Algebra Flashcards (Aleks)

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Questions and Answers

What is the result of using the multiplicative property of equality with signed fractions on the equation 9 = -3/4y?

y = 0

y = -12 (correct)

y = 6

y = 12

What is the simplified form of the ratio 30y^4/5y^7?

6/y^3

What is the value of x in the equation -6(3x-1)+4x = 1+2(2x-5)?

5/6

A^0 = 1 is true.

True Signup and view all the answers

What is the simplified form of the fraction 56(u-7)(2u-3) / 7(2u-3)(u+8)?

8(u-7) / (u+8) Signup and view all the answers

What is the result of sqrt(a) * sqrt(b)?

sqrt(ab) Signup and view all the answers

What is the result of 3/20 divided by (-21/16)?

-4/35 Signup and view all the answers

What values of w satisfy the equation (w + 7)(w - 8) = 0?

-7, 8 Signup and view all the answers

What is the product of the values p and q in the factoring of 14x^2 + 9x - 5?

-70 Signup and view all the answers

What property is used in evaluating functions?

Substitution property Signup and view all the answers

What is the final value when simplifying 2 * sqrt(72) * sqrt(98)?

168 Signup and view all the answers

Simplify the expression 3x - 4(4y - 3x) + 4y.

15x - 12y Signup and view all the answers

What is the simplified form of sqrt(2) / sqrt(3)?

sqrt(6) / 3 Signup and view all the answers

What is the value of w in the equation 3/2w - 1/7 = -8/5?

-34/35 Signup and view all the answers

What is the simplified ratio of 8w^2 - 12w / 4w^2 - 16?

2w - 3 / (w - 4) Signup and view all the answers

What is the degree and leading coefficient of the polynomial -5 - 10w + w^6?

Degree: 6, Leading Coefficient: 1 Signup and view all the answers

What does the LCM of 12a^4 and 9a^2 equal?

36a^4 Signup and view all the answers

Study Notes

Multiplicative Property of Equality

If ( 9 = -\frac{3}{4}y ), then multiplying both sides by the reciprocal (-\frac{4}{3}) leads to solving ( -12 = y ).

Simplifying Ratios of Monomials

For ( \frac{30y^4}{5y^7} ), divide coefficients and subtract exponents: ( \frac{30}{5} = 6 ) and ( y^{4-7} = \frac{1}{y^3} ), resulting in ( \frac{6}{y^3} ).

Solving Linear Equations with Variables on Both Sides

The equation ( -6(3x-1) + 4x = 1 + 2(2x-5) ) requires the distributive property, combining like terms, and isolating ( x ) to find ( x = \frac{5}{6} ).

Evaluating Expressions with Exponents

Any number raised to the power of zero equals one, ( a^0 = 1 ).

Simplifying Ratios of Factored Polynomials

For ( \frac{56(u-7)(2u-3)}{7(2u-3)(u+8)} ), cancel the common factor ( (2u-3) ) to simplify to ( \frac{8(u-7)}{u+8} ).

Basic Square Root Multiplication

The product property states ( \sqrt{a} \sqrt{b} = \sqrt{ab} ), simplifying gives results like ( 4\sqrt{3} ) from ( \sqrt{48} ).

Signed Fraction Division

For ( \frac{3}{20} \div \left(-\frac{21}{16}\right) ), take the reciprocal, cancel common factors leading to ( -\frac{4}{35} ).

Solving Equations in Factored Form

In ( (w + 7)(w - 8) = 0 ), set each factor to zero: solutions are ( w = -7 ) and ( w = 8 ).

Factoring Quadratics with Leading Coefficient Greater Than 1

For ( 14x^2 + 9x - 5 ), find integers ( p ) and ( q ) such that ( pq = -70 ) (from ( 14 \times -5 )) and ( p + q = 9 ).

Evaluating Functions

Use substitution property in functions involving linear, quadratic, or cubic equations to analyze outputs.

Advanced Square Root Multiplication

To simplify ( 2\sqrt{72} \sqrt{98} ), first simplify each square root, leading to answer ( 168 ) through ( \sqrt{7056} ).

Simplifying Multivariate Expressions

With ( 3x - 4(4y - 3x) + 4y ), apply distributive property, combine like terms, and simplify to yield ( 15x - 12y ).

Rationalizing Denominators

For ( \frac{\sqrt{2}}{\sqrt{3}} ), multiply numerator and denominator by ( \sqrt{3} ) to simplify the result to ( \frac{\sqrt{6}}{3} ).

Solving Two-Step Equations with Signed Fractions

With ( \frac{3}{2}w - \frac{1}{7} = -\frac{8}{5} ), eliminate fractions using LCD, apply the distributive property, and isolate ( w ) leading to ( w = -\frac{34}{35} ).

Simplifying Ratios of Polynomials Using GCF

Reducing ( \frac{8w^2 - 12w}{4w^2 - 16} ) involves factoring both numerator and denominator to arrive at ( \frac{2w - 3}{w - 4} ).

Degree and Leading Coefficient of a Polynomial

The polynomial (-5 - 10w + w^6) has a degree of ( 6 ) (highest exponent) and a leading coefficient of ( 1 ).

Simplifying Products with Square Roots

In the expression ( \sqrt{7}(\sqrt{6} - 11) ), apply distributive property and the product property of square roots for simplification.

Finding the LCM of Monomials

For monomials ( 12a^4 ) and ( 9a^2 ), the LCM is determined as ( 36a^4 ) combining the LCM of coefficients and highest powers of variables.

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Description

Explore essential algebra concepts with these flashcards based on the Aleks system. Each card covers important topics such as the multiplicative property of equality and simplifying ratios of monomials. Perfect for reinforcing your understanding and preparing for assessments.