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)
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?
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What is an equivalent equation solved for g in A = g/t?
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What is an equivalent equation solved for m in y = mx + b?
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What is the solution for a in the equation 7a - 2b = 5a + b?
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What is an equivalent equation solved for y in a = πxy?
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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?
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What is the solution for k in the equation 8k + 2m = 3m + k?
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If F = ma, what is the acceleration of an object with F = 7.92 newtons and m = 3.6 kilograms?
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What is the radius of a circle that has a circumference of 16, using the formula C = 2πr?
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What is an equivalent equation solved for r in C = 2πr?
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What is an equivalent equation solved for y2 in m = (y2 - y1) / (x2 - x1)?
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What is the solution for w in the equation 5w + 9z = 2z + 3w?
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What is the solution for a in K = 4a + 9ab?
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If S = 2πrh + 2πr², what is the equation solved for h?
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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.