Answer:
10 quarters, 23 dimes
Step-by-step explanation:
Make dimes = d and quarters = q. Let the number of dimes and quarters add up to 33 and the value of the dimes and quarters add up to 4.80. The system of equations should look like:
- d + q = 33
- 0.10d + 0.25q = 4.80
Solve for d in the first equation. Subtract q from both sides.
d = 33 - q
Substitute d into the second equation.
0.10(33 - q) + 0.25q = 4.80
Distribute 0.10 inside the parentheses.
3.3 - 0.10q + 0.25q = 4.80
Combine like terms.
3.3 + 0.15q = 4.80
Subtract 3.3 from both sides.
0.15q = 1.5
Divide both sides by 0.15.
q = 10
Substitute this value of q into where we solved for d (d = 33 - q).
d = 33 - (10)
d = 23
Answer:
600 cubic feet of water
Step-by-step explanation:
If the pool is filled 4 feet and the pool is 5 feet deep, that leaves 1 foot of depth left to fill. This makes the volume equation 30 x 20 x 1 which equals 600.
Answer: 2 deliveries per hour
Step-by-step explanation:
Answer:
y(x) = 7e^(5x)
Step-by-step explanation:
The question says that the slope of the curve at every point P is five times the y-coordinate of P. This means that
dy/dx = 5y
Refer to solutions of differential equations, dy/dt = ky, being in the form of y(t) = y(0) e^(kt)
Using the above stated law now, we can relate to our equation, saying that
y(x) = y(0) e^(5x)
The point given from the question is, (0, 7). This also means that y(0) = 7. So finally, we can have
y(x) = 7e^(5x)
And that is our needed equation of the curve
Step-by-step explanation:
1. We we can split 4p into 9p - 5p, and now we have 3p² + 9p - 5p - 15 = 0. We can take out 3p from the first 2 terms and -5 from the last 2 terms. This gets us 3p (p + 3) -5 (p + 3) = 0. These two terms have (p + 3) as a common facor, so we can take that out as well, which give us (p + 3)(3p - 5) = ). Using Zero Product Property, p + 3 = 0 and 3p - 5 = 0, and when we solve each equation, we get p = -3, p= 5/3.
2. We will use the same process.
6x² + 14x - 3x - 7 = 0
2x (3x+7) - 1 (3x+7) = 0
(3x + 7)(2x - 1) = 0
3x + 7 = 0, 2x - 1 = 0
x = -7/3, x=1/2
Hope this helps!
