Literal Equations: Quiz

The equation a = 1/2(b1 + b2)h can be used to determine the area, a, of a trapezoid with height, h, and base lengths, b1 and b2. Which are equivalent equations? Check all that apply.

1. 2a/h-b2=b1 2. 2a/b1+b2=h

Hallie can use the equation p = 4l + 4w + 4h to determine the sum of the lengths of the edges of a rectangular prism. She begins to solve the equation for h but runs out of time. Her partial work is shown below: p=4l+4w+4h p/4=4l+4w+4h/4 p/4=l+w+h h=p/4- Which expression should follow the subtraction in Hallie's equation?

A. (l+w)

The equation f = v + at represents the final velocity of an object, f, with an initial velocity, v, and an acceleration rate, a, over time, t. Which is an equivalent equation solved for a?

A. f-v/t=a

Nathaniel writes the general form of the equation gm = cm + rg for when the equation is solved for m. He uses the general form to solve the equation -3m = 4m - 15 for m. Which expression shows what Nathaniel will actually evaluate?

C. -15/-3-4

The equation K = 1/2mv2 represents the energy an object has based on its motion. The kinetic energy, K, is based on the mass of the object, m, and the velocity of the object, v. Lashandra is given K and v for 10 different objects. In order to make solving more efficient, she solves the equation for m : m = k/2v^2. After attempting to determine the mass of a few objects, Lashandra realizes there must be something wrong with her formula. What is Lashandra's error?

A. She should have multiplied by 2 instead of dividing by 2.

The tax rate as a percent, r, charged on an item can be determined using the formula c/p- 1 = r, where c is the final cost of the item and p is the price of the item before tax. Louise rewrites the equation to solve for the final cost of the item: c = p(1 + r). What is the final cost of a $40 item after an 8% tax is applied?

$43.20

Tahmar knows the formula for simple interest is I = Prt, where I represents the simple interest on an amount of money, P, for t years at r rate. She transforms the equation to isolate P : P l/rt= . Using this formula, what is the amount of money, P, that will generate $20 at a 5% interest rate over 5 years?

$80

Jalil and Victoria are each asked to solve the equation ax - c = bx + d for x. Jalil says it is not possible to isolate x because each x has a different unknown coefficient. Victoria believes there is a solution, and shows Jalil her work: ax - c = bx + d ax - bx = d + c x (a - b) = d + c x =d+c/a-b How can Victoria justify Step 3 of her work?

A. Rewrite the expression on the left using the distributive property.

Transform the equation to isolate x: ax = bx + 1. How is the value of x related to the difference of a and b?

Sample Answer: The equation ax = bx + 1 is the same as x = 1/(a - b) when solved for x. This means that x is equal to the reciprocal of the difference of a and b.

The equation a =180(n-2)/n represents the angle measures, a, in a regular n-sided polygon. When the equation is solved for n, n is equal to a fraction with a denominator of a - 180. What is the numerator of the fraction?

-360