Solving Equations and Area Formulas

The video tutorial covers translating word problems into literal equations and solving for specific variables. It includes examples of solving for width in a rectangle's perimeter, height in a cone's volume, and base in a trapezoid's area. The tutorial demonstrates different methods to manipulate equations, such as using the distributive property and reciprocal multiplication, to isolate and solve for the desired variable.

What is the first step in translating a word problem into a literal equation?

• Check the solution.

• Graph the equation.

• Identify the variables and constants.

• Solve for the unknown variable.

In the equation P = 2(L + W), what does P represent?

• The area of a rectangle.

• The perimeter of a rectangle.

• The volume of a rectangle.

• The diagonal of a rectangle.

Which method involves distributing the 2 in the equation P = 2(L + W)?

• Distributive property.

• Graphical method.

• Elimination method.

• Substitution method.

What is the result of dividing both sides of the equation P = 2(L + W) by 2?

• P = L + W

• P = 2L + 2W

• P/2 = L + W

• P/2 = 2L + 2W

How do you isolate W in the equation P/2 = L + W?

• Multiply both sides by 2.

• Subtract L from both sides.

• Add L to both sides.

• Divide both sides by L.

What is the first step in solving the equation P = 2(L + W) for W?

• Divide both sides by 2.

• Distribute the 2.

• Subtract L from both sides.

• Add L to both sides.

What is the result of subtracting L from both sides in the equation P/2 = L + W?

• P/2 = L

• P/2 + L = W

• P/2 - L = W

• P/2 = W

What is the formula for the volume of a cone?

• V = 1/3πr²h

• V = 2πr²h

• V = πr²h

• V = 1/2πr²h

How do you eliminate the fraction in the equation V = 1/3(B * H)?

• Divide both sides by 3.

• Multiply both sides by 3.

• Subtract 3 from both sides.

• Add 3 to both sides.

What is the reciprocal of 1/3?

• 1/2

• 1

• 3

• 1/3