2. A long distance phone company has a monthly fee of $7.95 and charges a rate of $0.05 per minute. Another long distance company has a monthly fee of $9.95 and charges a rate of $0.03 per minute. At how many minutes would the two companies have equal charges?
15. A boat travels 30 miles upstream in 4 hours. The trip downstream takes 2.5 hours. Find the rate of the boat in still water.
20. Solve: 5x^2 - 10x = 0
50. (x-1)(x^3 + x^2 + x) =?
Thanks
-MC
2. C1=C2 7.95+.05X=9.95+.03X
.05X-.03X=9.95-7.95
X=100 Minutes
CI=Cost at 1st company
C2=Cost at 2nd company
15. Rate upstream=30/4=7.5m/hr
Rate downstream=30/2.5=12m/hr
Rate in stillwater=(7.5+12)/2=9.75m/hr
50. (x-1)(x^3+x^2+x)=x^4+x^3+x^2-x^3-x^2-x=x^4-x=x(x^3-1)
2. To find the number of minutes at which the two companies have equal charges, we can set up an equation. Let's assume the number of minutes is represented by "m".
For the first long distance company, the total charge (C1) can be calculated as:
C1 = $7.95 (monthly fee) + $0.05 (per minute charge) * m (number of minutes)
For the second long distance company, the total charge (C2) can be calculated as:
C2 = $9.95 (monthly fee) + $0.03 (per minute charge) * m (number of minutes)
To find the value of "m" where the charges are equal, we set C1 equal to C2:
$7.95 + $0.05m = $9.95 + $0.03m
Now, we can solve the equation for "m" to find the number of minutes at which the charges are equal.
15. To find the rate of the boat in still water, we need to use the formula: speed = distance / time.
Let's assume the rate of the boat in still water is represented by "b" (in miles per hour). The rate of the current is represented by "c" (in miles per hour).
When the boat travels upstream, the effective speed will be the difference between the boat's rate in still water and the rate of the current. So, the effective speed when traveling upstream is b - c.
When the boat travels downstream, the effective speed will be the sum of the boat's rate in still water and the rate of the current. So, the effective speed when traveling downstream is b + c.
Given that the boat travels 30 miles upstream in 4 hours and 30 miles downstream in 2.5 hours, we can set up the following equations:
(30 miles) / (4 hours) = b - c
(30 miles) / (2.5 hours) = b + c
Now, we can solve these equations to find the rate of the boat in still water (b).
20. To solve the equation 5x^2 - 10x = 0, we can factor out the common term of x:
x(5x - 10) = 0
Now, we can set each factor equal to zero and solve for x:
x = 0 (from the first factor)
5x - 10 = 0 (from the second factor)
Solving the second equation, we get:
5x = 10
x = 2
Thus, the solutions to the equation 5x^2 - 10x = 0 are x = 0 and x = 2.
50. To solve the expression (x-1)(x^3 + x^2 + x), we will use the distributive property.
Multiplying (x-1) by each term of the binomial (x^3 + x^2 + x), we get:
(x-1)(x^3 + x^2 + x) = x(x^3 + x^2 + x) - 1(x^3 + x^2 + x)
Expanding further, we get:
= x^4 + x^3 + x^2 - x^3 - x^2 - x - x^3 - x^2 - x
Combining like terms:
= x^4 - x^3 + x^2 - 3x
So, (x-1)(x^3 + x^2 + x) simplifies to x^4 - x^3 + x^2 - 3x.