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?

B = 13 / 8 Signup and view all the answers

What is the midpoint of 12 and 22?

Midpoint = 17 Signup and view all the answers

What is the length between 8 and 17?

Length = 9 Signup and view all the answers

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

5 Signup and view all the answers

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

True Signup and view all the answers

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

True 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?

91 papers 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?

$0.05 Signup and view all the answers

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

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

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

X = 5 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?

10g of hydrogen and 80g of oxygen 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?

210 miles 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?

3 in 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?

180 ft Signup and view all the answers

What is 0.5% in decimal form?

0.005 Signup and view all the answers

What is the decimal and percentage equivalent of 0.5?

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

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

0.2, 20% Signup and view all the answers

What percent of 16 is 76?

475 Signup and view all the answers

36% of what number is 54?

150 Signup and view all the answers

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

X > -1 Signup and view all the answers

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

Undefined; none Signup and view all the answers

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

Perpendicular Signup and view all the answers

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

Neither Signup and view all the answers

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

(4, 0) Signup and view all the answers

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

1/2 Signup and view all the answers

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

32/21 Signup and view all the answers

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

-11/72 Signup and view all the answers

What is the opposite of negative 6?

6 Signup and view all the answers

What is eight less than five?

-3 Signup and view all the answers

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

-57 Signup and view all the answers

What is the sum of three cubed and four?

31 Signup and view all the answers

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

Y = 8.32 Signup and view all the answers

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

A = 24 Signup and view all the answers

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

K = 9/2 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?

92.2% Signup and view all the answers

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

X < 11 Signup and view all the answers

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

(4, 0), (0, -1) Signup and view all the answers

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

M = 0 Signup and view all the answers

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

No solutions; inconsistent Signup and view all the answers

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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Test your understanding of algebraic formulas and concepts with these flashcards. Each card focuses on key relationships and problem-solving techniques essential for mastering Algebra 1. Ideal for students using BJU curriculum.