Introduction To Algebra Test
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Questions and Answers
- 1.
Which word best describes the 2 in the expression 3x2 + 4x + 7.
- A.
Coefficient
- B.
Constant
- C.
Exponent
- D.
Term
- E.
Variable
Correct Answer
C. ExponentExplanation
The number 2 in the expression 3x2 + 4x + 7 is best described as an exponent. In this expression, the 2 is the exponent of the variable x, indicating that x is being raised to the power of 2. The exponent determines the degree of the term and represents how many times the base (in this case, x) is multiplied by itself.Rate this question:
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- 2.
Which word best describes the 3 in the expression 3x2 + 4x + 7.
- A.
Coefficient
- B.
Constant
- C.
Exponent
- D.
Term
- E.
Variable
Correct Answer
A. CoefficientExplanation
The word "coefficient" best describes the 3 in the expression 3x2 + 4x + 7. In algebraic expressions, a coefficient is a numerical or constant factor that multiplies a variable. In this case, the coefficient of the term 3x2 is 3, indicating that the variable x is multiplied by 3.Rate this question:
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- 3.
Which word best describes the x in the expression 3x2 + 4x + 7.
- A.
Coefficient
- B.
Constant
- C.
Exponent
- D.
Term
- E.
Variable
Correct Answer
E. VariableExplanation
The expression 3x^2 + 4x + 7 represents a quadratic equation with x as the variable. In algebraic equations, a variable is a symbol that represents an unknown value or quantity. In this case, x can take on different values, and its power (exponent) in the equation indicates its degree. Therefore, the word "Variable" best describes x in the given expression.Rate this question:
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- 4.
Which word best describes the 7 in the expression 3x2 + 4x + 7.
- A.
Coefficient
- B.
Constant
- C.
Exponent
- D.
Term
- E.
Variable
Correct Answer
B. ConstantExplanation
In the expression 3x2 + 4x + 7, the term "7" does not have any variable attached to it and does not change. It remains the same regardless of the value of x. Therefore, it can be described as a constant.Rate this question:
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- 5.
Which word best describes the 4x in the expression 3x2 + 4x + 7.
- A.
Coefficient
- B.
Constant
- C.
Exponent
- D.
Term
- E.
Variable
Correct Answer
D. TermExplanation
In the expression 3x^2 + 4x + 7, the term "4x" represents a single entity that includes both a coefficient (4) and a variable (x). A term is a combination of a coefficient and one or more variables, and it can be added or subtracted within an expression. Therefore, the word "Term" best describes the 4x in the given expression.Rate this question:
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- 6.
Simplify [ a2 – 2a + 7a2 + 9a + a – 4a2 ] by collecting like terms.
- A.
4a2 - 8a
- B.
- 4a2 + 8a
- C.
12a2+ 8a
- D.
4a2 + 8a
- E.
None of the above
Correct Answer
D. 4a2 + 8aExplanation
The given expression is simplified by combining like terms. In this case, the terms with the same variable (a) are combined. The terms 4a^2 and -4a^2 cancel each other out, leaving only the term 8a. Therefore, the simplified expression is 4a^2 + 8a.Rate this question:
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- 7.
Simplify [ –6p2 – 20p – 4p – 10p2 – 3 + 2p + 5 ] by collecting like terms.
- A.
16p2 – 22p + 2
- B.
–16p2 – 22p + 2
- C.
–16p2 – 22p – 2
- D.
16p2– 22p – 2
- E.
None of the above
Correct Answer
B. –16p2 – 22p + 2Explanation
The given expression can be simplified by combining like terms. The terms with the same variable and exponent can be added or subtracted together. In this case, the terms -6p^2 and -10p^2 can be combined to give -16p^2. The terms -20p, -4p, and 2p can be combined to give -22p. The constant terms -3 and 5 can be combined to give 2. Therefore, the simplified expression is -16p^2 - 22p + 2.Rate this question:
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- 8.
Simplify [ 2n2 + 2n + 1 – 10n2 – n – 15n + 9 – n ] by collecting like terms.
- A.
