Unit 1
Linear Equations, Expressions, and Inequalities
Linear Equations, Expressions, and Inequalities
Simplify the following expression:
9a + 4b - 5c - 1 - 3a + 4b + 5c
6a + 8b -1
A gym charges a one-time sign-up fee of $25 and $8 per class attended.
Write a function that represents the total cost y based on the number of classes x.
Then, find the total cost if someone attends 6 classes.
y = 8x + 25; total cost = $73
Are these lines parallel or perpendicular?
Slide #2
Neither
What is the value of (32)4 and what rule of exponents do you use?
38 Power of Power Rule
NO CALCULATOR!!!
Estimate what whole numbers the square root is between.
Square Root of 200
14 and 15
Graph this equation:
y =2/3x + 4
Graph
Convert to slope-intercept form:
3x+2y=8
y = -3/2x + 4
DOUBLE JEOPARDY!!!
Solve the system of equations:
2x - 4y = 6
4x + 4y = 10
(8/3,−1/6)
Convert the following number to scientific notation:
0.0000458
4.58×10-5
The city is working to replace the pipelines in the city. The pipeline needs to follow that will form a right-angle path beneath a city block. One section will measure 30 meters eastward and another 40 meters northward.
Determine the shortest distance the pipeline needs to cover to connect these two points.
50 Meters
Solve this equation:
2(x + 7) + 3x = 12
x=-2/5
Zoe surveyed her friends in her study group to find out how many hours they each spent studying and how many hours they watched TV. The table below displays her findings.
Is the relationship a function or not a function? Explain how you know.
Slide #3
Not a function
Solve the following system of equation using substitution (you must show me substitution method for credit)
3x - 2y = - 2
x + 3y = 14
x = 2, y = 4
DOUBLE JEOPARDY!!
Multiply and answer in scientific notation:
(3×108)(6.8×10-13)
2.04×10-4
Timothy designed a cylindrical soda tower to have at parties and events at his school.
His initial design measured 12 inches high with a diameter of 6 inches. Timothy wants to design another tower that holds more soda for larger events. He can’t decide whether to double the height or double the diameter. Which tower would hold more soda when filled? Explain your reasoning.
The tower with the doubled diameter would hold more soda.
How many solutions does this equation have?
4(2x−3)+3(x+5)−2(3x−1) = 3(x+1)−2(−x−1)
5x+5=5x+5 or infinite solutions
In a study analyzing the relationship between rainfall and crop yield, a line of best fit is drawn on a scatter plot. If a point representing a year's data falls significantly below the line of best fit, what can be inferred about that year?
A) There was a drought that year
B) There was excessive rainfall that year
C) The crop yield was higher than predicted
D) The crop yield was lower than predicted
D
Brenda's school is selling tickets to a spring musical. On the first day of ticket sales the school sold 3 senior citizen tickets and 9 child tickets for a total of $75. The school took in $67 on the second day by selling 8 senior citizen tickets and 5 child tickets. What is the price each of one senior citizen ticket and one child ticket?
senior citizen ticket: $4, child ticket: $7
Slide #4
B,C,E
A school is installing a diagonal walking path across a rectangular courtyard. The path will connect one corner of the courtyard to the opposite corner and will measure 26 meters long.
One side of the courtyard (the length along the building) is 10 meters.
To order materials, the construction team needs to know the width of the courtyard.
What is the width of the courtyard?
24 meters
Solve for p
(Jeopardy Slide #1)
p = m + s - (r/q)
A concert venue sells tickets with two different pricing options:
Questions:
A. Write a function for each pricing option.
B. At how many tickets will both options cost the same?
C. Which option is cheaper if a group buys 12 tickets? Show your work.
D. For what number of tickets is Option B the better deal? Explain your reasoning.
A: y=5x+20(Option A) y=2x+50(Option B)
B: x=10
C: Option B is Cheaper
D:After 10 tickets, option B is the better deal
The senior classes at High School A and High School B planned separate trips to New York City. The senior class at High School A rented and filled 1 van and 6 buses with 372 students. High School B rented and filled 4 vans and 12 buses with 780 students. Each van and each bus carried the same number of students. How many students can a van carry? How many students can a bus carry?
Van: 18, Bus: 59
Slide #5 :)
Irrational
You are an engineer tasked with designing a water tank for a residential building. The tank is cylindrical in shape. The available space allows for the water tank to have a maximum height of 10 meters. The tank needs to hold 150 cubic meters of water.
A.Calculate the minimum required radius for the cylindrical tank to meet this volume requirement (Round to the nearest hundredth).
2.18 Meters