Equations And Inequalities Algebra Rti Flash Cards Pt. 2

1. What is the standard way to represent a point on a coordinate plane?

Latitude and longitude

Ordered pair (x,y) (abscissa, ordinate)

Angle and direction

Point and line

In coordinate geometry, a point on a coordinate plane is represented by an ordered pair (x,y), where x is the abscissa or the horizontal coordinate, and y is the ordinate or the vertical coordinate.

Explanation

In coordinate geometry, a point on a coordinate plane is represented by an ordered pair (x,y), where x is the abscissa or the horizontal coordinate, and y is the ordinate or the vertical coordinate.

2. What is a linear equation?

Ax + By = C ( A, B and C are intergers; A and B cannot both equal zero.) The graph of a linear equation is a straight line and represents all solutions (x,y) of the equation.

A quadratic equation is represented by a linear function with a power greater than 2.

A cubic equation is represented by a linear function with a power greater than 3.

An exponential equation is represented by a linear function with a base greater than 1.

A linear equation is a mathematical equation that represents a straight line when graphed. It is characterized by having variables raised to the power of 1, making it a first-degree polynomial equation.

Explanation

A linear equation is a mathematical equation that represents a straight line when graphed. It is characterized by having variables raised to the power of 1, making it a first-degree polynomial equation.

3. Linear equation: standard form?

3x - 2y = 5

Ax + By = C (A,B, and c are intergers ; A and B cannot both equal zero.)

X + y = 1

Ax + By = C (A,B, and c can be any real numbers)

The standard form of a linear equation is Ax + By = C, where A, B, and C are integers. A and B cannot both be zero in order to avoid inconsistency.

Explanation

The standard form of a linear equation is Ax + By = C, where A, B, and C are integers. A and B cannot both be zero in order to avoid inconsistency.

4. What is a literal equation?

A formula or equation which consists primarily of variables

An equation with no variables

A mathematical expression with only numbers

A sentence written exactly as it sounds

A literal equation is a formula or equation where most of the characters are variables, representing different quantities or parameters.

Explanation

A literal equation is a formula or equation where most of the characters are variables, representing different quantities or parameters.

5. What is the equation of a vertical line?

Standard form: Ax + By = C, where B=0 for vertical lines.

Y= a (where a can be any real number) vertical lines have an undefined slope.

X= a (where a can ba any real number) vertical lines have an undefined slope

Slope-intercept form: y = mx + b where m = undefined for vertical lines.

Vertical lines are parallel to the y-axis and have an undefined slope according to the mathematical definition of slope.

Explanation

Vertical lines are parallel to the y-axis and have an undefined slope according to the mathematical definition of slope.

6. What is the equation of a horizontal line?

X = c (where c can be any real number)

Y = mx + b (where m is the slope)

Y = -c (where c can be any real number)

Y = c (where c can be any real number) horizontal lines have a slope of 0

A horizontal line has a slope of 0, meaning it does not change in the y-direction as x changes.

Explanation

A horizontal line has a slope of 0, meaning it does not change in the y-direction as x changes.

7. What is a Quadratic Equation?

2x + 3 = 0

3a - b = 0

Ax2 + bx + c = 0, a doesn’t equal 0.

X^3 + 4x^2 = 0

A quadratic equation is a polynomial equation in the form ax^2 + bx + c = 0, where 'x' represents an unknown variable, and 'a', 'b', and 'c' are constants with 'a' not equal to 0. The solutions to a quadratic equation can be found using the quadratic formula.

Explanation

A quadratic equation is a polynomial equation in the form ax^2 + bx + c = 0, where 'x' represents an unknown variable, and 'a', 'b', and 'c' are constants with 'a' not equal to 0. The solutions to a quadratic equation can be found using the quadratic formula.

8. What is the number of real solutions for a quadratic equation in the form of ax^2 + bx + c = 0 where a does not equal 0?

One

Three

None

Ax2 + bx + c = 0, a doesn’t equal.

A quadratic equation in the form of ax^2 + bx + c = 0 can have either two real solutions, one real solution, three real solutions, or no real solutions depending on the discriminant (b^2 - 4ac) of the equation.

Explanation

A quadratic equation in the form of ax^2 + bx + c = 0 can have either two real solutions, one real solution, three real solutions, or no real solutions depending on the discriminant (b^2 - 4ac) of the equation.

9. Identify the property of addition.

A + b = b + a

A + 0 = 0 = a = a

A * 0 = 0

A + a = 2a

10. What is the inverse property of addition?

A + 0 = a

A + (-a) = (-a) +a = 0

A + (-a) = 2a

A + a = a

The inverse property of addition states that when a number is added to its additive inverse, the result is always zero.

Explanation

The inverse property of addition states that when a number is added to its additive inverse, the result is always zero.

