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Questions and Answers
Identify the natural number 48 as prime or composite. If the number is composite, find its prime factorization.
Identify the natural number 48 as prime or composite. If the number is composite, find its prime factorization.
- prime
- 2, 2, 2, 2, 3 (correct)
- 4 · 8
- 2, 2, 3, 3
Evaluate the expression. $-3^2$
Evaluate the expression. $-3^2$
- -9 (correct)
- 9
- 6
- -6
Evaluate using the order of operations. $4 \cdot (6+5 \cdot 9 - 1)$
Evaluate using the order of operations. $4 \cdot (6+5 \cdot 9 - 1)$
- -46 (correct)
- -34
- -48
- 54
Evaluate using the order of operations. $(-2)^3 + 13 \cdot 5(4 - 2)$
Evaluate using the order of operations. $(-2)^3 + 13 \cdot 5(4 - 2)$
Evaluate using the order of operations. $2 - [8(2-4) - 6]$
Evaluate using the order of operations. $2 - [8(2-4) - 6]$
Evaluate using the order of operations. $3 \cdot 6(-1)^4 - 25 \div 5$
Evaluate using the order of operations. $3 \cdot 6(-1)^4 - 25 \div 5$
Evaluate using the order of operations. $\frac{-2 + 3^2 - (-8)}{2 - 9 + 12}$
Evaluate using the order of operations. $\frac{-2 + 3^2 - (-8)}{2 - 9 + 12}$
Evaluate using the order of operations. $-5|-4(11 - 9)|$
Evaluate using the order of operations. $-5|-4(11 - 9)|$
Evaluate the expression $-4x + y$ using the given values $x = 3, y = -2$.
Evaluate the expression $-4x + y$ using the given values $x = 3, y = -2$.
Evaluate the expression $-6xy + 2y - 9$ using the given values $x = 2, y = 1$.
Evaluate the expression $-6xy + 2y - 9$ using the given values $x = 2, y = 1$.
Evaluate the expression $5x^3 - 3x^2 + 4x + 2$ for $x = -2$.
Evaluate the expression $5x^3 - 3x^2 + 4x + 2$ for $x = -2$.
Evaluate the expression $\frac{4x - 6y}{x + 12}$ using $x = -2, y = 3$.
Evaluate the expression $\frac{4x - 6y}{x + 12}$ using $x = -2, y = 3$.
Evaluate the expression $\frac{2y - x + 18}{2x - y}$ given $x = -1, y = -7$.
Evaluate the expression $\frac{2y - x + 18}{2x - y}$ given $x = -1, y = -7$.
Evaluate the expression $|x - y|$ using $x = -3, y = 8$.
Evaluate the expression $|x - y|$ using $x = -3, y = 8$.
Evaluate the expression $|5x + 8y|$ using $x = -2, y = -3$.
Evaluate the expression $|5x + 8y|$ using $x = -2, y = -3$.
Use the formula $C = \frac{5}{9}(F - 32)$ for converting degrees Fahrenheit into degrees Celsius. Convert $F = 212^\circ$ to Celsius.
Use the formula $C = \frac{5}{9}(F - 32)$ for converting degrees Fahrenheit into degrees Celsius. Convert $F = 212^\circ$ to Celsius.
Perform the indicated operation. Where possible, reduce the answer to its lowest terms. $\frac{5}{6} - \frac{1}{8}$
Perform the indicated operation. Where possible, reduce the answer to its lowest terms. $\frac{5}{6} - \frac{1}{8}$
Perform the indicated operation. Where possible, reduce the answer to its lowest terms. $(\frac{3}{2}) \cdot (\frac{3}{2}) \cdot (\frac{3}{8})$
Perform the indicated operation. Where possible, reduce the answer to its lowest terms. $(\frac{3}{2}) \cdot (\frac{3}{2}) \cdot (\frac{3}{8})$
Perform the indicated operation. Where possible, reduce the answer to its lowest terms. $\frac{3}{20} \div \frac{7}{12}$
Perform the indicated operation. Where possible, reduce the answer to its lowest terms. $\frac{3}{20} \div \frac{7}{12}$
Perform the operations. $-12.5 - (-11.7)$
Perform the operations. $-12.5 - (-11.7)$
Perform the operations. $(6.7 - 8) \div 4 - 2 \cdot \sqrt{0.25}$
Perform the operations. $(6.7 - 8) \div 4 - 2 \cdot \sqrt{0.25}$
List all the elements of $B = {16, \sqrt{8}, -4, 0, \frac{8}{9}, -\frac{9}{8}, 7.5}$ that belong to the set Integers (Z).
