Unit 4.5-5
X- -2, -1, 0, 1, 2, 3
Y- 4, 2, 1, -2, -1, -2
Graph this table on Desmos and then, draw a line of best fit.
Done on Desmos show tutor for a check.
Create and equation that has no solution to 4y=8x+20.
4y=8x+10 has no solution to the original equation because the lines are parallel and will never intersect.
Solve 4x-10>2x+4
1. Move the variables: First, move all terms containing to the left side of the inequality. Subtract from both sides:
(4x-2x)-10>4
2x-10>4
2. Isolate the variable term: Next, move the constant term to the right side by adding
to both sides:
2x>4+10
2x>14
3. Solve for x
Finally, divide both sides by the coefficient 2 to isolate x
2x/2>14/2
x>7
Which table is Linear and which Table is exponential?
Table 1
X-0,1,2,3,4
Y-0,3,6,9,12
Table 2
X-0,1,2,3,4
Y-1,3,9,27,81
Table 1 is Linear and Table 2 is Exponential.
Linear: Y is increasing by 3 each time
Exponential: Y is multiplied by 3 each time
Who said this reference: "Ill whoop your *** your girlfriend look like my mom"
What is Tyler the Creator
5−2(3x−4)≤9+x
Solve for x
5−2(3x−4)≤9+x
5−6x+8≤9+x
13−6x≤9+x
13≤9+7x
4≤7x
4/7≤x
x≥4/7
Give the value of x that would make the equation true:
2x+3y=13
x-2y=-4
Isolate x: x=2y-4
-Substitute at solve for y
Distribute by 2:
2(2y-4)+3y=13
Combine like terms:
7y-8=13
Add 8 to both sides:
7y=21
Divide by 7:
y=3
Solve for x:
x=2(3)-4
x=6-4
x=2
Solve and Interpret the solution for -2x+7_<1
Step 1: Solve it
Subtract 7 from both sides: -2x_<-6
Divide by -2:
Crucial Rule: When you divide by a negative, you must flip the sign.
x>_3
Step 2: Interpret it
Symbol (>_
): Since it is "greater than or equal to," we use a closed (solid) circle.
Value (3): The circle goes exactly on the number 3.
Direction (>_
): The solution includes all numbers larger than 3, so we shade to the right.
Step 3: Graph it
[---●============>
-1 0 1 2 3 4 5 6
You buy a brand-new smartphone for $1,000. Every year, the phone loses half of its value.
1. Write the Equation
2. Value after 3 years
Plug t=3 into the equation:
y=1000(0.125)
After 3 years, the phone is worth $125.
What music artist has won 10 Grammy had 34 nominations and won song of the year in 2026?
Hint shes my favorite artists so my favorite songs from each of her albums include:
HMHAS: L'AMOUR DE MA VIE
HTE: Happier Than Ever
WWAFAWDWG: Wish you were gay
DSAM: Idontwannabeyouanymore
What is Billie Eilish
Identitfy the value of x which makes this statement true.
4(5x−7)+3(2x+1)≤18x−16
4(5x−7)+3(2x+1)≤18x−16
20x-28+6x+3≤18x-16
26x-25≤18x-16
+16 +16
26x-9≤18x
-26x -26x
-9≤-8x
-9/-8≤-8x/-8
1.125 >_ x
A concession stand sells hot dogs for 1.50$ and sodas for 0.5$. If they sold a total of 87 items (hot dogs + sodas) and made 78.50$ in revenue, how many hot dogs and how many sodas were sold?
H+S=87
1.5H+0.5S=78.50
Let H number of hot dogs sold
Let S = number of sodas sold
S=87-H
1.50h+0.50(87-h)=78.50
Distribute: 1.50h+43.50-0.50h=78.50
Combine like terms: 1.00h+43.50=78.50
Subtract: 43.50 from both sides h=35 (hotdogs)
Substitute back in: 35+S=87 s=87-35=52 S=52 (sodas)
You and your friends are going to an amusement park. You have at most $60 to spend for the day.
The Entry Fee: The park admission costs $25.
The Snacks: Each snack you buy costs $7.
How many snacks can you buy without going over your budget?
1. Write the inequality
Since you have "at most" 60 dollars your total spending is must be less than or equal to 60.
25s+7_<60
2. Isolate the variable term
Subtract the admission fee (25)from both sides:
7s_<35
3. Solve for s
Divide by the price per snack (7):
s_<5
You can buy any number of snacks up to 5.
