Algebra 1 BJU Flashcards

Algebraic Formulas and Definitions

• D = m/v: Rearranged to find mass m = dv.
• Y = Mx + b: To isolate x, use x = (Y - b) / m.

Problem Solving in Algebra

• Given the equation Z/5 - 6 = 84, the solution is Z = 450.
• From 4b = 7 - 4b + 6, solving gives B = 13/8.

Midpoint and Length Calculations

• For the numbers 12 and 22, the midpoint is 5, and the length is 34.
• For 8 and 17, the midpoint is 12.5, with a length also of 12.5.

Absolute Values and Solutions

• The absolute value of |-9| - |-4| results in 5.
• The value x = -2 is a solution to the equation x^2 - x = 6.
• Checking y = 1/2 in equation 2/3y - 3/4 = -5/12 confirms it as a solution.

Real-Life Application Problems

• If 1/7 of a paper boy’s route has 13 deliveries, he delivers 91 papers total.
• A candy bar priced at $0.95 is 19 times the price of a piece of hard candy, thus $0.05 per candy.
• From 12/25 = 20/y, solving gives Y ≈ 41.6.

Ratios and Scales

• In a mass ratio of hydrogen to oxygen 1:8, in 90g of water, amounts are 10g hydrogen and 80g oxygen.
• The distance between two towns 5.25 in. apart on a 1:40 scale translates to an actual distance of 210 miles.
• A 1:64 scale die-cast model of a 16-ft car would measure 3 inches.

Area and Dimensions

• A room measured at 7.5"x6" on a 1:24 scale requires 180 square feet of carpet.

Percent and Fraction Conversions

• 0.5% as a decimal is 0.005; fractional form is 1/200.
• 0.5 equates to 50% or 1/2.
• 1/5 expressed as a decimal is 0.2 or 20%.

Percentage Problems

• To find what percent of 16 is 76, the result is 475%.
• 36% of what number equals 54, solving gives 150.

Inequalities and Undefined Solutions

• For X > 3 or x > -1, the simplified statement is X > -1.
• When X = 4, it is classified as undefined; none.

Relations and Systems of Equations

• The equations 3x + y = 8 and -2x + 6y = 18 are perpendicular.
• 4x + 7y = 12 and 5x + 9y = 18 have no clear relation, i.e., neither.
• The solution set for X + 2y = 4 and 2x + 36 = 8 results in the point (4, 0).

Arithmetic Operations

• The result of 1/8 - (-3/8) simplifies to 1/2.
• Calculating 4/7 ÷ 3/8 results in 32/21.
• The difference 5/8 - 7/9 computes to -11/72.

Expressions and Results

• The opposite of -6 is 6.
• Five less than eight simplifies to -3.
• Calculating 15(-3) - 12 results in -57.
• The sum of 3 cubed and 4, where 3^3 + 4 equals 31.

Variable Isolation

• From Y + 0.38 = 8.7, solving gives Y = 8.32.
• Solving the equation 6a + 21 = 165 results in A = 24.
• From 4K/9 = 2, it simplifies to K = 9/2.

Percent Increase

• The stock's price increased from a low of $9.68 to $18.61, resulting in a 92.2% increase.

Additional Inequalities and Relationships

• From X - 17 < -6, it simplifies to X < 11.
• The points satisfying X - 4y = 4 are (4, 0) and (0, -1).
• The slope calculated between points (5, 9) and (3, 9) is M = 0 (indicating a horizontal line).
• The system X + y = 5 and X + y = 2 reveals no solutions; inconsistent.