8n2 – 15n + 10
- B.
–8n2 + 15n + 9
- C.
–8n2 – 15n – 1
- D.
–8n2 – 15n + 10
- E.
None of the above
Correct Answer
D. –8n2 – 15n + 10Explanation
The given expression is simplified by combining like terms. By combining the like terms, we get -8n^2 - 15n + 10.Rate this question:
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- 9.
Simplify [ –11x + 2y + 5 + 3y + 7 + 1 – 6x ] by collecting like terms.
- A.
17x – 5y + 13
- B.
–17x + 5y + 13
- C.
17x + 5y – 13
- D.
–17x – 5y + 13
- E.
None of the above
Correct Answer
B. –17x + 5y + 13Explanation
The given expression involves collecting like terms, which means combining the terms that have the same variables and exponents. By collecting like terms, we can simplify the expression. In this case, we have -11x and -6x, which can be combined to give -17x. We also have 2y and 3y, which can be combined to give 5y. Finally, we have 5, 7, and 1, which can be combined to give 13. Therefore, the simplified expression is -17x + 5y + 13.Rate this question:
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- 10.
Simplify [ 5a2 + 4a + 17 – 2a + 3a2 – 4 ] by collecting like terms.
- A.
8a2 –2a + 13
- B.
–8a2 + 2a + 15
- C.
8a2 + 2a + 13
- D.
8a2 + 2a + 17
- E.
None of the above
Correct Answer
C. 8a2 + 2a + 13Explanation
The given expression is simplified by combining like terms. The terms with the same variable and exponent are grouped together and their coefficients are added or subtracted. In this case, the terms 5a2 and 3a2 are combined to give 8a2. The terms 4a, -2a, and 2a are combined to give 4a. The constant terms 17 and -4 are combined to give 13. Therefore, the simplified expression is 8a2 + 2a + 13.Rate this question:
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- 11.
Which of the following is equivalent to the expression 3(x + 2) – 7?
- A.
3(x + 2 – 7)
- B.
3x + 6 – 7
- C.
3x + 6 – 21
- D.
3x – 5
- E.
None of the above
Correct Answer
B. 3x + 6 – 7Explanation
The expression 3(x + 2) - 7 can be simplified by distributing the 3 to both terms inside the parentheses. This gives us 3x + 6 - 7. Simplifying further, we combine like terms to get 3x - 1. Therefore, the expression 3x + 6 - 7 is equivalent to 3(x + 2) - 7.Rate this question:
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- 12.
Which of the following expressions mean the same thing? [Select two options]
- A.
2(4 + 5)
- B.
4 + 5(2)
- C.
(4 + 5)(2)
- D.
2(4) + 5
Correct Answer(s)
A. 2(4 + 5)
C. (4 + 5)(2)Explanation
The expressions 2(4 + 5) and (4 + 5)(2) mean the same thing because both of them represent the multiplication of the sum of 4 and 5 by 2.Rate this question:
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- 13.
Which of the following expressions mean the same thing? [Select two options]
- A.
5(2x + 7)
- B.
5(2x) + 7
- C.
2x + 7(5)
- D.
(2x + 7)(5)
Correct Answer(s)
A. 5(2x + 7)
D. (2x + 7)(5)Explanation
The expressions 5(2x + 7) and (2x + 7)(5) mean the same thing because they both represent the product of 5 and the sum of 2x and 7. In both expressions, the 2x and 7 are being multiplied by 5. The order in which the terms are written does not affect the result of the multiplication, so both expressions are equivalent.Rate this question:
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- 14.
Which of the following expressions mean the same thing? [Select two options]
- A.
–8(6x – 4)
- B.
–48x – 36
- C.
–48x + 32
- D.
–48x – 32
Correct Answer(s)
A. –8(6x – 4)
C. –48x + 32Explanation
The two expressions that mean the same thing are -8(6x - 4) and -48x + 32. Both expressions simplify to the same result when expanded and simplified.Rate this question:
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- 15.
Which expression shows –3(x + 5) in expanded form?
- A.
–3x + 15
- B.
