Data
A survey shows that x students prefer apples, 2x+5 prefer bananas, and the rest of the 50 students prefer oranges.
Express the number of students who prefer oranges in terms of x.
Total students = 50
A savings account has $1000 and earns 4% interest per year, compounded yearly.
(a) Write an expression for the amount after tt years.
(b) Find the amount after 5 years.
(a) Interest rate 4% = 1.04 multiplier:
A=1000×(1.04)^t
(b) After 5 years: 1217
A population of bacteria grows as P=50×2t. Find the smallest whole number t such that P>800.
t=5
Find the distance between points A(2,3). and B(5,7).
The distance between points A and B is 5.
solve.
x2−5x+6=0
x=2 or x=3
A survey found that x students like apples, and 2x+3 students like bananas. If there are 27 students total, how many students like apples?
x=8
A virus infects 150 people initially and increases by 50% daily.
(a) Write an expression for the number of infected people after dd days.
(b) Find the infected count after 4 days.
(a) Growth factor 1.5:
I=150×(1.5)^d
(b) After 4 days:
I=150×(1.5)4=150×5.0625=759.375
A car’s value depreciates by 15% yearly starting at $20,000. Find the number of years n until the car’s value is less than $10,000.
20000×(0.85)n<10000
Find the midpoint between points C(4,1) and D(8,5).
The midpoint between points C and D is (6,3).
solve.
x2−4x−5<0
−1< x <5
The ages of 5 participants are 20,22,20+t,20+2t,22+t. If the mode of the ages is 22, find t.
t=1
A product’s sales start at 300 units and increase by 8% each year.
(a) Write the formula for sales in year tt.
(b) Calculate sales after 6 years.
(a) Growth rate 8% = 1.08 multiplier:
S=300×(1.08)^t
(b) After 6 years: 476.07
What is a inequality?
A mathematical statement that compares two expressions and shows that one is greater than, less than, greater than or equal to, or less than or equal to the other.
Find the midpoint between points G(−3,4) and H(1,−2).
The midpoint between points G and H is (−1,1).
Define Quadratics
Quadratics are expressions or equations involving squared variables that model important patterns and problems in algebra and real life
Students scoring A, B, C are 3n+5, 2n+7, and n+8. Total students = 75. Find n.
n=9.17
A battery has a charge of 2500 mAh and loses 8% of its charge every hour.
(a) Write an expression for the charge after t hours.
(b) Find the charge after 7 hours.
(a) Decay factor: 1−0.08=0.92
Q=2500×(0.92)t
(b) After 7 hours: 1412
A car’s value depreciates by 15% yearly starting at $20,000. Find the number of years nn until the car’s value is less than $10,000.
n=5.
Find all points P(x,0) on the x-axis such that the distance from P to Q(3,4) is less than 5. Write the inequality and solve for x.
Find all points P(x,0) on the x-axis such that the distance from PP to Q(3,4)is less than 5. Write the inequality and solve for x.
A rectangular garden has an area of 24 square meters. Its length is x+2x+2 meters and width is x meters. Find x.
x=4
There are xx students who like apples and 2x+4 who like bananas. Total students = 40. Find how many like oranges when x=6.
18 students like oranges.
A tree loses 5% of its leaves each week. If it starts with 10,000 leaves:
(a) Write an expression for the number of leaves after w weeks.
(b) How many leaves remain after 6 weeks?
(a) Decay factor: 1−0.05=0.95
L=10000×(0.95)w
(b) After 6 weeks: 7351
A savings account grows at 5% yearly. Initial amount is $5000. Find after how many years t the balance exceeds $7000.
t=7.
Two points, A(2,3) and B(8,7) represent locations of two bacteria colonies. The bacteria population at each colony grows exponentially as P=P0×2t, where P0=100 is the initial population and t is time in hours.
(a) Find the distance between colonies A and B.
(b) Find the midpoint between colonies A and B.
(a) Distance between the two colonies is approximately 7.21units.
(b) The midpoint between the colonies is (5,5).
Find the root of x2=9
x=3, x=−3