Algebraic Math
Solve for x:
2x + 5 =15
What is 5?
2x = 10
x = 5
John has 3 times as many apples as Sarah. If Sarah has 5, how many does John have?
What is 15
Find the missing angle in a right triangle with angles 30° and ___?
What is 60°?
Factorize:
x2 - 9
what is (x-3)(x+3)
Use the "difference in squares"
A rectangle has a length 3 times its width. If the perimeter is 48, what is the width?
What is 6?
Let width = x, then length = 3x.
Perimeter formula: 2(x+3x)=48
Solving: 8x=48x
x = 6
Find the area of a triangle with base 10 and height 7.
What is 35?
A= (1/2) * b * h
A=(1/2)×10 × 7 = 35
Solve for x:
x3-9x=0
What is -3, 0, 3
Zero Product Property
x(x2-9)= 0
x(x-3)(x+3)= 0
x = 0
x-3 = 0, x = 3
x+3 = 0, x = -3
A car increases speed from 20 mph to 50 mph in 6 seconds. What is the acceleration? (State question with units)
What is 5mph/s?
a=Δv/Δt
a=(50mph−20mph)/6 - 0
a=30mph/6
a = 5 mph/s
Find the length of the hypotenuse of a right triangle with legs of 6 and 8.
What is 10?
c2=b2+a2
c2=62+82
c2=36+64
c2=100
sqrt(c2)=sqrt(100)
c = 10
Solve for x:
44(2x+1) + 12 * 2 + 2 = 0
What is 35/44?
44(2x+1) + 12 * 2 + 2 = 0
88x+44+24+2 = 0
88x + 70 = 0
88x = 70
x = 70/88, 35/44
A tank is filling at a rate of 2 gallons per minute. How much water is in it after 1.5 hours?
What is 180 gallons?
2 * (1.5×60)
2 * 90
180
A circle has a radius of 5. Find the circumference.
What is 10π?
C=2πr
2π(5)
10π
Find the sum of the root of x2-7x+12=0
-b/a
What is 7?
The sum of the root formula is -b/a
-(-7)/1 = 7
A train travels 120 miles in 3 hours, then 90 miles in 2 hours. What is its average speed? (use units!)
What is 42 mph?
Total distance(td): 120miles + 90miles = 210miles
Total time(tt): 3hrs + 2hrs = 5 hrs
td/tt =average speed
210/5
Answer: 42 mph
A cone has a base radius of 4 and a height of 9. Find its volume.
What is 48π?
V = (1/3)πr2h
V = (1/3)π429
V = (1/3)π(16)9
V = (1/3)π144
V=48π