–3x + 5
- C.
–3x – 8
- D.
–3x – 15
Correct Answer
D. –3x – 15Explanation
The given expression, -3(x + 5), can be expanded by distributing the -3 to both terms inside the parentheses. This means multiplying -3 with both x and 5. The result is -3x - 15, which matches the answer given.Rate this question:
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- 16.
Which of the following expressions mean the same thing? [Select all the correct options]
- A.
–9(6y – 4y)
- B.
–54y – 36y
- C.
–54y + 36y
- D.
–18y
- E.
18y
Correct Answer(s)
A. –9(6y – 4y)
C. –54y + 36y
D. –18yExplanation
The expressions -9(6y - 4y), -54y - 36y, and -18y all mean the same thing.Rate this question:
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- 17.
Which of the following is equivalent to the expression 8(2x + 2) – 3(4x + 6)?
- A.
4x + 10
- B.
28x + 34
- C.
4x – 2
- D.
4x + 34
Correct Answer
C. 4x – 2Explanation
The given expression can be simplified using the distributive property. Multiplying 8 by each term inside the parentheses, we get 16x + 16. Similarly, multiplying 3 by each term inside the other parentheses, we get 12x + 18. Subtracting these two expressions, we get 16x + 16 - (12x + 18). Simplifying further, we get 16x + 16 - 12x - 18. Combining like terms, we get 4x - 2, which is equivalent to the given expression.Rate this question:
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- 18.
Simplify the expression: ( - 8v4 + 4v3 + 3v) + (- 8v4 + 4v - 7)
- A.
-17v4 + 4v3 + 2v - 7
- B.
-16v4 + 4v3 + 7v - 7
- C.
-16v4 + 4v3 + 10v - 7
- D.
-16v4 + 4v3 + 2v - 7
Correct Answer
B. -16v4 + 4v3 + 7v - 7 -
- 19.
Simplify the expression: (–6p4 + p3 + 1) – ( 8p4–8p3 + 7)
- A.
–14p4 + 9p3 – 6
- B.
–14p4 + 9p3 – 1
- C.
–14p4 + 9p3 + 6
- D.
–15p4 + 9p3 + 6
Correct Answer
A. –14p4 + 9p3 – 6Explanation
The given expression is simplified by distributing the negative sign to each term inside the parentheses. This results in the expression -6p4 - p3 - 1 - 8p4 + 8p3 - 7. Combining like terms, we get -14p4 + 9p3 - 6. Therefore, the correct answer is -14p4 + 9p3 - 6.Rate this question:
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- 20.
Simplify the following expression (r2 + s2) – (5r2 + 4s2)
- A.
–4r2 +5s2
- B.
–4r2 – 3s2
- C.
–5r4 – 4s4
- D.
–4r2 + 3s2
Correct Answer
B. –4r2 – 3s2Explanation
The given expression is (r^2 + s^2) - (5r^2 + 4s^2). To simplify this expression, we need to distribute the negative sign to both terms inside the parentheses. This gives us -5r^2 - 4s^2. Combining like terms, we get -4r^2 - 3s^2. Therefore, the correct answer is -4r^2 - 3s^2.Rate this question:
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- 21.
The measure of two side of a triangle is x2+ 2x. If the perimeter is 4x2+ x, what is the measure of the third side?
- A.
3x2– x
- B.
4x2 + 2x
- C.
3x2 + 3x
- D.
3x2 + 2x
Correct Answer
A. 3x2– xExplanation
The perimeter of a triangle is the sum of the lengths of all three sides. In this case, the given perimeter is 4x^2 + x. We are also given that two sides of the triangle have a combined length of x^2 + 2x. To find the measure of the third side, we need to subtract the sum of the lengths of the two given sides from the perimeter. Therefore, the measure of the third side is 4x^2 + x - (x^2 + 2x) = 3x^2 - x.Rate this question:
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- 22.
Simplify the expression: (5b - 3b3 - 8b2) - (2b3 - 4b2 + 6b - 3b4)
- A.
3b4 - 5b3 - 11b2 - b
- B.
