Find x
2x + 4 = -6 x = ____
Answer: x = -5
The expression 2x² - x² is equivalent to
Answer: x²
What type of function is y = x² + 51x ?
Answer: This an example of a quadratic function because its
highest degree is 2.
To show that (w+5)(w+2) is equivalent w^2+7w+10. Which property do we need to use?
Answer: The Distributive Property
What is Like Terms?
Answer: Terms with the same variables (letters) and Exponents (powers).
The average of
Answer: x = -23
What is the answer when (x² - 5x - 2) is subtracted from (-6x² - 7x - 3) ?
Answer: -7x² -2x - 1
Organize the following function in ascending order:
m(x) = x² + 11x³ - 5 + 20x.
Answer: m(x) = -5 + 20x + x² + 11x³
If M, P and Q represent integers,
M +(P + Q) = (M + P) + Q
is an example of which property?
Answer: The Associative Property
What is Constant?
Answer: A Constant is a fixed value. In Algebra, a constant is a number on
its own, or sometimes a letter such as a, b or c to stand for a fixed
number. Example: in “4x - 7 = 5", 7 and 5 are constants.
a)3² X 4² = 12². Solve for x:
Answer: x = 12
Which expression is equivalent to
-3x(x - 4) - 2x(x + 3)?
Answer: -5x² + 6x
In a linear equation, the independent variable increases at a constant rate while the dependent variable decreases at a constant rate. What type of slope does this line have?
Answer: The slope of this line is negative.
Indicate if the following equation is sure to have a solution set of all real numbers. Explain your answer.
Answer: Yes, the two expressions are algebraically equivalent by application of the Commutative Property.
What is Algebraic Expression?
Answer: An algebraic expression is a mathematical phrase that can contain ordinary numbers, variables (like x or y) and operators (like add, subtract, multiply, and divide). Examples:
23
3p
4m²³
a + 1
a² - b
-5m³ + 2 n³+ 1
_1_ = _1_
x – 2 4
Answer: x = 6
What is the answer when (x² - 5x - 2) is subtracted from (-6x² - 7x - 3) ?
Answer: -7x² -2x - 1
Organize the following function in descending order and determine its degree:
m(x) = x² + 11x³ - 5 + 20x.
Answer: m(x) = 11x³ + x² + 20x – 5
and third degree
(cubic).
While solving the equation 4(x + 2) = 2, Kim wrote
4x + 2 = 28. Which property did she use?
1) distributive
2) associative
3) commutative
4) None of the above
Answer: 4) None of the above since the statement is false.
Identify the expressions and the equations
(1)14x³ + 19y² - 5z (2) 14m + 19 = 2m + 10
(3) -2y² + 19y = 5 (4) 5w
Answer: Expressions = 1 and 4 Equations = 2 and 3
Consider the algebraic equations
Answer: a) Yes, x = 3 is a solution to both equations.
b) x = -5
What is (5x – 4y) – (5x + 4y) equivalent to?
Answer: -8y
Amy tossed a ball in the air in such a way that the path of the ball was modeled by the equation y = −x² + 6x.
In the equation, y represents the height of the ball in feet and x is the time in seconds. At what time, x, is the ball at its highest point?
Answer: At x = 3 sec, the ball is at its highest point.
Indicate the properties illustrated in the following statements:
1) a + (-a) = 0
2) a (0) = 0
Answer: 1) The Additive Inverse Property
2) The Zero Property
4x³y²z
Name the coefficient, variables and exponents
Answer: Coefficient = 4
Variables = x, y, and z
Exponents = 3, 2, and 1