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In this equation, k is a constant…

Some help please, Mike?

x^2 – 12x +k = 0 In this equation, k is a constant. For which values of k does the equation have only one solution? I know I can set the discriminant to zero and solve for k. But is there another way to solve? Thanks!

Test 8 Section 3 Question 6

Hello Mike, I was struggling to make sense of question #6 on the Math (No calculator) section on the SAT Practice Test #8. Can you please explain the steps to properly solve it. Thank you for your time.

The lengths of the sides of a rectangle are a and b…

The lengths of the sides of a rectangle are a and b, where a > b The sum of the lengths of the two shorter sides and one of the longer sides of the rectangle is 36. What value of a maximizes the area of the rectangle?

A .9
B. 12
C. 18
D. 24

The answer is C. I suspect there is an easier way to solve than completing the square and finding the vertex of the resulting quadratic function. What is your most direct, easy to understand solution to this calculator-allowed question?

For the given function g, which of the following equivalent forms…

g(x) = 1/5 (5)^(x+4)

For the given function g, which of the following equivalent forms shows the y-coordinate of the y-intercept of the graph of y=g(x) in the xy-plane as a constant or coefficient?

A. g(x) = 125(5)^x

B. g(x) = 25(5)^(x+1)

C. g(x) = 5(5)^(x+2)

D. g(x) = (5)^(x+3)

Choice A is correct, but why?

The function f is defined by a polynomial…

x f(x)
____________
-5 0
-1 36
0 0
1 6
2 0

The function f is defined by a polynomial. Some values of x and f(x) are shown in the table above. Which of the following could define f?

A) (x – 5) (x + 2)
B) (x + 5)^2 (x – 2)^3
C) x^2 (x + 5) (x – 2)^2
D) x (x + 5) (x – 2)

Specifically, can you explain why C is correct but D cannot be?