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Solve the formula for the indicated variable.
T=3UE
, for U
To solve for U in the formula T = 3UE, we need to isolate U on one side of the equation.
First, divide both sides of the equation by 3 to get rid of the coefficient of U:
T/3 = 3UE/3
Simplifying the right side of the equation, we get:
T/3 = UE
To isolate U, we divide both sides of the equation by E:
(T/3)/E = (UE)/E
Simplifying the right side of the equation, we get:
(T/3)/E = U
So the formula for U is:
U = (T/3)/E
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Solve the equation.
0.25r−0.125+0.5r=0.5+r
(2 points)
To solve the equation 0.25r - 0.125 + 0.5r = 0.5 + r, we will combine like terms and isolate the variable.
First, let's group the terms with r together:
0.25r + 0.5r - r = 0.5 + 0.125
To combine the terms with r, we can simplify the left side of the equation:
(0.25 + 0.5 - 1)r = 0.5 + 0.125
Simplifying the coefficients, we get:
0.75r - r = 0.625
Combining like terms on the left side, we have:
-0.25r = 0.625
Next, we need to isolate r by dividing both sides of the equation by -0.25:
-0.25r / -0.25 = 0.625 / -0.25
This simplifies to:
r = -2.5
Therefore, the solution to the equation is r = -2.5.
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Adam is building a rectangular swimming pool. The perimeter of the pool must be no more than 120 feet. If the length of the pool is 22 feet, write and solve an inequality that represents what the width of the pool must be.
(2 points)
Let's assume the width of the pool is represented by the variable w.
The perimeter of a rectangle is given by the formula: P = 2l + 2w, where l is the length and w is the width.
Since the length of the pool is given as 22 feet, we can substitute the values into the formula: P = 2(22) + 2w.
The problem states that the perimeter of the pool must be no more than 120 feet. So we can write the inequality as: 2(22) + 2w ≤ 120.
Simplifying, we have: 44 + 2w ≤ 120.
Next, we subtract 44 from both sides: 2w ≤ 120 - 44.
This simplifies to: 2w ≤ 76.
Finally, divide both sides of the inequality by 2 to solve for w: w ≤ 76/2.
The final answer is w ≤ 38.
Therefore, the width of the pool must be no more than 38 feet to satisfy the given conditions.
To solve the formula T = 3UE for U, we need to isolate U on one side of the equation.
To do this, we can divide both sides of the equation by 3E:
T/(3E) = (3UE)/(3E)
This simplifies to:
T/(3E) = U
So the solution for U is:
U = T/(3E)
To solve for U in the formula T=3UE, we need to isolate U on one side of the equation.
Step 1: Divide both sides of the equation by 3E to get U alone on one side.
T/(3E) = (3UE)/(3E)
Step 2: Simplify the right side of the equation by canceling out the 3E terms.
T/(3E) = U
Step 3: Rearrange the equation to have U on the left side.
U = T/(3E)
Therefore, the solution for U in the formula T=3UE is U = T/(3E).