Algebra 1 Math Test 6 Flashcards (2023)

Questions and Answers

What property was used to manipulate the expression $a(bc) + 4 = (ab)c + 4$?

Associative

In which quadrant does the point (5, -3) lie?

What kind of interval does the following graph illustrate? Open dot at -2 with a straight line to an open dot at 5.

open

How many solutions does an inconsistent system have?

0 Signup and view all the answers

If the following polynomial is reordered by a descending degree of x, what is this polynomial? $x^3 + z^3 - x^3z + x^4z^4$?

x^4z^4 + x^3 - x^3z + z^3 Signup and view all the answers

Which of the following correctly translates 'three times a number increases four'?

3x + 4 Signup and view all the answers

What is $3.25 × 10^{-6}$?

0.00000325 Signup and view all the answers

What is $1.104 × 10^5$?

110400 Signup and view all the answers

What is $(15x - 3y) - (3x + 8y)$?

12x - 11y Signup and view all the answers

What is $(2x + 6)(3x + 2)$?

6x^2 + 22x + 12 Signup and view all the answers

What is $(3a^3)^2$ outside the parentheses?

9a^6 Signup and view all the answers

What is $(2b - 5c)(2b + 5c)$?

4b^2 - 25c^2 Signup and view all the answers

What is $(x - 2)(-4x^2 - 7x + 10)$?

-4x^3 + x^2 + 24x - 20 Signup and view all the answers

What is $rac{3q^3r^2 - 2qr}{3qr}$?

q^2r - rac{2}{3} Signup and view all the answers

What is $rac{a^2 - a - 20}{a + 4}$?

a - 5 Signup and view all the answers

What is $(2.5 × 10^{-2})(5.0 × 10^{7})$?

1.25 × 10^{4} Signup and view all the answers

What is $rac{8.0 × 10^{-4}}{2.0 × 10^{5}}$?

4 × 10^{-9} Signup and view all the answers

What is the solution to the equation $16x + 2 = x + 17$?

x = 1 Signup and view all the answers

What is the solution to $(x - 3)(x + 4) = (x + 2)^2 - 1$?

x = -5 Signup and view all the answers

What are the solutions to $|x + 2| - 4 = 12$?

x = -18, 14 Signup and view all the answers

Given the points (3, -2) and (5, 4), what is the equation of the line?

y = 3x - 11 Signup and view all the answers

Given the point (9, -1) parallel to $y = 5x - 4$, what is the equation of the line?

5x - 46 Signup and view all the answers

What does the expression $2x + 7 < 3$ represent?

Closed dot on 4 with a line to the left and closed dot on 2 to the right Signup and view all the answers

Solve the system graphically: $2x + y = -4$ and $x + 3y = 3$.

(-3, 2) Signup and view all the answers

The cost for 2 adults and 5 children to eat at the local buffet restaurant is $46.50. The cost for 1 adult and 1 child is $15. What is the cost of a child's meal?

$5.50 Signup and view all the answers

Study Notes

Algebra Concepts

The Associative Property is used in rearranging expressions, demonstrated by ( a(bc) + 4 = (ab)c + 4 ).
The point (5, -3) is located in the IV quadrant of the Cartesian plane.
An interval illustrated by an open dot at -2 to an open dot at 5 indicates an open interval.
An inconsistent system of equations will have no solutions, denoted as 0.

Polynomial Manipulation

The polynomial ( x^3 + z^3 - x^3z + x^4z^4 ) can be reordered to ( x^4z^4 + x^3 - x^3z + z^3 ) by descending degree of ( x ).

Translating Expressions

The phrase "three times a number increases four" translates to the algebraic expression ( 3x + 4 ).

Scientific Notation

The expression ( 3.25 \times 10^{-6} ) equals ( 0.00000325 ).
The number ( 1.104 \times 10^{5} ) converts to ( 110,400 ).

Simplifying Expressions

The expression ( (15x - 3y) - (3x + 8y) ) simplifies to ( 12x - 11y ).
The binomial product ( (2x + 6)(3x + 2) ) results in ( 6x^2 + 22x + 12 ).
Raising the term ( (3a^3) ) to the exponent of 2 results in ( 9a^6 ).
Factoring ( (2b - 5c)(2b + 5c) ) yields ( 4b^2 - 25c^2 ).
The product ( (x - 2)(-4x^2 - 7x + 10) ) simplifies to ( -4x^3 + x^2 + 24x - 20 ).
The expression ( \frac{3q^3r^2 - 2qr}{3qr} ) is simplified to ( q^2r - \frac{2}{3} ).

Rational Expressions

The rational expression ( \frac{a^2 - a - 20}{a + 4} ) simplifies to ( a - 5 ).

Calculating with Scientific Notation

Multiplying ( (2.5 \times 10^{-2})(5.0 \times 10^{7}) ) results in ( 1.25 \times 10^{4} ).
Dividing ( 8.0 \times 10^{-4} ) by ( 2.0 \times 10^{5} ) simplifies to ( 4 \times 10^{-9} ).

Solving Equations

The linear equation ( 16x + 2 = x + 17 ) has the solution ( x = 1 ).
The equation ( (x - 3)(x + 4) = (x + 2)^2 - 1 ) results in ( x = -5 ).
The equation ( |x + 2| - 4 = 12 ) yields solutions ( x = -18 ) and ( x = 14 ).

Line Equations and Systems

The line passing through points (3, -2) and (5, 4) has the equation ( y = 3x - 11 ).
A line parallel to ( y = 5x - 4 ) through point (9, -1) is described by the equation ( 5x - 46 ).

Interval Notation

The expression ( 2x + 7 \geq 3 ) corresponds to a graph with a closed dot on 4 extending to the left and a closed dot on 2 extending to the right.

Graphical Solutions

The graphical solution to the system of equations ( 2x + y = -4 ) and ( x + 3y = 3 ) is found at the point ( (-3, 2) ).

Word Problems

In a situation with costs for meals at a buffet, the cost of a child's meal was calculated as $5.50 using the equations derived from given costs for adults and children.

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Description

Test your knowledge with these flashcards from Algebra 1, focusing on key concepts and properties of algebraic expressions. This quiz covers topics such as the associative property, quadrants, and types of intervals in graphs. Challenge yourself to review and reinforce your understanding of essential algebra principles.