Unit 1 Solving Equations
Solve the following equation:
3(2x+4) + 5 = 4(2x+1) - 6
What is 19/2 or 9.5?
Give me the slope-intercept form of an equation, where m is the slope and b is the y-intercept.
What is y = mx + b?
Which test is used to determine if a graph represents a function?
What is the Vertical Line Test?
TRUE OR FALSE? (You MUST answer both parts correctly to get any points!)
a. A point on a dashed line is a solution to an inequality.
b. A point on a solid line is a solution to an inequality.
What is
a. FALSE
b. TRUE
TRUE OR FALSE?
The pattern that an exponential function gives will add the same number continuously.
What is FALSE?
Solve the following inequality:
-3y > 21
What is y < -7?
A pair of lines that never cross each other are called what?
What are Parallel lines?
Suppose f is a function. If 10 = f(-4), give the coordinates of a point on the graph of f.
What is (-4, 10)?
What is the solution to the following system of linear equations? (Hint: You MUST give the entire decimal for both numbers to get points!)
y = 4x + 3
5x + 3y = 1
What is (-0.471, 1.118)?
What is the axis of symmetry for the quadratic equation x2 + 4x + 7?
What is x = -2?
A checking account is set up with an initial balance of $4800, and $400 is removed from the account each month for rent (no other transactions occur on the account).
Write an equation whose solution is the number of months, m, it takes for the account balance to reach $2,000.
What is 2000 = -400m + 4800?
Find a linear equation in slope-intercept form so that (0,6) and (4,-3) are both solutions to the equation.
What is y = -(9/4)x + 6?
Complete the table by finding the numbers for the question marks, where the table MUST represent a function:
x f(x)
3 6
7 ?
? 4
What is
x = any # EXCEPT 3 and 7;
f(x) = any number
WITHOUT GRAPHING, how many solutions does the following system of linear equations have?
y = 5x + 3
y = 5x - 4
What is no solutions?
For (a)-(c), determine whether the quantity is changing in a linear or exponential fashion.
a. A liter of water evaporates from a swimming pool every day.
b. A savings account, which earns no interest, receives a deposit of $723 per month.
c. The value of a machine depreciates by 17% per year.
What is
a. Linear
b. Linear
c. Exponential
A government buys 5 fighter planes at $15 million dollars each, and y tons of wheat at $300 per ton. It spends a total of $100 million dollars.
Write an equation in the form B = xz +yw, where x is the number of fighter planes, z is the amount of money each fighter plane costs, y is the number of tons of wheat, and w is the cost of each ton of wheat.
Then, determine how many tons of wheat the government bought. (This will be the answer I am looking for! Round your answer to the nearest whole number!)
What is 83,333 tons?
A ball thrown vertically upward at a speed of v ft/sec rises a distance d feet in t seconds, given by
d = 6 + vt - 16t2
Write an equation whose solution is the time it takes a ball thrown at a speed of 88ft/sec to rise 20 feet. (I am only looking for an equation here!)
What is 20 = 6 + 88t - 16t2?
YOU MUST ANSWER BOTH PARTS CORRECTLY TO GET ANY POINTS!!!
A restaurant is open from 2PM - 2AM on a certain day, and a maximum of 200 clients can fit inside. If f(t) is the number of clients in the restaurant t hours after 2PM that day,
a. What is a reasonable domain for f?
b. What is a reasonable range for f?
What is
a. 2PM - 2AM
b. 0 - 200 clients
Give 3 points that are solutions to the following system of linear inequalities:
y > 3x + 1
y < -4x
What is .....?
Give the vertex and axis of symmetry for the expression (x - 4)2 + 6, along with determining if the expression has a minimum or maximum.
You must give all 3 correctly to get any points!
What is:
Minimum
Vertex: (4, 6)
Axis of Symmetry: x = 4
If F denotes a temperature in degrees Fahrenheit and C is the same temperature measured in degrees Celsius, then F and C are related by the equation
F = (9/5)C + 32
Rewrite this expression to solve C in terms of F.
What is C = (5/9)F - 160/9?
Identify the differences between the following 2 equations: (Hint: There should be 3 differences here!)
y = 2x
6x + 2y = 3
What is
1. Slopes are different
2. 1 is in slope-intercept form, and the other is in standard form
3. There is no y-intercept in the first equation.
Consider the following arithmetic sequence:
34, 59, 84, 109, ...
What is the 93rd term to the sequence?
What is 2,334?
Construct a system of two linear equations where (2, 8) is a solution to the first equation but not to the second equation, and where (-3, -2) is a solution to your system.
What is
y = -2
y = 2x + 4
(Any other equation will be tested!)
(100 points for each part answered correctly, +100 if all are answered correctly)
Suppose h(t) = -5t2 + 10t + 3 is the height of a diver above the water (in meters) t seconds after the diver leaves the springboard.
a. How high above the water is the springboard?
b. When does the diver hit the water?
c. At what time on the diver's descent toward the water is the diver again at the same height as the springboard?
d. At what time does the diver reach the peak of the dive?
What is
a. 3 meters
b. 2.265 seconds
c. 2 seconds
d. 1 second