d his summer job. If he earned the
amount each week, how much die
each week?
Answer: x = -8 or x = 2
Step-by-step explanation: Follow your rule for solving absolute value equations. Since the absolute value is isolated on one side of the equation, we can split the problem up into two separate equations.
The first equation will be identical to the original except it won't have the absolute value signs which are the vertical bars.
In this case, that equation is x + 5 = -3.
The second equation will look like the first, only the right side will be changed to a positive. So in this case, that equation is x + 5 = 3.
Now simply solve each equation to get x = -8 or x = -2.
You can check both of these answers by plugging them back in for x in the original problem and you will see that they both work.
Answer: this equation is false
which would be x= undefined
Step-by-step explanation:
Answer:
Maritza has not enough sugar to make the cookies.
Step-by-step explanation:
Missing data
The recipe requires 3 eggs for every 2 cups of sugar.
Maritza determined she would need 12 eggs.
Her mom bought 6 cups of sugar.
Writing data as a proportion gives
(3 eggs)/(2 cups of sugar) = (12 eggs)/(x cups of sugar)
Omitting units
3/2 = 12/x
Multiplying by x in both sides
3/2 *x = 12
Dividing by 3 and multiplying by 2 on both sides
x = 12*2/3
x = 8 cups of sugar
So, 6 cups are not enough.
George must run the last 1/2 mile at a speed of 2/3 mile per hour to arrive just as school begins today.
To find the speed George must run the last 1/2 mile in order to arrive just as school begins today, we can start by calculating the time it took for George to walk the first 1/2 mile at a speed of 2 miles per hour. We can use the formula Time = Distance / Speed to calculate the time: Time = (1/2) mile / 2 miles per hour = 1/4 hour = 15 minutes.
We know that George arrives just as school begins, so the total time it takes for him to walk 1 mile is the same as the total time it takes for him to walk the first 1/2 mile at 2 miles per hour, plus the time it takes for him to run the last 1/2 mile at a new speed. Therefore, the total time is 15 minutes + time to run the last 1/2 mile. We can set up the equation: (15 minutes) + (1/2 mile / speed) = 60 minutes (as 60 minutes is one hour). We can then solve for the speed by subtracting 15 minutes from both sides and rearranging the equation:
1/2 mile / speed = 45 minutes = 3/4 hour. Multiplying both sides of the equation by the speed:
(1/2 mile) = (3/4 hour) * speed
speed = (1/2 mile) / (3/4 hour) = (1/2 mile) * (4/3 hour) = (1/2)(4/3) = 2/3 mile per hour.
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