List all the elements of $B = {16, \sqrt{8}, -4, 0, \frac{8}{9}, -\frac{9}{8}, 7.5}$ that belong to the set Integers (Z).
List all the elements of $B = {19, \sqrt{7}, -9, 0, \frac{0}{3}, -3, 4.4}$ that belong to the set Natural numbers (N).
List all the elements of $B = {19, \sqrt{7}, -9, 0, \frac{0}{3}, -3, 4.4}$ that belong to the set Natural numbers (N).
List all the elements of $B = {14, \sqrt{7}, -17, 0, \frac{0}{7}, 0.47}$ that belong to the set Rational numbers (Q).
List all the elements of $B = {14, \sqrt{7}, -17, 0, \frac{0}{7}, 0.47}$ that belong to the set Rational numbers (Q).
List all the elements of $B = {12, \sqrt{8}, -22, 0, \frac{0}{4}, 0.09, -8\pi, 0.252525...}$ that belong to the set Irrational numbers.
List all the elements of $B = {12, \sqrt{8}, -22, 0, \frac{0}{4}, 0.09, -8\pi, 0.252525...}$ that belong to the set Irrational numbers.
Write the rational number $-\frac{7}{9}$ as a decimal and state whether the decimal is repeating or terminating.
Write the rational number $-\frac{7}{9}$ as a decimal and state whether the decimal is repeating or terminating.
Indicate the property of real numbers. $3 + 4 = 4 + 3$
Indicate the property of real numbers. $3 + 4 = 4 + 3$
Indicate the property of real numbers. $14(tu) = (14t)u$
Indicate the property of real numbers. $14(tu) = (14t)u$
Indicate the property of real numbers. $8n + 8m = 8(n + m)$
Indicate the property of real numbers. $8n + 8m = 8(n + m)$
Indicate the property of real numbers. $4 + (-4) = 0$
Indicate the property of real numbers. $4 + (-4) = 0$
Indicate the property of real numbers. $-4\frac{3}{7} + 0 = -4\frac{3}{7}$
Indicate the property of real numbers. $-4\frac{3}{7} + 0 = -4\frac{3}{7}$
Indicate the property of real numbers. $(-3.1)1 = -3.1$
Indicate the property of real numbers. $(-3.1)1 = -3.1$
Indicate the property of real numbers. $\frac{1}{5} \cdot 5 = 1$
Indicate the property of real numbers. $\frac{1}{5} \cdot 5 = 1$
Insert <, >, or = to make the statement true. $7 ____ -6$
Insert <, >, or = to make the statement true. $7 ____ -6$
Insert <, >, or = to make the statement true. $-6.4 ____ -8.2$
Insert <, >, or = to make the statement true. $-6.4 ____ -8.2$
Insert <, >, or = to make the statement true. $1/3 ____ 0.33$
Insert <, >, or = to make the statement true. $1/3 ____ 0.33$
Insert <, >, or = to make the statement true. $3.14 ____ \pi$
Insert <, >, or = to make the statement true. $3.14 ____ \pi$
Use the given real number line to compute the distance. Find d(A, B).
Use the given real number line to compute the distance. Find d(A, B).
Find the distance between $\frac{7}{15}$ and $-\frac{3}{10}$.
Find the distance between $\frac{7}{15}$ and $-\frac{3}{10}$.
Find the distance between $-3\frac{5}{6}$ and $-6\frac{3}{8}$.
Find the distance between $-3\frac{5}{6}$ and $-6\frac{3}{8}$.
Flashcards
Divisible by 2
Divisible by 2
Last digit is 0, 2, 4, 6, or 8.
