Literal Equations Test Flashcards

Questions and Answers

What is an equivalent equation solved for V in the equation d = m/v?

m/d = V

Which are equivalent equations for the lateral area of a right cone, LA = πrs? (Select all that apply)

s = LA / πr (correct)

s = πrLA

r = LA / πs (correct)

LA = πrs

What is the equation solved for C in K = C + 273.15?

C = K - 273.15

What is an equivalent equation solved for t in f = v + at?

t = (f - v) / a Signup and view all the answers

What is an equivalent equation solved for g in A = g/t?

g = At / 60 Signup and view all the answers

What is an equivalent equation solved for m in y = mx + b?

m = (y - b) / x Signup and view all the answers

What is the solution for a in the equation 7a - 2b = 5a + b?

a = 3/2b Signup and view all the answers

What is an equivalent equation solved for y in a = πxy?

y = a / (πx) Signup and view all the answers

Using the formula w = V/(lh), what is the width of a rectangular prism with a volume of 138.24 cubic inches, height of 9.6 inches, and length of 3.2 inches?

4.5 inches Signup and view all the answers

What is the solution for k in the equation 8k + 2m = 3m + k?

k = m / 7 Signup and view all the answers

If F = ma, what is the acceleration of an object with F = 7.92 newtons and m = 3.6 kilograms?

2.2 m/s² Signup and view all the answers

What is the radius of a circle that has a circumference of 16, using the formula C = 2πr?

r = 8 Signup and view all the answers

What is an equivalent equation solved for r in C = 2πr?

r = C / (2π) Signup and view all the answers

What is an equivalent equation solved for y2 in m = (y2 - y1) / (x2 - x1)?

y2 = m(x2 - x1) + y1 Signup and view all the answers

What is the solution for w in the equation 5w + 9z = 2z + 3w?

w = -7/2z Signup and view all the answers

What is the solution for a in K = 4a + 9ab?

a = K / (4 + 9b) Signup and view all the answers

If S = 2πrh + 2πr², what is the equation solved for h?

h = S / (2πr) - r Signup and view all the answers

Study Notes

Density Calculation

Density (d) is calculated from mass (m) and volume (v) using the formula d = m/v.
Rearranging this equation for volume gives V = m/d.

Right Cone Geometry

The lateral area (LA) of a right cone is given by LA = πrs.
This formula can be rearranged to find slant height (s) as s = LA / (πr) and radius (r) as r = LA / (πs).

Temperature Conversion

Kelvin (K) is derived from Celsius (C) using the equation K = C + 273.15.
The rearranged formula for Celsius is C = K - 273.15.

Motion Formula

The formula for final velocity is f = v + at.
To solve for time (t), the equivalent formula is t = (f - v) / a.

Hockey Goalie Statistics

Goals against average (A) is calculated with A = g / t * 60, where g is goals scored against the goalie and t is time in minutes.
Rearranging for goals gives g = (A * t) / 60.

Slope-Intercept Form

The slope-intercept form of a linear equation is y = mx + b, with m representing the slope.
To find slope (m), rearranged equation is m = (y - b) / x.

Algebraic Rearrangement

From the equation 7a - 2b = 5a + b, rearranging yields a = (3/2)b.

Ellipse Area Calculation

The area (a) of an ellipse is calculated by a = πxy, where x and y are half the lengths of the respective diameters.
Rearranging for y gives y = a / (πx).

Rectangular Prism Volume

The volume (V) of a rectangular prism is determined by V = lwh, where l, w, and h are length, width, and height.
For a prism with V = 138.24 in³, h = 9.6 in, and l = 3.2 in, the width (w) is found to be 4.5 in.

Physics: Force and Acceleration

The relationship of force (F) to mass (m) and acceleration (a) is expressed as F = ma.
Rearranging for acceleration gives a = F / m. For F = 7.92 N and m = 3.6 kg, acceleration results in approximately 2.2 m/s².

Circumference and Radius

The circumference (C) of a circle is formulated as C = 2πr.
Rearranging for radius (r) gives r = C / (2π). For a circle with C = 16, the radius is calculated as r = 8.

Slope From Ordered Pairs

Slope (m) between two points can be found using m = (y2 - y1) / (x2 - x1).
To find y2 based on known values, rearranging results in y2 = m(x2 - x1) + y1.

Additional Algebraic Rearrangements

From 5w + 9z = 2z + 3w, solving for width (w) yields w = -7/2z.
From K = 4a + 9ab, when solving for a, the formula is a = K / (4 + 9b).
For the surface area equation S = 2πrh + 2πr² rearranging to solve for height (h) results in h = (S/(2πr)) - r.

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Description

This quiz focuses on solving literal equations, including applications such as calculating density and the lateral area of cones. Test your understanding of rearranging formulas to isolate variables and identify equivalent equations. Perfect for students looking to reinforce their algebra skills.