Solve for p.
3(p + q) = p
(1 point)
Can you explain your answer as well?
To solve for p in the equation 3(p + q) = p, we can start by distributing the 3 to both terms inside the parentheses:
3p + 3q = p
Next, let's move all the terms containing p to one side of the equation by subtracting 3p from both sides:
3q = p - 3p
Simplifying further, we combine like terms on the right side:
3q = -2p
Now, let's isolate p by dividing both sides of the equation by -2:
p = -3q/-2
Finally, we simplify the fraction:
p = 3q/2
Therefore, the solution for p is p = 3q/2.
Solve for b, then find the value of b when a = 3.
4a = 2b − 7
(1 point)
Responses
–nine-halves
– Image with alt text: nine-halves
five-halves
Image with alt text: five-halves
nineteen-halves
Image with alt text: nineteen-halves
17
17
To solve for b in the equation 4a = 2b - 7, we can follow these steps:
1. Add 7 to both sides of the equation to isolate the term containing b:
4a + 7 = 2b
2. Divide both sides of the equation by 2 to solve for b:
(4a + 7) / 2 = b
Therefore, the value of b is (4a + 7) / 2.
Now, to find the value of b when a = 3, we substitute a = 3 into the equation:
b = (4(3) + 7) / 2
b = (12 + 7) / 2
b = 19 / 2
Therefore, when a = 3, b is equal to 19/2 or nineteen-halves.
Solve for r.
d = rt
(1 point)
To solve for r in the equation d = rt, we can divide both sides of the equation by t:
d / t = r
Therefore, the solution for r is r = d / t.
Find the width of a rectangle with a perimeter of 90 and a length of 15.
(1 point)
Responses
90
90
15
15
45
45
30
To find the width of a rectangle with a perimeter of 90 and a length of 15, we can use the formula for the perimeter of a rectangle:
Perimeter = 2(length + width)
Let's substitute the known values into the equation:
90 = 2(15 + width)
Now, let's simplify and solve for width:
90 = 2(15 + width)
90 = 30 + 2width
90 - 30 = 2width
60 = 2width
Next, divide both sides of the equation by 2:
60 / 2 = 2width / 2
30 = width
Therefore, the width of the rectangle is 30.