Question

Solve and show steps. Solve the formula for the indicated variable.
T=3U/E , solve for U

Answer 1

0.25 r – 0.125 + 0.5 r = 0.5 + r . Solve for r. show your work

Answer 2

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

Answer 3

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.

Answer 4

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.

Answer 5

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.