Sharon
high school level 11-12
student
Help!!!!

If f(4)=0 and f(6)=6, which of the following could represent f (x)?

A. 2/3x-4 B. x+2 C. x-4 D. 3/2x+6 E. 3x-12

these are problems to study for a test so I need to know the answer and how it was solved!

I have one more question

If 180^o < theta < 270^o and tan theta = 4/3, then sin theta =?

A. 5/4 B. -4/5 C. 3/5 D. 12/5 E. -3/5

Please help as fast as you can. This is my first time using this program and I am using it as a last resort that is why I need the answers so soon!!!!!

Thanks
Sharon

For your first problem there are two conditions that need to be satisfied, f(4) = 0 and f(6) = 6. I would start by trying the first condition on each of the five options.

• A. 2/(3x-4) = 2/(12-4) = 2/8 which is not zero.
   
  
• B. x+2 = 4+2 = 6 which is not zero.
   
  
• C. x-4 = 4-4 = 0
   
  
• D. 3/(2x+6) = 3/(8+6) = 3/14 which is not zero.
   
  
• E. 3x-12 = 12-12 = 0

Thus only options C and E satisfy the first condition.

Now see if either of C or E satisfies the second condition, f(6) = 6.

• C. x-4 = 6-4 = 2 which is not 6.
   
  
• E. 3x-12 = 12-12 = 0

Thus only option E satisfies both conditions. Hence f(x) = 3x - 12.

For your second problem since the tangent of theta is 4/3 I would draw he diagram below. I used the theorem of Pythagoras to find the third side of the triangle.

From the diagram the sine of the angle t is 4/5. But theta is in the third quadrant where the sine is negative and thus the sine of theta is -4/5.