Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
Solve the equation.
0.25r−0.125+0.5r=0.5+r
To solve the equation, let's combine like terms on the left side of the equation first:
0.25r + 0.5r - 0.125 = 0.5 + r
0.75r - 0.125 = 0.5 + r
Next, let's subtract r from both sides of the equation:
0.75r - r - 0.125 = 0.5 + r - r
0.75r - r - 0.125 = 0.5
Combining like terms again, we have:
0.75r - r = 0.5 + 0.125
0.75r - r = 0.625
Next, let's combine the terms on the left side of the equation:
(0.75 - 1)r = 0.625
Now, let's simplify the left side of the equation:
-0.25r = 0.625
To isolate r, let's divide both sides of the equation by -0.25:
r = 0.625 / -0.25
r = -2.5
Therefore, the solution to the equation is 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 suppose the width of the pool is denoted by "w".
To find the perimeter of a rectangle, we sum up all four sides. Since the length of the pool is given as 22 feet, and the width is denoted as "w", the perimeter of the pool is:
Perimeter = 2(length) + 2(width) = 2(22) + 2w = 44 + 2w
The problem states that the perimeter of the pool must be no more than 120 feet. Therefore, we can write the following inequality:
44 + 2w ≤ 120
To solve for w, we need to isolate it on one side of the inequality. Let's subtract 44 from both sides:
44 + 2w - 44 ≤ 120 - 44
2w ≤ 76
Now, divide both sides of the inequality by 2:
2w/2 ≤ 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.
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided. 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.
We know that the perimeter of a rectangle is given by the formula:
Perimeter = 2(length) + 2(width)
In this case, the length of the pool is given as 22 feet, so the perimeter can be written as:
Perimeter = 2(22) + 2(width)
Simplifying this equation, we get:
Perimeter = 44 + 2(width)
The problem states that the perimeter of the pool must be no more than 120 feet, so we can write this as an inequality:
44 + 2(width) ≤ 120
Now, let's solve this inequality for the width of the pool:
44 + 2(width) ≤ 120
Subtract 44 from both sides:
2(width) ≤ 120 - 44
2(width) ≤ 76
Divide both sides by 2:
(width) ≤ 76/2
(width) ≤ 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 this equation, we need to combine like terms and isolate the variable r.
Step 1: Combine like terms
0.25r + 0.5r - 0.125 = 0.5 + r
0.75r - 0.125 = 0.5 + r
Step 2: Simplify both sides of the equation
Subtract r from both sides:
0.75r - r - 0.125 = 0.5 + r - r
0.75r - r - 0.125 = 0.5
Simplify:
0.75r - r - 0.125 = 0.5
Combine like terms:
(0.75 - 1)r - 0.125 = 0.5
-0.25r - 0.125 = 0.5
Step 3: Isolate the variable r
Add 0.125 to both sides:
-0.25r - 0.125 + 0.125 = 0.5 + 0.125
-0.25r = 0.625
Step 4: Solve for r
Divide both sides by -0.25:
(-0.25r) / (-0.25) = 0.625 / (-0.25)
r = -2.5
Therefore, the solution to the equation 0.25r - 0.125 + 0.5r = 0.5 + r is r = -2.5.
To solve the equation 0.25r - 0.125 + 0.5r = 0.5 + r, we need to simplify and rearrange the terms to isolate the variable, 'r', on one side of the equation.
Step 1:
Combine like terms on both sides of the equation:
0.25r + 0.5r - r = 0.5 + 0.125
Step 2:
Perform the addition and subtraction operations on both sides:
0.75r - r = 0.625
Step 3:
Combine like terms on the left side of the equation:
(0.75 - 1)r = 0.625
Step 4:
Simplify the left side of the equation:
-0.25r = 0.625
Step 5:
To solve for 'r', divide both sides of the equation by -0.25:
r = 0.625 / -0.25
Step 6:
Perform the division operation:
r = -2.5
Therefore, the solution to the equation 0.25r - 0.125 + 0.5r = 0.5 + r is r = -2.5.