3b4 - 5b3 - 11b2 - 9b
- C.
3b4 - 5b3 - 11b2 - 15b
- D.
3b4 - 5b3 - 4b2 - b
Correct Answer
D. 3b4 - 5b3 - 4b2 - bExplanation
By simplifying the expression, we can combine like terms by adding or subtracting their coefficients. In this case, we have the terms with b raised to different powers: b, b^2, b^3, and b^4. By combining the coefficients of these terms, we get 3b^4 - 5b^3 - 4b^2 - b as the simplified expression.Rate this question:
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- 23.
Simplify the expression: (7k + 2k3 - 8k4) - (4k3 - 5k + 4k2 - 7k4)
- A.
-k4 - 2k3 - 4k2 + 12k
- B.
-2k3 - 7k2 + 12k + 4k4
- C.
-2k3 - 4k32 + 12k + 4k4
- D.
-2k3 - 4k2 + 12k
Correct Answer
A. -k4 - 2k3 - 4k2 + 12kExplanation
The given expression involves subtracting two sets of terms. To simplify the expression, we combine like terms by adding or subtracting coefficients with the same variable and exponent. In this case, we have terms with the variable k raised to different powers. By rearranging the terms and combining like terms, we obtain the answer: -k^4 - 2k^3 - 4k^2 + 12k.Rate this question:
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- 24.
Expand and Simplify: (5x + 2) (x2 – 3x + 6)
- A.
5x3 – 17x2 + 24x + 12
- B.
5x3 + 17x2 – 24x + 12
- C.
5x3 – 13x2 + 24x + 12
- D.
5x3 + 13x2 – 24x – 12
Correct Answer
C. 5x3 – 13x2 + 24x + 12Explanation
The correct answer is 5x3 – 13x2 + 24x + 12. This is the correct answer because when we expand and simplify the given expression, we multiply each term in the first polynomial (5x + 2) by each term in the second polynomial (x2 – 3x + 6). After combining like terms, we get the expression 5x3 – 13x2 + 24x + 12.Rate this question:
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- 25.
Is the polynomial expression in standard form? 7x3 – 8x2 + 9
- A.
True
- B.
False
Correct Answer
A. TrueExplanation
The polynomial expression is in standard form because the terms are arranged in descending order of their exponents. The highest exponent is 3, followed by 2, and then there is a constant term.Rate this question:
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- 26.
Choose all the polynomial expressions that are in standard form (Multiple options might be correct)
- A.
2x + 4x3 – 9
- B.
7x3 – 3x2
- C.
9 + 2x + 3x2
- D.
3x9 + 4x2 – 6x + 10
Correct Answer(s)
B. 7x3 – 3x2
D. 3x9 + 4x2 – 6x + 10Explanation
The polynomial expressions 7x^3 - 3x^2 and 3x^9 + 4x^2 - 6x + 10 are in standard form because they are written in descending order of the exponents of the variables, with the coefficients of each term included.Rate this question:
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- 27.
Simplify: 5(3x+2) + (2x - 3)
- A.
15x + 10
- B.
17x + 7
- C.
15x + 7
- D.
17x + 13
Correct Answer
B. 17x + 7Explanation
The given expression is 5(3x+2) + (2x - 3). To simplify this expression, we can distribute the 5 to both terms inside the parentheses, which gives us 15x + 10. Then, we can combine like terms by adding the 15x and 2x, which gives us 17x. Finally, we add the constant terms 10 and -3 to get 7. Therefore, the simplified expression is 17x + 7.Rate this question:
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- 28.
Which expression is equivalent to 2(3g - 4) - (8g + 3)?
- A.
-2g - 1
- B.
-2g - 5
- C.
-2g - 7
- D.
-2g - 11
Correct Answer
D. -2g - 11Explanation
To simplify the expression, we distribute the 2 to both terms inside the parentheses: 2(3g - 4) becomes 6g - 8. Then, we distribute the negative sign to both terms inside the parentheses: -(8g + 3) becomes -8g - 3. Now we can combine like terms: 6g - 8 - 8g - 3 = -2g - 11. Therefore, the expression is equivalent to -2g - 11.Rate this question:
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- 29.
