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X Marks the Spot
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Lines Galore
Exponents, Logarithms, and More
Potpourri
100
This is the solution to the equation: |x - 2| - 8 = 2
What is x = {-8, 12}?
100
The solution to the equation: x^2 + 6x - 55 = 0
What is x = {-11, 5}?
100
The equation of a line that has a slope of -2 and a y-intercept of 5.
What is y = -2x + 5?
100
The solution to the equation: 4^x = 17 (Round to the nearest 100th.)
What is x = 2.044?
100
The pH of lemon juice if its concentration of hydrogen ions [H+] is 5.01 x 10^-3 moles/liter.
What is pH = 2.3?
200
The solution to the equation: sqrt(3x + 13) - 3 = x
What is x = 1?
200
The solution to the equation: x^2 - 169 = 0
What is x = {-13, 13}?
200
The graph of the line y = 1/5x - 3. Label at least two points.
What is the graph on the board?
200
The solution to the equation: ln(x - 3) + 5 = 9 (Round to the nearest 1,000th.)
What is x = 57.598?
200
The solution to the equation: log(3x - 41) = 3
What is x = 347?
300
The solution to the equation in interval notation: 7 < 6x - 5 < 49
What is (2,9)?
300
The solution to the equation: 4x^2 + 4x = 35
What is x = {-7/2, 5/2}?
300
Ava recently purchased a home in crescent Beach, Florida. Her property taxes for the first year are $2742. Ava estimates that her property taxes will increase at a rate of $52 per year. Write a linear function that can be used to compute Ava's yearly property taxes.
What is f(x) = 52x + 2742?
300
The amount of money that will be in Tina's account in 10 years, if she deposits $12,413 in an account that pays 8% annual interest, compounded semiannually.
What is $27,198.41?
300
Sid takes twice as long to do a job as Gus. Together they can dig a garden in 4 hours. Find the time it would it take each person working alone.
What is 6 hours for Gus and 12 hours for Sid?
400
The solution to the equation: 1 + 11/x - 42/x^2 = 0
What is x = {-14, 3}?
400
The solution to the equation: 3x^2 + 4x + 8 = 0
What is x = {(-2 - 2isqrt(5))/3, (-2 + 2isqrt(5))/3}?
400
Ross decides to sell calendars that feature the pictures of 12 renowned mathematicians. To do this, he must pay $50 for a business license. Each calendar costs Ross $1.25 to produce, and he plans to sell them for $9.95 each. Find the cost function C(x), the Revenue function R(x), and the profit function P(x).
What is C(x) = 1.25x + 50, R(x) = 9.95x, P(x) = 8.70x - 50?
400
The value of a new car, in dollars, x years after its purchase can be approximated by the function f(x) = 24,000(0.8)^x. Use this function to determine when the value of the car will be $5,000.
What is 7 years?
400
Mia sells used MP3 players. The average cost to package MP3 players is given by the function C(x) = 2x^2 - 40x + 2200, where x is the number of MP3 players she packages in a week. How many players must she package in a week to minimize her average cost?
What is 10 MP3 players must be packaged per week?
500
The solution to the equation: x/(x^2 + 13x + 40) + 3/(x^2 + 2x -15) = 4/(x^2 + 5x -24)
What is x = 2?
500
A golf ball is launched by a slingshot at an initial velocity of 88 feet per second from a platform that is 95 feet height. Find the times when the golf ball will be at a height of 175 feet.
What is 1.15 seconds and 4.35 seconds?
500
Masaru has a small business in which he caters sushi parties. He charges a flat party fee in addition to a charge for each person to cover the food costs. He charges a total of $319.50 for a party with 10 guests and $618.75 for a party with 25 guests. Find a linear function whose input is the number of guests and whose output is the total charge for the party.
What is f(x) = 19.95x + 120?
500
In 2000, Home Depot had 1,134 stores nationwide. By 2002, this total had grown to 1,532. If the number of stores continues to grow exponentially at the same rate, how many stores will there be in 2016?
What is 12,583 Home Depot stores in 2016?
500
A movie theater charges $7 for adults, $5 for children under age 17, and $4 for seniors over age 60. for one showing of Batman the theater sold 222 tickets and took in $1,383. If the number of adult tickets sold is 46 more than twice the number of children's tickets sold, find how many tickets of each kind were sold.
What is 148 adult tickets, 51 children's tickets, and 23 senior tickets?