11. What is the commutative property of addition?

A = b = b +a

A - b = b - a

A * b = b * a

A / b = b / a

The commutative property of addition states that changing the order of the numbers being added does not change the sum.

Explanation

The commutative property of addition states that changing the order of the numbers being added does not change the sum.

12. What is the Associative property of addition?

(A +b) + c + a + (b + c)

A + b + c = (a + b) - c

A + (b + c) = (a + b) + c

A + c + b = (b + a) + c

The Associative property of addition states that changing the grouping of the numbers being added does not change the sum.

Explanation

The Associative property of addition states that changing the grouping of the numbers being added does not change the sum.

13. What is the identity property of multiplication?

Multiplication by 0 results in 0.

The identity property of multiplication is adding the numbers.

3 is the multiplicative identity.

A (1) = 1 (a) = a One is the multiplicative identity

The identity property of multiplication states that when any number is multiplied by 1, the result is the same number. Therefore, one is the multiplicative identity.

Explanation

The identity property of multiplication states that when any number is multiplied by 1, the result is the same number. Therefore, one is the multiplicative identity.

14. What is the inverse property of multiplication?

D (a) = 1/a (1) = 1 (a doesn’t equal 0)

B (1/a) = a (1) = 1 (a doesn’t equal 0)

C (1/a) = 1 (a) = 1 (a doesn’t equal 0)

A (1/a) = 1/a (a) = 1 (a doesn’t equal 0), the multiplicative inverse of a is 1/a

The inverse property of multiplication states that the multiplicative inverse of a number is such that when multiplied with the original number, the result is 1. In this case, 1/a is the multiplicative inverse of a.

Explanation

The inverse property of multiplication states that the multiplicative inverse of a number is such that when multiplied with the original number, the result is 1. In this case, 1/a is the multiplicative inverse of a.

15. What is the commutative property of multiplication?

Ab = ba

Ba = Ab

Ba = ab

Ab = ab

The commutative property of multiplication states that the order of the factors does not affect the result of the multiplication. In other words, for any two numbers a and b, multiplying a by b will give the same result as multiplying b by a.

Explanation

The commutative property of multiplication states that the order of the factors does not affect the result of the multiplication. In other words, for any two numbers a and b, multiplying a by b will give the same result as multiplying b by a.

16. What is the associative property of multiplication?

The associative property of multiplication states that a(b-c) = ab - ac.

(Ab)c = a(bc)

The associative property of multiplication states that a(b+c) = ab + ac.

The associative property of multiplication allows for changing the order of the factors without changing the result.

The associative property of multiplication states that (a+b)c = ac + bc.

The correct answer showcases how the order of multiplication of three numbers does not affect the final result, highlighting the associative nature of multiplication.

Explanation

The correct answer showcases how the order of multiplication of three numbers does not affect the final result, highlighting the associative nature of multiplication.

17. What is the Distributive property?

A(b - c) = ab - ac

( a + b )² = a² + 2ab + b²

A/b = b/a

A( b+ c) = ab +ac

The Distributive property states that multiplying a number by the sum of two other numbers is the same as multiplying the number by each of the other two numbers separately and then adding the products.

Explanation

The Distributive property states that multiplying a number by the sum of two other numbers is the same as multiplying the number by each of the other two numbers separately and then adding the products.

18. What is the distributive property?

4(y + 2) = 4y * 2

4 (y+ 2) = 4y + 4(2)

4(y + 2) = 4y + 8

4(y + 2) = 4y + 2

The distributive property states that multiplying a number by a sum is the same as multiplying the number by each addend separately and then adding the products.

Explanation

The distributive property states that multiplying a number by a sum is the same as multiplying the number by each addend separately and then adding the products.

19. What is the multiplicative property of Zero?

A (0) = 0 or 0 (a) = 0

A (0) = 5 or 0 (a) = 5

A (0) = -1 or 0 (a) = -1

A (0) = 1 or 0 (a) = 1

The correct multiplicative property of Zero is that any number multiplied by zero results in zero. Therefore, A (0) = 0 and 0 (a) = 0.

Explanation

The correct multiplicative property of Zero is that any number multiplied by zero results in zero. Therefore, A (0) = 0 and 0 (a) = 0.

20. What does the substitution property state?

If a < b, then a can be replaced in a given equation or inequality.

If a does not equal b, then a cannot be replaced in a given equation or inequality.

If a > b, then a can be replaced in a given equation or inequality.

If a = b, then can replace a in a given equation or inequality

The substitution property allows for the replacement of variables that are equal to each other in an equation or inequality, ensuring that the result remains unchanged.

Explanation

The substitution property allows for the replacement of variables that are equal to each other in an equation or inequality, ensuring that the result remains unchanged.

