Interpreting Equations
Which statement is true about a system of linear equations that has no solution?
a) The graphs of the equations are parallel lines.
b) The graphs of the equations are the same line.
c) The graphs of the equations are perpendicular lines.
d) The graphs of the equations are non-perpendicular intersecting lines.
a) The graphs of the equations are parallel lines.
An arithmetic sequence is shown.
5, 10, 15, 20, 25, ...
What is the next number in the sequence?
30
Coach Hamzeh made a mistake solving the linear equation 2x+5=14+x.
In which step does the first error occur? What is the actual answer?
Given: 2x+3=15+x
Step 1: 2x=18+x.
Step 2: 3x=18
Step 3: x=6
Step 2. Should be x=18
Coach Popa hires some students to clean 15 whiteboards at STEM HS. The students charges $9 per hour and a $2 supply fee per whiteboard cleaned. Coach Popa uses a Mythic BeakBuck for a free 30 minutes of cleaning.
Create an equation to represent the amount of money, c, in dollars, that Coach Popa will pay for a cleaning job of h hours.
When is the Algebra OST?
Wednesday the 22nd of April
A health club charges new members a one-time start-up fee in addition to a monthly fee. The cost, in dollars, of the membership for x months is modeled by the function f(x)=80+30x.
What does the 80 represent in the function?
One time start-up fee
A geometric sequence is shown.
3, 6, 12, 24, 48, ...
What is the next term?96
Coach Hamzeh's AI model is trying to solve this equation: 2(2x-2)=18-x
In which step does the first error occur? What is the actual answer?
Given: 2(2x-2)=18-x
Step 1: 4x-2=18-x
Step 2: 5x-2=18
Step 3: 5x=20
Step 4: x=4
Step 1. Should be 4.4
Coach D'Andrea scored 42 points during a recent basketball game. He made only 2-point shots and 3-point shots. In total, Coach D'Andrea made 19 shots.
Create two unique equations that model the number of 2-point shots, x, and the number of 3-point shots, y, that Coach D'Andrea made in the game.
y+x=19
2x+3y=42
What are the host(s) of the 2026 World Cup? (name all)
Canada, Mexico, USA
A fitness club charges members an initial fee and a separate monthly membership fee. The equation of the function given models the total fee, f(x), in dollars, that a person pays for x months of membership.
f(x)=30x+25
What does the number 30 represent in this situation?
The monthly membership fee
The first four terms of an arithmetic sequence are given.
27, 32, 37, 42, . . .
What is the 21st term of the sequence?
127
An equation is given. (π is the symbol for pi)
A=4πr2
r=sqrt*(A/4π)
Coach Graber buys pineapples, watermelons, and a bag of grapes for a fruit salad. He spends a total of $29.68 on the fruit salad. Pineapples cost $2.15 each, and watermelons cost $3.75 each. The bag of grapes costs $4.48.
Create an equation to model this situation, where p represents the number of pineapples Coach Graber can purchase and w represents the number of watermelons he can purchase.
29.68=2.15p+3.75+4.48
What is the only place in the world where Alligators and Crocodiles live in the same habitat?
Florida
Isaac deposits money into a new bank account that earns interest. He does not make any other deposits. The expression shows the total amount of money in his account n years after the deposit.
200(1+0.08)n
What does the number 200 represent in this situation?
The original amount of money deposited into the account.
The first five terms of a sequence are shown.
2, 9, 16, 23, 30, …
Write a function to model the value of the nth term in the sequence.
f(n)=
f(n)=2+(n-1)7
Coach Hamzeh's dog is trying to solve the equation ½(x+18)=4(2x-6)-9x
In which step does the first error occur? What is the actual answer?
Given: ½(x+18)=4(2x-6)-9x
Step 1: x+18=8(2x-6)-18x
Step 2: x+18=16x-6-18x
Step 3: x+18=-6-2x
Step 4: 3x+18=-6
Step 5: 3x=12
Step 6: x=4
Step 2. Should be -22
Stephanie adds pennies, nickels and quarters to a scale until the mass of the combined coins is 75 grams. Each penny has a mass of 2.5 grams, each nickel has a mass of 5 grams and each quarter has a mass of 5.7 grams.
Create an equation to model this situation, where x is the number of pennies, y is the number of nickels and z is the number of quarters that Stephanie can put on the scale so that the mass of the combined coins is exactly 75 grams.
2.5x+5y+5.7z=75
What is the maximum amount of days that a year can have?
A scientist studies the population of an insect colony. She begins her study with 1,000 insects in the colony and measures the population of the colony each year. She uses the given formula to model the insect population, P, x years since the beginning of the study.
P=1,000(1.15)x
By what percent does the insect population grow each year?
15%
The first five terms of a sequence are shown.
4, 12, 36, 108, 324, …
Write a function to model the value of the nth term in the sequence.
f(n)=
f(n)=4*3n-1
The equation shown is used to find the force of gravity, F, between two objects, where
G is the gravitational constant,
m1 and m2 are the masses of the two objects, and
r is the distance between the two objects.
F=(Gm1m2)/r2
Which equation correctly shows the distance between the two objects?
r=sqrt*(Gm1m2/F)
Trent plants a sunflower that is 6 inches tall. The sunflower is expected to grow at an average rate of 1.5 inches per day during the next month.
A.Create an equation that Trent can use to find the number of days, x, it will take the sunflower to grow to a height of 45 inches.
B.How many days will it take the sunflower to grow to a height of 45 inches?
a. 1.5x+6=45
b. 26 days
What is the formula for the area of a rectangle?
A=L*W