Geometry and Population Modeling Problems

The video tutorial covers solving equations by factoring and using the zero product property, calculating the perimeter of a right triangle using the Pythagorean theorem, modeling population growth with quadratic equations, and determining if a projectile can reach a specific height. Each section provides step-by-step explanations and examples to enhance understanding.

What two numbers multiply to 600 and add to -70?

• -10 and -60

• 10 and 60

• -15 and -40

• 15 and 40

What is the factored form of the equation given the factors x - 10 and x - 60?

• (x + 10)(x + 60)

• (x - 10)(x - 60)

• (x + 10)(x - 60)

• (x - 10)(x + 60)

Which value of x is inadmissible in the context of the problem?

• x = 10

• x = 60

• x = -10

• x = -60

What is the perimeter of a right triangle with legs 6 cm and 3 cm?

• 12 cm

• 15 cm

• 9 cm

• 18 cm

What is the hypotenuse of a right triangle with legs 6 cm and 3 cm?

• √36

• √45

• √54

• √81

What is the perimeter of the triangle in simplest form?

• 9 + 3√5

• 12 + 3√5

• 15 + 3√5

• 18 + 3√5

What is the initial population of the city in the model?

• 60,000

• 40,000

• 30,000

• 50,000

What is the population in the year 2020 according to the model?

• 70,000

• 80,000

• 60,000

• 50,000

In what year is the population predicted to be 300,000?

• 2025

• 2030

• 2020

• 2017

Can the projectile ever reach a height of 9 meters?

• Yes

• No

• Only if launched at a lower angle

• Only if launched at a higher speed