Algebraic Equations and Inequalities

The video tutorial covers various mathematical problems, including analyzing bus ride times using equations, modeling scenarios with graphs, factoring equations, solving distance and time-related problems, and addressing age and integer-related problems. The tutorial emphasizes understanding equations, graphing, and problem-solving techniques.

What is the equation representing Jesse's bus ride time if it is 5 minutes more than 2/3 of Robert's bus ride time?

• y = 2x + 5/3

• y = 5x + 2/3

• y = 2/3x + 5

• y = 3/2x + 5

Which of the following inequalities represents the scenario where the number of pounds of apples minus twice the number of pounds of oranges is at most five?

• y + 2x ≤ 5

• y + 2x ≥ 5

• y - 2x ≤ 5

• y - 2x ≥ 5

What is the factored form of the expression T^2 - 36?

• (T - 9)(T + 4)

• (T - 4)(T + 9)

• (T - 6)(T + 6)

• (T - 3)(T + 12)

If the floor of a rectangular cage has a length 4 feet greater than its width W, and both dimensions are increased by 2 feet, what is the new area?

• W^2 + 6W + 8

• W^2 + 12W + 20

• W^2 + 10W + 16

• W^2 + 8W + 12

Shawn walks at 5 feet per second and starts 20 seconds before Curtis, who walks at 6 feet per second. After how many seconds will they have walked the same distance?

• 160 seconds

• 140 seconds

• 120 seconds

• 100 seconds

If 60 candy bars and 110 drinks sell for $265, and 120 candy bars and 90 drinks sell for $270, what is the price of a candy bar?

• $1.25

• $1.00

• $0.75

• $0.50

What is the smallest of three consecutive positive integers if the product of the smaller two is five less than five times the largest?

• 3

• 4

• 5

• 6

How many seconds does it take for an object launched with the function h(t) = -5t^2 + 20t + 60 to hit the ground?

• 4 seconds

• 5 seconds

• 6 seconds

• 7 seconds

If Antonio's age is represented by A and Sarah's age is 5 times Antonio's, what is Sarah's age if 2A + 3S = 34?

• 8

• 10

• 12

• 14

What is the equation for the new area of a rectangular cage if its length is 4 feet more than its width W, and both dimensions are increased by 2 feet?

• (W + 2)(W + 4)

• (W + 2)(W + 8)

• (W + 6)(W + 2)

• (W + 4)(W + 6)