Divisible by 3
Divisible by 3
Sum of the digits is divisible by 3.
Divisible by 5
Divisible by 5
Last digit is 5 or 0.
Prime Number
Prime Number
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Evaluating an Expression
Evaluating an Expression
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Order of operations
Order of operations
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Least Common Multiple (LCM)
Least Common Multiple (LCM)
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Rational Number (Q)
Rational Number (Q)
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Irrational numbers
Irrational numbers
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Real numbers (R)
Real numbers (R)
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Solving Linear equation STEP 2
Solving Linear equation STEP 2
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Solving Linear equation STEP 3
Solving Linear equation STEP 3
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Solving Linear equation STEP 1
Solving Linear equation STEP 1
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Formula C
Formula C
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Solve a Formula for a Specific Variable
Solve a Formula for a Specific Variable
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Distance between two real numbers
Distance between two real numbers
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Multiplicative Inverse Property: a
Multiplicative Inverse Property: a
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Additive Identity Property
Additive Identity Property
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Additive Inverse Property
Additive Inverse Property
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Multiplicative Identity Property
Multiplicative Identity Property
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Study Notes
Divisibility Rules
- A number is divisible by 2 if its last digit is 0, 2, 4, 6, or 8
- A number is divisible by 3 if the sum of its digits is divisible by 3
- A number is divisible by 5 if its last digit is 5 or 0
Prime Numbers
- Determined by counting numbers
- A prime number is greater than 1
- Prime numbers only have 1 and itself as a factor
Signed Numbers: Addition & Subtraction
- The sign of the larger number, in absolute value form is maintained
- Add numbers if they have the same sign
- Subtract numbers if they have a different sign
Signed Numbers: Multiplication & Division
- A positive result occurs if the numbers have the same sign
- A negative result occurs if the numbers have different signs
Order of Operations
- Parentheses come first
- Exponents come second
- Multiplication and Division (from left to right) come third
- Addition and Subtraction (from left to right) come last
Evaluating Expressions
- Find the value of the expression when its variable is replaced with a given number
LCM
- A least common multiple of two numbers is the smallest multiple for both numbers
Real numbers contain decimals
- Includes fractions in decimal form
- For example: 0.5, 0.75, 2.35, -0.073, 0.3333, 2.142857
Real Numbers also contain irrational numbers
- Includes numbers such as π, √2
- Every real number corresponds to a point on the number line.
Commutative Property
- Addition: a + b = b + a
- Multiplication: a × b = b × a
Associative Property
- Addition: (a + b) + c = a + (b + c)
- Multiplication: (a × b) × c = a × (b × c)
Distributive Property of Multiplication over Addition
- Defines that a(b + c) = ab + ac
- (a+b)c can also be written as ac + bc
Additive Identity Property
- a + 0 = a
Additive Inverse Property
- a + (− a) = 0
Multiplicative Identity Property
- a × 1 = a
Multiplicative Inverse Property
1
- a × = 1 when a ≠0 a
Distance Between Real Numbers
- d = |a - b| or d = |b - a|
Solving Linear Equations: General Strategy
- STEP 1: Distribute if there are any parentheses
- STEP 2: Combine like terms on either side
- STEP 3: Remove the smaller term of x, using inverse operations
- STEP 4: Isolate the term of x, using inverse operations
- STEP 5: Solve for x by dividing both sides by the coefficient of x
Integer Exponent Rules
- These rules apply when a, b ≠0
Zero-Exponent Rule
- a0 = 1
Product Rule
- Defines that am â‹… an = am + n
Quotient Rule
am
- Defines that = am - n an
One-Exponent Rule
- a1 = a
Power Rule
- Defines that (am)n = am â‹… n
Negative Exponent Rule
1
- Defines that a-n = an
Power of a Product
- (a â‹… b)m = am â‹… bm
Power of a Quotient
am
am bm
Negative Power of a Quotient
a −m bm
b am
Factoring Special Products
- a2 - b2 = (a - b)(a + b)
- a3 - b3 = (a - b)(a2 + ab + b2)
- a3 + b3 = (a + b)(a2 - ab + b2)
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