Literal Equations

The equation d = m/v can be used to caculate the density, d, of an object with mass, m, and volume, V. Which us an equivalent equation solved for V?

m/d = V

Solve for k. 8k + 2m = 3m + k

k = m/7

The slope-intercept form of a linear equation is y = mx + b, where x and y are coordinates of an ordered pair, m is the slope of the line, and b is where the line crosses the y-axis. Which is an equivalent equation solved for the slope, m?

m = V-b/x

In physics class, Carrie learns that a force, F, is equal to the mass of an object, m, times its acceleration, a. She writes the equation as F = ma, then realizes that each of her homework problems asks her to solve for acceleration. She rewrites the formula as f/m = a. Using this formula, what is the acceleration of an object with F = 7.92 newtons and m = 3.6 kilograms? Express your answer to the nearest tenth.

2.2 m/s2

The volume, V, of a rectangular prism is determined using the formula , where l is the length, w is the width, and h is the height of the prism. Carltren solves for w and writes the equivalent equation w = V/lh. Using this formula, what is the width of a rectangular prism that has a volume of 138.24 cubic inches, a height of 9.6 inches, and a length of 3.2 inches?

4.5 inches

The goals against average (A) for a professional hockey goalie is determined using the formula A = 60 . In the formula, g represents the number of goals scored against the goalie and t represents the time played, in minutes. Which is an equivalent equation solved for g?

At/60 = g

The temperature measured in Kelvin (K) is the temperature measured in Celsius (C) increased by 273.15. This can be modeled by the equation K = C + 273.15. When solved for C, the equation is

C = K - 273.15

Marta is solving the equation S= 2πrh + 2πr2 for h. Which should be the result?

S/2πr -r = h

Solve for a. 7a - 2b = 5a + b

a = 3/2b

Solve the equation for a. K = 4a + 9ab

a = K/ 4 + 9b

The formula for the circumference of a circle is C = 2πr, where r is the radius and C is the circumference. The equation solved for r is r =c/π2 . Find the radius of a circle that has a circumference of 16.

r = 8

The circumference of a circle can be found using the formula C = 2πr. Which is an equivalent equation solved for r?

r = C/2π

The formula for the lateral area of a right cone is LA = πrs, where r is the radius of the base and s is the slant height of the cone. Which are equivalent equations? Check all that apply.

s = LA / πr r = LA / πs

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 t?

t = f-v/a

Solve for w. 5w + 9z = 2z + 3w

w = -7/2z

The area, a, of an ellipse can be determined using the formula a = πxy, where x and y are half the lengths of the largest and smallest diameters of the ellipse. Which is an equivalent equation solved for y?

y = a / (πx)

The slope, m, of a linear equation can be found using the formula m= y2 - y1/ x2 - x1, where the x- and y-values come from two ordered pairs, and (x1, y1) and (x2, y2). What is an equivalent equation solved for y2?

y2 = m(x2 - x1) + y1