If C = 2a2−5 and D = 3 – a , then C – 2D equals to:
- A.
2a2 + a – 8
- B.
2a2 – a– 8
- C.
2a2 + 2a – 11
- D.
2a2 – a – 11
Correct Answer
C. 2a2 + 2a – 11Explanation
The given expression is C - 2D. Substituting the values of C and D, we get (2a^2 - 5) - 2(3 - a). Simplifying further, we have 2a^2 + a - 8. Therefore, the correct answer is 2a^2 + a - 8.Rate this question:
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- 30.
Simplify: (2x + 8) – 3(x - 2)
- A.
X + 2
- B.
–x + 14
- C.
6x2 + 16
- D.
–x + 10
Correct Answer
B. –x + 14Explanation
The given expression is (2x + 8) - 3(x - 2). To simplify the expression, we distribute the -3 to both terms inside the parentheses: 2x + 8 - 3x + 6. Combining like terms, we get -x + 14.Rate this question:
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- 31.
Jim is twice as old as John. If x represents John's age, which expression represents how old Jim is in six years?
- A.
N2 + 6
- B.
2n - 6
- C.
N + 6
- D.
2n + 6
Correct Answer
D. 2n + 6Explanation
Jim is twice as old as John, so if x represents John's age, then Jim's age can be represented as 2x. In six years, both John and Jim will be six years older. Therefore, Jim's age in six years can be represented as 2x + 6.Rate this question:
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- 32.
Expand and Simplify (2x + 1)(x - 5)
- A.
3x - 4
- B.
2x2 - 6x - 4
- C.
2x2 - 9x - 5
- D.
3x2 - 10 - 5
Correct Answer
C. 2x2 - 9x - 5Explanation
The given expression is a product of two binomials: (2x + 1) and (x - 5). To expand and simplify this expression, we can use the distributive property. By multiplying each term in the first binomial by each term in the second binomial, we get: 2x * x + 2x * (-5) + 1 * x + 1 * (-5). Simplifying this further, we have: 2x^2 - 10x + x - 5. Combining like terms, we get the final simplified expression: 2x^2 - 9x - 5.Rate this question:
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- 33.
The length of a rectangle is four more than the width. The width is equal to x. Find the area of the rectangle. [ Hint: A = LW ]
- A.
4x
- B.
X2 + 4x
- C.
4x + 8
- D.
X2 + 4
Correct Answer
B. X2 + 4xExplanation
The area of a rectangle is calculated by multiplying its length and width. In this case, the length of the rectangle is given as "four more than the width". Since the width is equal to x, the length can be expressed as (x + 4). Therefore, the area of the rectangle is (x * (x + 4)), which simplifies to x^2 + 4x.Rate this question:
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- 34.
Which of the following expressions has 3 unlike terms?
- A.
2x2+ 9x2 + 2
- B.
6x2 + 6x + 8
- C.
2x - 9x + 2
- D.
2x2 y5 + 2 - 3
Correct Answer
B. 6x2 + 6x + 8Explanation
The expression 6x2 + 6x + 8 has 3 unlike terms because each term has a different variable or exponent. The term 6x2 has a different exponent than the term 6x, and both of these terms have different variables than the constant term 8. Therefore, this expression has 3 unlike terms.Rate this question:
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- 35.
Expand and Simplify: -4x (3x2 - 2x + 1)
- A.
-12x2 + 8x - 4
- B.
-12x3 -2x + 1
- C.
-12x3 - 8x2 +4x
- D.
-12x3 + 8x2 - 4x
Correct Answer
D. -12x3 + 8x2 - 4xExplanation
The given expression is a multiplication of -4x with the expression (3x^2 - 2x + 1). To expand and simplify, we distribute -4x to each term inside the parentheses. This gives us -12x^3 + 8x^2 - 4x. Therefore, the answer is -12x^3 + 8x^2 - 4x.Rate this question:
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- 36.
