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Questions and Answers
How many terms are in the expression $3x + \frac{5a}{2y}$?
How many terms are in the expression $3x + \frac{5a}{2y}$?
2
In the expression $2y - 7z^3$, which of the following is an exponent?
In the expression $2y - 7z^3$, which of the following is an exponent?
In the expression $6x^2 + 5$, which of the following correctly identifies the 6?
In the expression $6x^2 + 5$, which of the following correctly identifies the 6?
Which notation best represents the relationship between the two numbers plotted on the number line below?
Which notation best represents the relationship between the two numbers plotted on the number line below?
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In the expression $[1 + 7 \cdot (2 - 9)] \div 3 + 12$, which of the following operations is done first?
In the expression $[1 + 7 \cdot (2 - 9)] \div 3 + 12$, which of the following operations is done first?
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What is the opposite of 6?
What is the opposite of 6?
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What type of number is $\sqrt{23}$?
What type of number is $\sqrt{23}$?
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Which of the following is true for multiplying two signed numbers with opposite signs?
Which of the following is true for multiplying two signed numbers with opposite signs?
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What is an unknown value called?
What is an unknown value called?
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What are natural numbers and zero called?
What are natural numbers and zero called?
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What is a number's distance from zero called?
What is a number's distance from zero called?
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What are quantities combined by only addition or subtraction called?
What are quantities combined by only addition or subtraction called?
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Express the sum of x and 3 divided by 2.
Express the sum of x and 3 divided by 2.
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Half of g multiplied by t squared is equal to d.
Half of g multiplied by t squared is equal to d.
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The length l of a rectangle is equal to its area A divided by its width w.
The length l of a rectangle is equal to its area A divided by its width w.
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Represent the length of the other piece if a piece of yarn 29 inches long is cut into two parts, with one part being m inches long.
Represent the length of the other piece if a piece of yarn 29 inches long is cut into two parts, with one part being m inches long.
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The perimeter of a rectangle is twice the sum of its length l and width w.
The perimeter of a rectangle is twice the sum of its length l and width w.
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The circumference C of a circle is equal to the product of π and the diameter d.
The circumference C of a circle is equal to the product of π and the diameter d.
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Express the gross profit GP of an item if the selling price p minus the cost of 2 dollars is considered.
Express the gross profit GP of an item if the selling price p minus the cost of 2 dollars is considered.
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Evaluate the expression $4 + 3^2 ÷ (-1)(4)(-2) - 1$.
Evaluate the expression $4 + 3^2 ÷ (-1)(4)(-2) - 1$.
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What is the value of $-3^2/2^3 + 1$?
What is the value of $-3^2/2^3 + 1$?
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What is the result of $\frac{5}{12} + \frac{1}{12} -\frac{1}{4}$?
What is the result of $\frac{5}{12} + \frac{1}{12} -\frac{1}{4}$?
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Simplify $3x + 2y + 5x - y$.
Simplify $3x + 2y + 5x - y$.
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Simplify $8mn + 10 - 2(3mn - 1) + 2mn - 5 + 8$.
Simplify $8mn + 10 - 2(3mn - 1) + 2mn - 5 + 8$.
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Simplify $a + [a + b - a - (2a - b)]$.
Simplify $a + [a + b - a - (2a - b)]$.
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If $x = -3$ and $y = 5$, find the value of the expression $2x^2 + 4y - 5$.
If $x = -3$ and $y = 5$, find the value of the expression $2x^2 + 4y - 5$.
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If $a = -2$, find the value of the expression $|2a + 5|$.
If $a = -2$, find the value of the expression $|2a + 5|$.
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Phil drove for 5 hours at 65 miles per hour. How far did he drive if $d = rt$?
Phil drove for 5 hours at 65 miles per hour. How far did he drive if $d = rt$?
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Find the value of A in the formula $A = \frac{1}{2}h (a + b)$ when $h = 6$ in., $a = 12$ in., and $b = 8$ in.
