Linear Linear Linear!!
What is the slope of the line that passes through the points (1,2) and (3,8)? (with slope formula for 50 extra points).
3
Extra: y=3x-1
Solve the system:
x + 2y = 5
3x - y = 9
x = 3
y = 1
If f(x) = 3x - 5, what is f(-2)?
f(-2) = -11
What is the probability of getting heads on a fair coin flip followed by a 6 on a fair six-sided die?
1/12
A company offers a discount of 20% on the first item, and 30% on any additional items. If a customer buys two items that originally cost $50 and $80 respectively, how much did they pay in total after both discounts, including a 10% sales tax on the discounted price? (show your work 😈)
They paid $117.81 after all discounts and tax.
Solve for x if 3(2x−5) = 4x + 11.
x = 13
Solve for x and y:
2x - y = 7
4x + 2y = 8
x = 3
y = -1
What is the range of the fuction f(x) = x2 + 3?
y is less than equal to 3
If a bag contains 7 red, 5 blue, and 8 green marbles, what is the probability of drawing a green marble?
Extra
Give me a simplified version of the fraction (50)
8/20 = 2/5
A city has 5 bridges connecting two sides of a river. If each bridge has a 10% chance of being closed on any given day, what is the probability that exactly 2 bridges are closed?
(5/2) × (0.1)2 × (0.9)3 ≈ 0.0729.
if y = 2/3x - 7, what is the value of y when x = 12.
(50 more points if you graph the you got from the equation)
y = 1
Extra:
How many solutions does the system have?
4x−2y=10
8x−4y=20
Infinite amount of solutions
Is the function f(x) = x3 + 2x2 + 4 increasing or decreasing at x = 1?
Extra:
What is this type of function? (10)
Graph the function on a graph (50)
Increasing
Extra:
Cubic Function (this happens when the exponent is raised to the power of 3)
Graph:
The mean of four test scores is 82. If the first three scores are 85, 78, and 90, what is the fourth score?
75
A rectangular garden has a length of 4 meters longer than its width. A walkway of uniform width is added around the garden, increasing its total area by 80 square meters. If the original width of the garden is 6 meters, what is the width of the walkway?
The width of the walkway is 1 meter.
The sum of two consecutive even integers is 86. What are the integers?
42 and 44.
Solve the system:
5x + y = 14
3x - 2y = 4
x = 2
y = 4
For the function h(x) = x2 - 4x + 7, find the x-coordinate of the vertex.
x = 2
A card is drawn from a standard deck of 52 cards. What is the probability of drawing a king or a red card?
Extra:
Simplified version of fraction (50)
28/52 or 7/13
A car dealership sells two models of cars, Model A and Model B. The number of Model A cars sold is double the number of Model B cars sold. Each Model A car costs $25,000, and each Model B car costs $40,000. If the dealership sold enough cars to make $3 million in revenue, how many cars of each model were sold?
They sold 80 Model A cars and 40 Model B cars.
A phone company charges $40 per month for a base plan and an additional $0.05 per text message. If someone’s bill is $55, how many text messages did they send?
For Extra Points
Make a slope equation for this situation (50)Tell me what this means in the context of this situation. (100)
The person sent 300 text messages.
Extra:
y = 0.05x + 4 (50)
(80)
The slope, 0.05, means each text adds $0.05 to the bill. The intercept, $40, is the base charge, so even with 0 texts, you still pay $40. (100)
A company produces two types of pens, one selling for $1.50 and the other for $2.00. If the company sold 500 pens for a total of $850, how many pens of each type were sold?
300 pens at $1.50 and 200 pens at $2.00
The profit P(x) for selling x products is modeled by P(x)= −5x2 + 300x − 2000. How many products must be sold to maximize profit, and what is the maximum profit?
Extra:
What type of function is this? (10)
Graph this equation
30 products, maximum profit = $2,500
Extra:
Quadratic (10)
Graph:
A school survey finds that 60% of students like basketball, 50% like soccer, and 30% like both sports. What is the probability that a randomly chosen student likes at least one of these sports?
80%
A farmer owns a triangular plot of land with a base of 100 meters and a height of 80 meters. The farmer wants to build a rectangular barn inside the triangle, with one side of the barn running along the base of the triangle. The other two sides of the barn must be parallel to the triangle’s sides (i.e., they’ll lie on lines that connect the top vertex of the triangle to the base). The barn must have a width of 40 meters.
The barn must also have a minimum distance of 10 meters from the top vertex of the triangle. The farmer wants to maximize the area of the barn while keeping it inside the triangle.
16 meters (100)
640 square meters (500)