Find the perimeter of the rectangle { Hint: P = 2L + 2W)
- A.
6x + 11
- B.
8x + 24
- C.
12x + 22
- D.
8x2 + 28x + 24
Correct Answer
C. 12x + 22Explanation
The given answer, 12x + 22, is the correct expression for finding the perimeter of a rectangle. The formula for the perimeter of a rectangle is P = 2L + 2W, where L represents the length and W represents the width. In this case, the length is represented by 6x and the width is represented by 11. Therefore, substituting these values into the formula, we get P = 2(6x) + 2(11) = 12x + 22.Rate this question:
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- 37.
Simplify the algebraic expression: (3x2 + 2x - 4) - (5x2 + 6x + 2) + (4x2 - x + 1)
- A.
2x2 - 5x - 5
- B.
2x2 - 4x - 5
- C.
6x2 - 4x - 1
- D.
12x2 + 9x + 7
Correct Answer
A. 2x2 - 5x - 5Explanation
The given algebraic expression involves adding and subtracting terms with the same variable, x, and different exponents. By combining like terms, we can simplify the expression. In this case, we combine the terms with x^2, the terms with x, and the constant terms separately. After simplifying, the resulting expression is 2x^2 - 5x - 5.Rate this question:
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- 38.
Simplify the expression: 4(5y - 2y2 + 11) - 2y2
- A.
-8y2 + 18y + 44
- B.
-10y2 + 20y + 44
- C.
6y2 + 20y + 44
- D.
10y2 + 20y + 44
Correct Answer
B. -10y2 + 20y + 44Explanation
The expression is simplified by distributing the 4 to each term inside the parentheses, resulting in 20y - 8y^2 + 44. Then, subtracting 2y^2 from this expression gives -10y^2 + 20y + 44.Rate this question:
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- 39.
Expand and Simplify the expression: 4 (6y2 - 2y) - 3y (4y - 3)
- A.
12y2- 8y+9
- B.
12y2- 17y
- C.
36y2 +y
- D.
12y2 +y
Correct Answer
D. 12y2 +yExplanation
The given expression is a combination of terms that can be simplified by applying the distributive property and combining like terms. By multiplying 4 with each term inside the parentheses and then multiplying -3y with each term inside the second set of parentheses, we can expand the expression. This results in 24y^2 - 8y - 12y^2 + 9y. Combining like terms, we get 12y^2 + y.Rate this question:
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- 40.
Simplify the expression. -4(9 + 3x) - 4(x - 2)
- A.
-16x-28
- B.
-16x-44
- C.
20x - 12
- D.
30x - 9
Correct Answer
A. -16x-28Explanation
To simplify the expression, we need to distribute the -4 to both terms inside the parentheses. This gives us -36 - 12x - 4x + 8. Combining like terms, we get -16x - 28.Rate this question:
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- 41.
Simplify the expression -6x - 5(10x + 3)
- A.
-56x - 15
- B.
-56x+15
- C.
44x+15
- D.
-44x-15
Correct Answer
A. -56x - 15Explanation
The expression is simplified by distributing the -5 to both terms inside the parentheses. This gives us -6x - 50x - 15. Combining like terms, we get -56x - 15.Rate this question:
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- 42.
Simplify the expression. -6(10n + 7) + 9n
- A.
-51n - 45
- B.
-51n - 42
- C.
-106 + 100n
- D.
-51n - 51
Correct Answer
B. -51n - 42Explanation
The expression -6(10n + 7) + 9n can be simplified by distributing the -6 to both terms inside the parentheses, resulting in -60n - 42. Then, adding 9n to this expression gives -51n - 42.Rate this question:
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- 43.
Simplify x2(2x+3)
- A.
X2+2x+3
- B.
2x+3
- C.
2x2+3x
- D.
2x3+3x2
Correct Answer
D. 2x3+3x2Explanation
The given expression is x^2(2x+3). To simplify this expression, we need to distribute the x^2 to both terms inside the parentheses. This gives us 2x^3 + 3x^2. Therefore, the correct answer is 2x^3 + 3x^2.Rate this question:
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- 44.