Find the value of A in the formula $A = \frac{1}{2}h (a + b)$ when $h = 6$ in., $a = 12$ in., and $b = 8$ in.
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What property is represented by $(a + b)c = ac + bc$?
What property is represented by $(a + b)c = ac + bc$?
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What property is represented by $r(s + t) = (s + t)r$?
What property is represented by $r(s + t) = (s + t)r$?
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What property is represented by $\frac{3}{5}(\frac{2}{5}) = \frac{3}{5}$?
What property is represented by $\frac{3}{5}(\frac{2}{5}) = \frac{3}{5}$?
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What property is represented by $x + (y + z) = (x + y) + z$?
What property is represented by $x + (y + z) = (x + y) + z$?
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What property is represented by $3x + 0 = 3x$?
What property is represented by $3x + 0 = 3x$?
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Study Notes
Algebra Expressions and Terms
- The expression 3x + 5a/2y contains two terms.
- In 2y − 7z³, the number 3 is identified as the exponent of z.
- The coefficient in 6x² + 5 is 6.
Mathematical Relationships and Inequalities
- The notation -1 < 5 illustrates the relationship between the two plotted numbers on a number line.
Order of Operations
- In the expression [1 + 7 · (2 − 9)] ÷ 3 + 12, the first operation performed is 2 − 9.
Number Properties
- The opposite of the number 6 is -6.
- The value of √23 is classified as an irrational number.
- When multiplying two numbers with opposite signs, the resultant product is negative.
Fundamental Algebra Concepts
- Variable represents an unknown value in algebra.
- Whole numbers include natural numbers and zero.
- Absolute value measures a number's distance from zero in a number line.
Composition of Expressions
- Terms are quantities combined solely through addition or subtraction.
- The expression for “the sum of x and 3 divided by 2” can be written as (x + 3) ÷ 2.
Formulas and Equations
- The relationship for half of g multiplied by t squared equal to d is represented by 1/2gt² = d.
- The formula for the length l of a rectangle is l = A/w where A is the area and w is the width.
- The perimeter of a rectangle is calculated as P = 2(l + w).
Mathematical Constants and Dimensions
- The circumference C of a circle is expressed as C = πd.
Financial Calculations
- The gross profit GP from an item is calculated as GP = p - 2, where p is the selling price.
Simplifying Mathematical Expressions
- The expression 4 + 3² ÷ (-1)(4)(-2) − 1 simplifies to 75.
- The result of -3²/2³ + 1 is -1.
- The expression 5/12 + 1/12 − 1/4 simplifies to 1/4.
Combining Like Terms
- The expression 3x + 2y + 5x − y can be simplified to 8x + y.
- For 8mn + 10 − 2(3mn − 1) + 2mn − 5 + 8, the result is simplified to 4mn + 15.
Value Evaluation Examples
- When substituting x = -3 and y = 5 in the expression 2x² + 4y − 5, the resulting value is 33.
- If a = -2, the absolute value expression | 2a + 5 | evaluates to 1.
Real-life Applications
- Phil drives for 5 hours at a rate of 65 miles per hour, covering a total distance of 325 miles.
- In the formula A = 1/2h(a + b) with values h = 6 in, a = 12 in, b = 8 in, the area A is calculated as 60 sq. in..
Algebraic Properties
- The distributive property states that (a + b)c = ac + bc.
- The commutative property highlights that r(s + t) = (s + t)r.
- The identity property is demonstrated with the expression 3/5(2/5) = 3/5.
- The associative property allows for grouping changes as shown in x + (y + z) = (x + y) + z.
- The expression 3x + 0 = 3x exemplifies the identity property in algebra.
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Test your understanding of 9th grade Algebra 1 concepts with these flashcards. Each card presents a question related to algebraic expressions, coefficients, and exponents. Challenge yourself to recall definitions and solve problems to excel in your studies.
