Solve and show steps. Solve the formula for the indicated variable.
T=3U/E , solve for U
To solve for U, we can start by isolating U on one side of the equation.
Given: T = 3U/E
To isolate U, let's first multiply both sides of the equation by E:
ET = 3U
Next, divide both sides by 3:
ET/3 = U
Therefore, U = ET/3.
0.25 r – 0.125 + 0.5 r = 0.5 + r . Solve for r. show your work
To solve for r, we can start by combining like terms on both sides of the equation.
Given: 0.25r - 0.125 + 0.5r = 0.5 + r
First, let's combine the r terms on the left side:
0.25r + 0.5r - r = 0.5 + 0.125
Simplifying the left side:
0.75r - r = 0.625
Now, let's combine the r terms:
0.75r - r = 0.625
0.75r - r is equivalent to (0.75 - 1)r, which simplifies to -0.25r:
-0.25r = 0.625
To solve for r, we can now divide both sides by -0.25:
(-0.25r) / -0.25 = 0.625 / -0.25
Simplifying:
r = -2.5
Therefore, r = -2.5.
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
Let's denote the width of the pool as w.
The formula for the perimeter of a rectangle is P = 2(l + w), where l is the length and w is the width.
Given that the length of the pool is 22 feet, we can substitute these values into the perimeter formula:
P = 2(22 + w)
According to the problem, the perimeter of the pool must be no more than 120 feet. Therefore, we can set up the following inequality:
2(22 + w) ≤ 120
Next, we can simplify the inequality:
44 + 2w ≤ 120
Subtracting 44 from both sides of the inequality:
2w ≤ 120 - 44
2w ≤ 76
Finally, dividing both sides of the inequality by 2:
w ≤ 76/2
w ≤ 38
Therefore, the width of the pool must be less than or equal to 38 feet in order to satisfy the given conditions.
To solve for U in the formula T = 3U/E, we can follow these steps:
Step 1: Multiply both sides of the equation by E to isolate U.
T × E = (3U × E)/E
Step 2: Simplify the right side of the equation.
TE = 3U
Step 3: Divide both sides of the equation by 3.
TE/3 = (3U)/3
Step 4: Simplify the right side of the equation.
TE/3 = U
Therefore, the solution for U is U = TE/3.
To solve the formula T=3U/E for the variable U, we'll follow these steps:
Step 1: Multiply both sides of the equation by E.
T * E = 3U
Step 2: Divide both sides of the equation by 3.
(T * E) / 3 = U
Step 3: Simplify the expression on the left side by multiplying T and E, then dividing the result by 3.
U = (T * E) / 3
Therefore, the solution for U in terms of T and E is U = (T * E) / 3.