Understanding Box Volume and Solving Quadratic Equations

The video tutorial explains how to calculate the volume of a box with given dimensions. It starts by introducing the concept of volume and the dimensions of the box. The tutorial then sets up a quadratic equation to solve for the unknown variable x, representing one of the box's dimensions. The process involves distributing terms, factoring the quadratic equation, and finding possible solutions for x. The tutorial concludes by validating the solution to ensure the dimensions are positive and realistic, confirming the calculated volume matches the given value.

What is the volume of the box in cubic units?

• 450

• 405

• 500

• 360

If the length of the box is x, what is the expression for the width?

• x + 8

• x + 2

• x + 4

• x + 6

What is the height of the box?

• 7

• 8

• 9

• 10

Which equation represents the volume of the box?

• x(x + 4) = 405

• 9x(x + 4) = 405

• x(x + 9) = 405

• 9(x + 4) = 405

What is the first step in simplifying the quadratic equation?

• Add 405 to both sides

• Subtract 405 from both sides

• Multiply both sides by 9

• Divide both sides by 9

What common factor can be divided out from the quadratic equation?

• 7

• 5

• 3

• 9

What are the two numbers that multiply to -45 and add to 4?

• 9 and -5

• 7 and -3

• 6 and -6

• 8 and -4

What are the possible values of x after factoring the equation?

• -9 and 5

• 5 and 9

• 9 and -5

• -5 and 9

Why is x = -9 not a valid solution for the box dimensions?

• It results in a negative volume

• It results in negative dimensions

• It results in zero dimensions

• It results in zero volume

What is the final valid dimension for the length of the box?

• 5

• 6

• 7

• 8