Algebra 1 BJU Flashcards

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Questions and Answers

What is the formula to solve for m in the equation D = m/v?

M = dv

What is the formula to solve for x in the equation Y = Mx + b?

Y - b / m = x

What is the value of Z in the equation Z / 5 - 6 = 84?

Z = 450

What is the value of b in the equation 4b = 7 - 4b + 6?

<p>B = 13 / 8</p> Signup and view all the answers

What is the midpoint of 12 and 22?

<p>Midpoint = 17</p> Signup and view all the answers

What is the length between 8 and 17?

<p>Length = 9</p> Signup and view all the answers

What is the value of | -9 | - | -4 |?

<p>5</p> Signup and view all the answers

Is -2 a solution to the equation X^2 - x = 6?

<p>True (A)</p> Signup and view all the answers

Is y = 1/2 a solution to the equation 2/3y - 3/4 = -5/12?

<p>True (A)</p> Signup and view all the answers

If the deliveries to an apartment complex compose one-seventh of the route, how many papers does the paper boy deliver?

<p>91 papers</p> Signup and view all the answers

What is the price of a hard candy if a candy bar is $0.95 which is nineteen times its price?

<p>$0.05</p> Signup and view all the answers

What is the value of y in the equation 12/25 = 20/y?

<p>Y = 125/3 ~ 41.6</p> Signup and view all the answers

What is the value of X in the equation X - 1 / 6 = x + 1 / 9?

<p>X = 5</p> Signup and view all the answers

If the ratio of masses of hydrogen and oxygen is 1:8, how many grams of each are in 90g of water?

<p>10g of hydrogen and 80g of oxygen</p> Signup and view all the answers

What is the actual distance between two towns that are 5.25 inches apart on a map with a scale of 1 inch : 40 miles?

<p>210 miles</p> Signup and view all the answers

How long is a model car if the actual car is 16ft long and the scale is 1:64?

<p>3 in</p> Signup and view all the answers

How many square feet of carpet are needed for a room with dimensions drawn at 7.5" x 6" on a plan that has a scale of 1:24?

<p>180 ft</p> Signup and view all the answers

What is 0.5% in decimal form?

<p>0.005</p> Signup and view all the answers

What is the decimal and percentage equivalent of 0.5?

<p>50%, 1/2</p> Signup and view all the answers

What is the decimal and percentage equivalent of 1/5?

<p>0.2, 20%</p> Signup and view all the answers

What percent of 16 is 76?

<p>475</p> Signup and view all the answers

36% of what number is 54?

<p>150</p> Signup and view all the answers

What can be determined about the inequality X > 3 or x > -1?

<p>X &gt; -1</p> Signup and view all the answers

What is the solution for X in the expression X = 4?

<p>Undefined; none</p> Signup and view all the answers

What is the relationship between the equations 3x + y = 8 and -2x + 6y = 18?

<p>Perpendicular</p> Signup and view all the answers

What is the relationship between the equations 4x + 7y = 12 and 5x + 9y = 18?

<p>Neither</p> Signup and view all the answers

What is the solution for the system of equations X + 2y = 4 and 2x + 36 = 8?

<p>(4, 0)</p> Signup and view all the answers

What is the result of 1/8 - (-3/8)?

<p>1/2</p> Signup and view all the answers

What do you get when you divide 4/7 by 3/8?

<p>32/21</p> Signup and view all the answers

What is the result of 5/8 - 7/9?

<p>-11/72</p> Signup and view all the answers

What is the opposite of negative 6?

<p>6</p> Signup and view all the answers

What is eight less than five?

<p>-3</p> Signup and view all the answers

What is the product of fifteen and negative three decreased by 12?

<p>-57</p> Signup and view all the answers

What is the sum of three cubed and four?

<p>31</p> Signup and view all the answers

What is the value of Y in the equation Y + 0.38 = 8.7?

<p>Y = 8.32</p> Signup and view all the answers

What is the value of A in the equation 6a + 21 = 165?

<p>A = 24</p> Signup and view all the answers

What is the value of K in the equation 4K / 9 = 2?

<p>K = 9/2</p> Signup and view all the answers

What is the percent increase of a stock that rose from a yearly low of $9.68 to 18.61?

<p>92.2%</p> Signup and view all the answers

What is the solution to the inequality X - 17 < -6?

<p>X &lt; 11</p> Signup and view all the answers

What are the solutions for the equation X - 4y = 4?

<p>(4, 0), (0, -1)</p> Signup and view all the answers

What is the slope M between the points (5, 9) and (3, 9)?

<p>M = 0</p> Signup and view all the answers

What can be said about the equations X + y = 5 and X + y = 2?

<p>No solutions; inconsistent</p> Signup and view all the answers

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Study Notes

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.

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