21. What is the Reflexive property of equality?

A = B, where A and B are any real numbers.

A= a a is any real number

A = 0, where A is any real number.

A = a, where a is any integer.

The Reflexive property of equality states that any number is equal to itself, hence A = A where A can be any real number. The incorrect answers are based on mistaken interpretations of the property.

Explanation

The Reflexive property of equality states that any number is equal to itself, hence A = A where A can be any real number. The incorrect answers are based on mistaken interpretations of the property.

22. What is the symmetric property of equality?

If a = b, then a = b.

If a = b, then a < b.

If a = b, then a > b.

If a= b. Then b=a

The symmetric property of equality states that if two values are equal (a = b), then the order of the values can be reversed and still hold true (b = a). This property is essential in mathematics and logic for establishing equality relationships.

Explanation

The symmetric property of equality states that if two values are equal (a = b), then the order of the values can be reversed and still hold true (b = a). This property is essential in mathematics and logic for establishing equality relationships.

23. What is the Transitive Property of Equality?

If a = b and b = c, then a = b.

If a = b and b = c, then a ≠ c.

If a = b and c = b, then a = c.

If a= B and B=c, then a = c

The Transitive Property of Equality states that if two quantities are equal to a third quantity individually, then they are also equal to each other.

Explanation

The Transitive Property of Equality states that if two quantities are equal to a third quantity individually, then they are also equal to each other.

24. What is an inequality?

An algebraic sentence comparing two quantities

A number that is divisible by 2.

A geometric shape with equal sides and angles.

A math formula expressing equality between two variables.

In mathematics, an inequality is a relation that holds between two values when they are different (i.e., not equal). An algebraic inequality is a mathematical sentence comparing two quantities using inequality signs such as , ≤, or ≥.

Explanation

In mathematics, an inequality is a relation that holds between two values when they are different (i.e., not equal). An algebraic inequality is a mathematical sentence comparing two quantities using inequality signs such as , ≤, or ≥.

25. What does the graph of an inequality look like?

Less than or equal to closed circle in graph

Greater than or equal to open circle in graph

Greater than or less than open circle in graph, equal to or greater than or equal to or less than closed circle, and not equal to open circle with line both ways

Equal to closed circle in graph

Inequalities can be represented graphically using open or closed circles to represent the values included in the solution set.

Explanation

Inequalities can be represented graphically using open or closed circles to represent the values included in the solution set.

26. What is the transitive property of inequality?

If A C. If A > B and B > C, then A < C.

Ac and if a> B and B> c then a>c

If A > B and B < C, then A > C. If A C, then A < C.

If A C, then A < C. If A > B and B < C, then A > C.

The transitive property of inequality states that if A is less than B and B is less than C, then A must be less than C. Similarly, if A is greater than B and B is greater than C, then A must be greater than C. This property helps simplify comparisons and relations between different values.

Explanation

The transitive property of inequality states that if A is less than B and B is less than C, then A must be less than C. Similarly, if A is greater than B and B is greater than C, then A must be greater than C. This property helps simplify comparisons and relations between different values.

27. What is the Addition/Subtraction Property of Inequality?

If a> b then a+ c > b+c

If a > b, then a / c > b / c

If a > b, then a - c > b - c

If a > b, then a * c > b * c

The correct answer follows the addition/subtraction property of inequality, where adding/subtracting the same value on both sides of an inequality preserves the inequality relationship.

Explanation

The correct answer follows the addition/subtraction property of inequality, where adding/subtracting the same value on both sides of an inequality preserves the inequality relationship.

28. What is the division property of inequality?

If A < B and C < 0, then A/C < B/C.

If A > B and C > 0, then A/C < B/C.

If A 0, then A/C > B/C.

A 0 then a/c < b/c

The division property of inequality states that if A 0, then dividing both sides of the inequality by a positive number C does not change the direction of the inequality symbol, as shown in the correct answer. The incorrect answers provide examples where the conditions are altered, resulting in incorrect statements.

Explanation

The division property of inequality states that if A 0, then dividing both sides of the inequality by a positive number C does not change the direction of the inequality symbol, as shown in the correct answer. The incorrect answers provide examples where the conditions are altered, resulting in incorrect statements.

29. What is the slope-intercept form of a linear equation?

Y = mx - b

Y = xm + b

Y = bx + m

Y = mx+ b (slope is m and y-intercept is b)

The correct form of a linear equation in slope-intercept form is Y = mx + b, where 'm' represents the slope and 'b' represents the y-intercept. The other options provided do not follow this standard form.

Explanation

The correct form of a linear equation in slope-intercept form is Y = mx + b, where 'm' represents the slope and 'b' represents the y-intercept. The other options provided do not follow this standard form.