1,280 - 30h = 0
Therefore, the answer is C.
Justify your steps using the properties of equality and determine the number of solutions to the equation.
3/2(4 - 8x) + 5x = 1 - 7x
To justify the steps using the properties of equality, we can simplify and solve the equation step by step:
1. Distribute the 3/2 to the terms inside the parentheses:
(3/2)(4) - (3/2)(8x) + 5x = 1 - 7x
6 - 12x/2 + 5x = 1 - 7x
6 - 6x + 5x = 1 - 7x
2. Combine like terms on both sides of the equation:
6 - x = 1 - 7x
3. Add x to both sides of the equation:
6 - x + x = 1 - 7x + x
6 = 1 - 6x
4. Add 6x to both sides of the equation:
6 + 6x = 1 - 6x + 6x
6 + 6x = 1
5. Simplify the equation:
6x + 6 = 1
6. Subtract 6 from both sides of the equation:
6x + 6 - 6 = 1 - 6
6x = -5
7. Finally, divide both sides of the equation by 6 to solve for x:
(6x)/6 = (-5)/6
x = -5/6
Therefore, there is one solution to the equation.
Using the properties of inequality, justify both steps in solving the inequality 2/5m - 7 <_17
To justify the steps, we can solve the inequality step by step using the properties of inequality:
1. Add 7 to both sides of the inequality:
(2/5)m - 7 + 7 ≤ 17 + 7
This is justified by the addition property of inequality, which states that if a < b, then a + c < b + c.
2. Simplify both sides of the inequality:
(2/5)m ≤ 24
Therefore, the inequality is now simplified to (2/5)m ≤ 24. Both steps are justified using the properties of inequality.
Note: The inequality sign remains the same throughout both steps because no multiplication or division by a negative number occurred.
Rewrite the equation 4x/3x-12 + 3 = 10 in two equations joined by "and."
To rewrite the equation 4x/3x - 12 + 3 = 10 as two equations joined by "and," we can split up the equation at the addition sign:
First equation: 4x/3x - 12 = 10 - 3
Second equation: 4x/3x - 12 = 7
Therefore, the equation 4x/3x - 12 + 3 = 10 can be rewritten as:
(4x/3x - 12 = 10 - 3) and (4x/3x - 12 = 7)
Rearrange the slope formula y = mx + b for the quantity of interest m. Make sure to show each step.
To write an equation to show how long the water in the cooler will last, we need to consider the amount of water being removed every hour and the initial amount of water in the cooler.
Since each hour, 30 ounces of water are removed from the cooler, the equation should account for this constant reduction. Let's use 'h' to represent the number of hours the water has been consumed.
The initial amount of water in the cooler is 1,280 ounces (10 gallons = 1,280 ounces). Therefore, the equation becomes:
1,280 - 30h = 0
Option C. 1,280 - 30h = 0 is the equation that correctly represents how long the water in the cooler will last.