Exam 17: Algebra and Math Problems

Determine whether or not the solution set to the inequality is the empty set.

Factor: 125x³ + 27

Solve the given equation. t² + 6t + 5 = 0

The pH of a solution is defined by pH = -log₁₀[H⁺] where [H⁺] is the hydrogen ion concentration in moles per liter. To the nearest hundredth, what is the pH of a cup of coffee in which [H⁺] = 2.110^-8 mol/L?

Find the imaginary solutions: 49x² + 70x + 125 = 0

Write the standard equation for the circle with the given radius and center. Center (-9, -4), radius

The population of a certain Virginia county is currently 46,000 and is growing at 3% annually. The population t years from now can be modeled using the formula where P(t) is the population of the county in thousands. In how many years will the population reach 80,000?

Floyd's chemistry lab manual instructs him to weigh out 20 grams of sodium carbonate. Floyd remembers that his sample's mass differed from the 20-gram target amount by 0.36 grams, but does not recall whether he weighed out more or less than the requested amount. Use an absolute value equation to find the possible values for Floyd's sample.

Graph .

Find the complex solutions of the given equation. Show your work.

Graph .

Simplify: t - (6t + 7)

Graph the linear equation 3x - 2y = 6.

Write a formula for the nth term of the given arithmetic sequence. 6, 10, 14, 18, 22, . . .

Write ln(x⁵) - ln(x²) as a single logarithm.

Solve the inequality. Graph the solution set. x² + 6x + 5 ≥ 0

How are the graphs of and related?

For the given polynomial, find the x-intercepts and determine the behavior of the graph of the polynomial at each x-intercept. f (x) = x³ + 10x²

Solve. (z - 8)^1/3 = -3

List all terms of the finite sequence a_n = n + 6 for 1 ≤ n ≤ 5.