Question 1

Simplify the complex fraction. 
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Simplify the complex fraction. 
A) 
B) 
C)...

Question 2

Simplify the complex fraction. 
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Simplify the complex fraction. 
A) 
B) 
C)...

Question 3

Simplify the complex fraction. 
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Simplify the complex fraction. 
A) 
B) 
C)...

Question 4

Simplify the complex fraction. 
A) 
B) 
C) 
D) 
E)

Accepted Answer

Without knowing the actual complex fraction, it is impossible to determine the answer. The given options are simply random strings of letters and numbers, so none of them can be considered a simplified form of the original fraction.

Question 5

Simplify the complex fraction. 
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Simplify the complex fraction. 
A) 
B) 
C)...

Question 6

Simplify the complex fraction. 
A) 
B) 
C) 
D) 
E)

Accepted Answer

Without the original complex fraction given, it is impossible to determine the correct answer.

Question 7

Simplify the complex fraction. 
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Simplify the complex fraction. 
A) 
B) 
C)...

Question 8

Graph  and  on the same coordinate system. At what points do the two graphs intersect?
A) 
B) 
C) 
D)

Accepted Answer

The answer of Graph  and  on the same...

Question 9

A water faucet can fill a sink in 10 minutes, whereas the drain can empty it in 8 minutes. If the sink is full, how long will it take to empty if both the faucet and the drain are open?
A) 80 minutes
B) 18 minutes
C) 40 minutes
D) 10 minutes
E) 9 minutes

Accepted Answer

The answer of A water faucet can fill a sink...

Question 10

A bathtub can be filled by the cold water faucet in 12 minutes and by the hot water faucet in 13 minutes. The drain can empty the tub in 5 minutes. Can the tub be filled if both faucets and the drain are open?
A) Yes
B) No

Accepted Answer

Let the capacity of the bathtub be 156 units (LCM of 12, 13, and 5)
In one minute, the cold water faucet can fill 13 units (156/12) and the hot water faucet can fill 12 units (156/13).
So, in one minute both faucets together can fill 25 units (13+12).
But since the drain can empty the tub in 5 minutes, it can empty 31.2 units (156/5) in one minute.
Therefore, the net filling capacity per minute is -6.2 units (25-31.2)
Hence, the tub will not be filled and the answer is B.

Question 11

Simplify the complex fraction. 
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Simplify the complex fraction. 
A) 
B) 
C)...

Question 12

A bathtub can be filled by the cold water faucet in 12 minutes and by the hot water faucet in 15 minutes. How long does it take to fill the tub if both faucets are open?
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of A bathtub can be filled by the...

Question 13

Graph  and  on the same coordinate system. At what points do the two graphs intersect?
A) 
B) 
C) 
D)

Accepted Answer

The answer of Graph  and  on the same...

Question 14

Simplify the complex fraction. 
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Simplify the complex fraction. 
A) 
B) 
C)...

Question 15

Simplify the complex fraction. 
A) 
B) 
C) 
D) 
E)

Accepted Answer

Without the exact expression presented, it is impossible to provide a specific simplification.

Question 16

Simplify the complex fraction. 
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Simplify the complex fraction. 
A) 
B) 
C)...

Question 17

Travis paddles his kayak in the harbor at Morro Bay, California, where the incoming tide has caused a current in the water. From the point where he enters the water, he paddles 4 miles against the current, then turns around and paddles 4 miles back to where he started. His average speed when paddling with the current is 1 mile per hour faster than his speed against the current. If the complete trip (out and back) takes him 1.8 hours, find his average speed when he paddles against the current. 
 
 __________ miles per hour

Accepted Answer

The answer of Travis paddles his kayak in the harbor...

Question 18

A sink can be filled by the cold water faucet in 6 minutes. The drain can empty a full sink in 9 minutes. If the sink is empty and both the cold water faucet and the drain are open, how long will it take the sink to overflow?
A) 18 minutes
B) 16 minutes
C) 19 minutes
D) 21 minutes
E) 15 minutes

Accepted Answer

The cold water faucet fills the sink at a rate of 1/6 of the sink per minute, and the drain empties it at a rate of 1/9 of the sink per minute. The net rate of filling is 1/6 - 1/9 = 3/18 - 2/18 = 1/18 of the sink per minute. Therefore, it will take 18 minutes to fill the sink.

Question 19

A water tank can be filled in 28 hours by an inlet pipe and emptied in 36 hours by an outlet pipe. How long will it take to fill the tank if both pipes are left open?
A) 64 hours
B) 32 hours
C) 126 hours
D) 36 hours
E) 72 hours

Accepted Answer

The inlet pipe fills the tank at a rate of 1/28 of the tank per hour, and the outlet pipe empties it at a rate of 1/36 of the tank per hour. When both pipes are open, the net rate of filling the tank is (1/28 - 1/36) of the tank per hour. Finding a common denominator (252), this becomes (9/252 - 7/252) = 2/252 = 1/126 of the tank per hour. Therefore, it will take 126 hours to fill the tank.

Question 20

Simplify the complex fraction. 
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Simplify the complex fraction. 
A) 
B) 
C)...

Quiz 7: Rational Expressions

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

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

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

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

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

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

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

Graph and on the same coordinate system. At what points do the two graphs intersect?

A water faucet can fill a sink in 10 minutes, whereas the drain can empty it in 8 minutes. If the sink is full, how long will it take to empty if both the faucet and the drain are open?

A bathtub can be filled by the cold water faucet in 12 minutes and by the hot water faucet in 13 minutes. The drain can empty the tub in 5 minutes. Can the tub be filled if both faucets and the drain are open?

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

A bathtub can be filled by the cold water faucet in 12 minutes and by the hot water faucet in 15 minutes. How long does it take to fill the tub if both faucets are open?

Graph and on the same coordinate system. At what points do the two graphs intersect?

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

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

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

A sink can be filled by the cold water faucet in 6 minutes. The drain can empty a full sink in 9 minutes. If the sink is empty and both the cold water faucet and the drain are open, how long will it take the sink to overflow?

A water tank can be filled in 28 hours by an inlet pipe and emptied in 36 hours by an outlet pipe. How long will it take to fill the tank if both pipes are left open?

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