Linear Equations & Inequalities, Rational Exponents
Solve. x/5 + 1/3 = x + 9/2
-125/24
What are the x and y intercepts of the linear function? 4x + 12y = -24
x-intercept: (-6,0)
y-intercept: (0,-2)
Multiply. (x2-6)(2x2+3x-1)
2x4+3x3-13x2-18x+6
Consider the function {(4,1), (2,-3), (a,-a), (0,5)}. What is a possible value for a?
Anything except for 4,2, or 0
Write the linear equation in slope intercept form. What does each parameter represent?
y=mx+b; m is the slope; b is the y-intercept
Solve. 1/2(2x + 5) > 2/3(6x -10)
x < 55/18
Lucy pays $225 in advance on her account at the health club. Each time she visits, $7 is deducted from her account. a)Write an equation to model the situation. b)How much will she have remaining on her account in 17 years?
y=225-7x; $106
Solve. x2 - 6x = -9
x=3
f(x)=x3-x2 What is the average rate of change of f(x) on the interval x=-1 to x=2?
2
What is the formula for the exponential function, and what does each parameter represent?
y=abx; a is the y-intercept, b is the constant ratio
Solve for b1. A = 1/2(b1+b2)h
b1 = 2A/h - b2
I have a jar of coins that contains only nickels and dimes. I know that I have more dimes than nickels, and that altogether, there is at least $5.50 worth of coins in the jar. Write a system of inequalities to model the situation.
0.05x + 0.1y greater than or equal to 5.5
y>x
Solve by completing the square. x2+12x+32=0
x= -4, x= -8
The weights of the players on a professional football team are normally distributed with a mean of 237 lbs and a standard deviation of 41 pounds. What is the probability a player's weight is greater than 278 lbs?
16%
Write the 3 forms of the quadratic function. What does each form reveal?
y=ax2+bx+c: y-intercept
y=k(x-a)(x-b): zeros
y=a(x-h)2+k: vertex
Simplify. Write in the form xn. cube root of x5 * 4th root of x
x23/12
Solve the system and determine the number of solutions. x+4y=10; y=14x+10
One Solution; (-30/57, 50/19)
The number of mosquitoes in Anchorage, Alaska (in millions of mosquitoes) as a function of rainfall (in centimeters) is modeled by:
m(x)=-x2+14x What is the maximum possible number of mosquitoes?
49 million
No Correlation? Correlation without Causation? Correlation with Causation?
A local news agency is concerned with the number of shark attacks on Florida’s beaches. They perform a study which reveals that on Fort Myers Beach when 24 ice creams were bought there were 2 shark attacks in the state and when there were 56 ice creams bought on Fort Myers Beach there were 11 shark attacks in the state. The news agency concluded that with the more ice cream sold on Fort Myers Beach, there is an increased likelihood of a shark attack in the state.
Correlation without Causation
What is the formula for completing the square and axis of symmetry respectively?
CTS: b2/4a; AOS: x= -b/2a
Two numbers have a product that is Rational. One of the two numbers is irrational. What can you conclude about the other number? A) Rational, B) Irrational C) Could be either D) insufficient information
C) It could be either rational or irrational. (think: sq rt of 2*sq rt of 8 vs. sq rt of 2*0)
A new car costs $32,000. It depreciates at a rate of 15% each year. a) Write an equation to model the situation. b) Find the value of the car after 6 years.
y=32,000(1-.15)^x OR y=32,000(.85)^x; The car will be worth approx $12,068.78 after 6 years.
A ball in thrown into the air with an initial height of 6 feet and a vertical velocity of 20 feet/sec. It landed on a small hill, 2 feet above the ground. How long did it take for the ball to land on the hill? Round your solution to the nearest tenths place. Hint: Use projectile motion formula.
It took the ball approx. 1.4 seconds to land on the hill.
How do you know when a residual plot shows a bad fit model to the scatter plot data?
It is patterned OR not random and further from the x-axis
What general transformation rule is shown and how do you apply it? f(1/3x)
horizontal stretch by a factor of 3, (1/a)