Deck 17: Algebra and Math Problems

Question 1

Solve the equation. Watch for extraneous solutions.

Answer 1

No solution

Question 2

Simplify.

Answer 2

Question 3

Find four consecutive integers whose sum is 138.

Answer 3

33, 34, 35, 36

Question 4

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.

Question 5

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

Question 6

The formulas
b = 0.03t + 2.13
and
m = 0.22t + 1.12
give an approximate model for the yearly average price b of a bushel of barley and m of a bushel of millet over the past five years, where t is the number of years since 1994. What is the first year in which the price of barley exceeded $2.19/bu and the price of millet exceeded $2.00/bu? Show your work.

Question 7

If a golf ball is dropped from a tall building, the distance it has fallen in feet is given by 16t², where t is the time in seconds since the ball was dropped. How far has the ball fallen after 13 seconds?

Question 8

Simplify: t - (6t + 7)

Question 9

Simplify.

Question 10

Together, Paul and Quincy weigh 333 pounds, Quincy and Ramon weigh 326 pounds, and Paul and Ramon weigh 325 pounds. How much does each weigh individually?

Question 11

Graph the solution to the compound inequality:

Question 12

Write the expression without negative exponents.

Question 13

Justin is shopping for new tires for his 4-wheel-drive truck. In addition to the price of the tires, there is a 5% sales tax plus a state-mandated $36 fee for disposing of his old tires. If Justin has determined that he will spend less than $502.20 total, then what is the price range he can spend on the tire set?

Question 14

Factor: 125x³ + 27

Question 15

Find the product.
(3a + 4)(2a + 1)

Question 16

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

Question 17

Conrad builds picnic tables and porch swings which he sells at flea markets. A picnic table requires six 2 $\times$ 4's and nine 1 $\times$ 6's. A swing uses three 2 $\times$ 4's and six 1 $\times$ 6's. Conrad currently has 120 2 $\times$ 4's and 198 1 $\times$ 6's in his inventory. If tables sell for $60 and swings sell for $25, how many of each items should Conrad make in order to maximize his revenue?

Question 18

Write an equation that represents a line l that goes through (10, 0) and has a slope of .

Question 19

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

Question 20

Raphael can load a large shipping truck in 15 hours. Working together, Raphael and Jana can load the same truck in 6 hours. How long would it take Jana to load the truck by herself?

Question 21

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?

Question 22

Graph .

Question 23

If $1,300 is deposited in an account paying 11% compounded continuously, then what amount will be in the account after 3 years?

Question 24

Determine all asymptotes for the graph of the given function. Show your work.

Question 25

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

Question 26

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

Question 27

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

Question 28

How are the graphs of and related?

Question 29

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

Question 30

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 $\times$ 10^-8 mol/L?

Question 31

Graph .

Question 32

Find the midpoint and length of the line segment with the endpoints (2,2) and (12,26).

Question 33

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

Question 34

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

Question 35

Solve the given system of equations.
y = x²
y = 5

Question 36

Solve 3^{10x - 8} = 9^{4x - 1}.

Question 37

The owner of a hobby store bought a case of 9-volt batteries for $70.00. He marked the price up such that his profit was $2.80 per battery. After selling 20 batteries, the store owner had recovered his cost. How many 9-volt batteries are in a case?

Question 38

Find the complex solutions.

Question 39

Find the inverse of the given function and include any domain restrictions.
f (x) = (x - 4)²

Question 40

Find all real solutions of the given equation.
(x² + 2x)² - 5(x² + 2x) - 24 = 0

Question 41

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

Question 42

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

Question 43

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

Question 44

Use the binomial theorem to expand the given binomial.
(m + 1)³

Question 45

Which, if any, of the ordered pairs (1, 2), (-1, 4), (-1, -1), and (5, -3) satisfy the system of inequalities?
x - y > 0
4x² + y² ≥ 4

Question 46

Complete the rewriting of the given series using the new index as indicated. (4i + 4) =

Question 47

Write the given equation in the form y = a(x - h)² + k and identify the vertex, focus, and directrix. Show your work.
y = 2x² - 5x + 2

Question 48

Graph both equations of the system on the same coordinate axes. Use elimination to find all points of intersection.
y = - x²
2x² - y² = 1

Question 49

Write a formula for the nth term of the given geometric sequence.
1, 6, 36, 216, 1296, . . .

Question 50

Find the sum of the given infinite geometric series.
36 + 30 + 25 + ...