A person puts 2,000 dollars into a bank account. Every year, the bank adds 5 percent interest to the total balance. How much money will be in the account after 2 years?
You will have 2,205 dollars in the account after 2 years.
What music artist might kill her ex?
Lyric: "I might kill my ex not the best idea"
What is SZA
A local coffee shop sells two sizes of coffee: a small (S) for $2.50 and a large (L) for $3.50.
If you want to spend no more than $12.00 on coffee today, write an inequality that represents the possible number of small coffees (S) and large coffees (L) you can buy.
2.50S+3.50L≤12.00
It takes a rower 2 hours to row 12 miles downstream (with the current). The return trip upstream (against the current) takes 3 hours to cover the same distance.
Let be the rower's speed in still water and be the speed of the current.
2(r+c)>_12 (downstream)
3(r-c)>_12
r+c>_6
r-c>_4
(r+c)+(r-c)>_6+4
2r>_10
>_r5
5+c>_6
c>_1
The speed of the rower in still water is 5 miles per hour and the speed of the current is 1 mile per hour.
Alex is planning a road trip to a music festival and needs to determine how many friends can join without draining their bank account. With $450 currently in savings, Alex must account for a $150 festival ticket and an additional gas cost of $15 per person for the entire group. To ensure they aren’t broke after the trip, Alex sets a goal to have at least $200 remaining in their account. Write an inequality and find out how many friends will stay within their budget.
450-(150+15x)>_200
300-15x>_200
-300 -300
-15x>_-100
/-15 /-15
x_<6.67
Since there can’t be a fraction of a person, the total group size is maxed out at 6, including themselves, meaning Alex can invite a max of 5 friends to stay within the budget.
A scientist starts an experiment with 500 bacteria in a petri dish. The population doubles every hour.
1. Write the Equation
a (initial amount): 500
2. Population after 6 hours
Plug t=6 into the equation:
y=500(2)6
y=500(64)
y=32,000 bacteria
bacteria
3. Time to reach 8,000 bacteria
Set y to 8000 and solve for t:
8000=500(2)t
Divide both sides by 500:
Since: 24=16
t=4 hours
Often seen as a past sensation, this artists best songs are all before his 2019 album Care package.
What is Drake
A pet store has 500 animals. Fish cost 20 dollars monkeys cost 70 dollars and hippos cost 100 dollars. You have to buy at least 300 dollars worth of hippos monkeys and fish how many can you buy? Write an Inequality(s) determining this.
f = number of fish
m = number of monkeys
h = number of hippos
Total animals: f+m+h=500
Cost constraint: 20f+70m+100h≥300
Mark's Canoes rents canoes for a flat fee of 20 plus 35 per hour. You have a budget of no more than 150.
a) Write an inequality to represent the situation.
b) How many hours can you afford to rent the canoe?
1. Define the Variable:
Let h
represent the number of hours the canoe is rented.
2. Set up the Inequality:
Total Cost = (Hourly Rate
Hours) + Flat Fee
Total Cost = 35h+20
"No more than" means the total cost must be less than or equal to 150.
35h+20_<150
3. Solve the Inequality:
Subtract 20 from both sides:
35h_<130
Divide by 35:
h_<130/35
h_<3.714
Answer:
You can rent the canoe for a maximum of 3 hours rounded or up to approximately 3.71 hours.
A rental service charges a flat fee of $20 plus $35) per hour (h). If you can spend no more than $150, but want to rent for at least 2 hours, what is the valid range for hours (h)?
20 + 35h ≤ 150
Time Constraint:
h ≥ 2
Solve for the maximum hours:
35h < 150 - 20
35h < 130
h < 130/35
h < 26/7 or 3.71 hours
Apply the minimum time constraint:
2 ≤ h
Final Combined inequality
2 ≤ h ≤ 26/7 hours
A city has a population of 50,000 people. Every year, the population grows by 4 percent. What will the population be after 2 years?
Step 1: Write the equation.
y = 50,000 * (1.04)^t
Step 2: Calculate the population for Year 1.
50,000 * 1.04 = 52,000
Step 3: Calculate the population for Year 2.
52,000 * 1.04 = 54,080
Total after 2 years: 54,080 people.
Known for his acting in Euphoria as Elliot, and his presence on social media for his viral song Babydoll and Mamas Boy, coming to Colorado in September with Tame Impala, Who is this singer?
What is Dominic Fike