- A.
8x4
- B.
8x8
- C.
6x4
- D.
6x8
Correct Answer
A. 8x4Explanation
The correct answer is 8x4 because when you multiply 8 by 4, you get the product of 32.Rate this question:
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- 45.
- A.
12w 2 − 12w + 9
- B.
5w 2 − 4w + 3
- C.
12w 2 − 9w + 6
- D.
5w 2 − 12w+ 9
Correct Answer
B. 5w 2 − 4w + 3 -
- 46.
- A.
-5x10
- B.
4x4 + 18x6
- C.
-6x4 + 16x2
- D.
4x4 - 9x2
Correct Answer
D. 4x4 - 9x2Explanation
In the given expression, we have a combination of multiplication and addition/subtraction operations. The expression can be simplified by performing the multiplication first and then the addition/subtraction.
-5x10 = -50
4x4 = 16
18x6 = 108
-6x4 = -24
16x2 = 32
Now, substituting these values back into the expression, we get:
-50 + 16 + 108 - 24 + 32
Simplifying further, we get:
-50 + 16 + 108 - 24 + 32 = 82
Therefore, the correct answer is 82.Rate this question:
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- 47.
4k2(6k2 + 9kq - 5q2)
- A.
24k2 + 36k3q - 20k2q2
- B.
24k4 + 36kq - 20k2q2
- C.
24k4 + 36k3q - 20k2q2
- D.
24k + 36 kq - 20 k2q
Correct Answer
C. 24k4 + 36k3q - 20k2q2Explanation
The given expression is a product of two terms: 4k^2 and (6k^2 + 9kq - 5q^2). To simplify the expression, we need to distribute 4k^2 to each term inside the parentheses. This results in 24k^4 + 36k^3q - 20k^2q^2. Therefore, the correct answer is 24k^4 + 36k^3q - 20k^2q^2.Rate this question:
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- 48.
Simplify 7x2y3 (2x4y5+6xy3)
- A.
14x8y15+42x2y9
- B.
9x6y8+13x3y6
- C.
14x6y8+42x3y6
- D.
14x6y8+42x2y6
Correct Answer
C. 14x6y8+42x3y6Explanation
The given expression is the product of 7x^2y^3 and the sum of (2x^4y^5 + 6xy^3). To simplify, we need to distribute the 7x^2y^3 to each term inside the parentheses. This gives us 14x^6y^8 + 42x^3y^6. Therefore, the correct answer is 14x^6y^8 + 42x^3y^6.Rate this question:
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- 49.
The perimeter of the garden in the diagram is 170 m. Determine the value of w and the length of each side.
- A.
32 m (w = 15)
- B.
34 m (w = 10)
- C.
34 m (w = 15)
- D.
36 m (w = 12)
Correct Answer
C. 34 m (w = 15)Explanation
Based on the given information, the perimeter of the garden is 170 m. The perimeter of a rectangle is calculated by adding the lengths of all four sides. Let's assume the length of the garden is L and the width is W. The formula for the perimeter is P = 2L + 2W. Since we are given that the perimeter is 170 m, we can set up the equation as 170 = 2L + 2W. We are also told that the width is equal to 15, so we can substitute W with 15. Solving the equation, we get 170 = 2L + 2(15), which simplifies to 170 = 2L + 30. By subtracting 30 from both sides, we have 140 = 2L. Dividing both sides by 2, we get L = 70. Therefore, the length of each side is 70 m and the width is 15 m, giving us the answer 34 m (w = 15).Rate this question:
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- 50.
Solve for x: –2x + 3 = –5
- A.
8
- B.
4
- C.
- 8
- D.
- 4
Correct Answer
B. 4Explanation
To solve for x, we need to isolate the variable on one side of the equation. By adding 2x to both sides of the equation, we can eliminate the -2x term on the left side. This leaves us with 3 = -5 + 2x. Next, we can simplify the equation by adding 5 to both sides, resulting in 8 = 2x. Finally, by dividing both sides of the equation by 2, we find that x = 4.Rate this question:
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