Question 1

Simplify the complex fraction.
-

Accepted Answer

The answer of Simplify the complex fraction.
-
...

Question 2

Solve
- =

Accepted Answer

The answer of Solve
- = 
...

Question 3

Solve
- =  +

Accepted Answer

The answer of Solve
- =  + 
...

Question 4

Solve
-P =  for t

Accepted Answer

The answer of Solve
-P =  for t
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Question 5

Solve the problem.
-The speed of a stream is 4 mph. If a boat travels 64 mi downstream in the same time that it takes to travel 32 mi upstream, what is the speed of the boat in still water?

Accepted Answer

The boat's speed in still water is 12 mph. Let the speed of the boat in still water be x mph. Downstream speed is (x + 4) mph and upstream speed is (x - 4) mph. The time taken for both journeys is the same, so 64/(x + 4) = 32/(x - 4). Solving this equation gives x = 12 mph.

Question 6

Solve the problem.
-One maid can clean the house in 7 hr. Another maid can do the job in 4 hr. How long will it take them to do the job working together?

Accepted Answer

The answer of Solve the problem.
-One maid can clean the...

Question 7

Solve the problem.
-If m varies directly as p, and m = 20 when p = 5, find m when p is 8.

Accepted Answer

Since m varies directly as p, we have m = kp for some constant k. Given m = 20 when p = 5, we find k = 20/5 = 4. Therefore, when p = 8, m = 4 * 8 = 32.

Question 8

Solve the problem.
-The amount of time it takes a swimmer to swim a race varies inversely as the average speed of the swimmer. A swimmer finishes a race in 60 seconds with an average speed of 5 feet per second. Find the average speed of the swimmer if it takes 100 seconds to finish the race.

Accepted Answer

The relationship between time and speed is given by the formula $T = \frac{k}{S}$, where $T$ is the time, $S$ is the speed, and $k$ is a constant. Given $T_1 = 60$ seconds and $S_1 = 5$ ft/sec, we can find $k = T_1 \times S_1 = 60 \times 5 = 300$. For $T_2 = 100$ seconds, we solve for $S_2$ in $100 = \frac{300}{S_2}$, giving $S_2 = 3$ ft/sec.

Quiz 8: Roots and Radicals

Simplify the complex fraction. - $Simplify the complex fraction. - A) B) C) D)$

Solve - =

Solve - = +

Solve -P = for t

Solve the problem. -The speed of a stream is 4 mph. If a boat travels 64 mi downstream in the same time that it takes to travel 32 mi upstream, what is the speed of the boat in still water?

Solve the problem. -One maid can clean the house in 7 hr. Another maid can do the job in 4 hr. How long will it take them to do the job working together?

Solve the problem. -If m varies directly as p, and m = 20 when p = 5, find m when p is 8.

Solve the problem. -The amount of time it takes a swimmer to swim a race varies inversely as the average speed of the swimmer. A swimmer finishes a race in 60 seconds with an average speed of 5 feet per second. Find the average speed of the swimmer if it takes 100 seconds to finish the race.