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1. Solve: 7^3x-4=49

2. Let f(x)=x^2+10x40
-find vertex
-state the range of the function
-on what interval is the function increasing?

3. Multiply and Simplify (7+6i)(2+9i)
Write the answer in the form a+bi, where a and b are real numbers.

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SOLUTION This solution is FREE courtesy of BrainMass!

1. Solve: 7^3x-4=49

Solution. As 49=7^2, 7^3x-4=49 <==> 7^3x-4=7^2.
So, 3x-4=2
i.e., 3x=6
So, x=6/3=2

2. Let f(x)=x^2+10x 40
- find vertex
- state the range of the function
- on what interval is the function increasing?

Solution: ******** I assume that f(x)=x^2+10x +40 *******

We can rewrite f(x) as f(x)=(x+5)^2+15
So,
(1) the vertex of the parabola is (-5, 15);
(2) As f(x)>=15, the range of f(x) is [15, infinity)
(3) As the parabola is open upward, the function is increasing on [-5, infinity)

3. Multiply and Simplify (7+6i)(2+9i)
Write the answer in the form a+bi, where a and b are real numbers.

Solution. Using the fact that i^2=-1, we have
(7+6i)(2+9i) =7*(2+9i) +(6i)*(2+9i)
=[14+63i]+ [12i - 54]
=(14-54)+ (63+12)i
= -40+75i.

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