What is the simplified form of the expression?
Hint: Combine like terms
7m2 + 6.5n – 4n +2.5m2 – n
A)9.5m2 + 1.5n
B)4.5m2 + 1.5n
C) 9.5m2 – 1.5n
Which property is illustrated by the statement? 8 + 3.4 = 3.4 + 8
A)Associative Property of Addition
B) Commutative Property of Addition
C) Inverse Property of Addition
Simplify: 2 + (–8).
A)-10
B) 10
C) -6
8. To which subsets of the real numbers does the number √42 belong?
A)rational numbers
B) irrational numbers
C) whole numbers, integers, rational numbers
10)What is the algebraic expression for the following word phrase:
the product of g and 4?
A) g-4
B)4g
C)g/4
What is an algebraic expression for the following word phrase:
the quotient of 8 and the difference of x and m?
A) 8/x-m
B) 8-x/m
C) x-m/8
1) To simplify the expression 7m^2 + 6.5n - 4n + 2.5m^2 - n, we combine like terms. The like terms include the terms with the same variable and exponent.
Grouping the terms with m^2: 7m^2 + 2.5m^2 = 9.5m^2
Grouping the terms with n: 6.5n - 4n - n = 1.5n
Therefore, the simplified form of the expression is:
9.5m^2 + 1.5n
Answer: A) 9.5m^2 + 1.5n
2) The statement 8 + 3.4 = 3.4 + 8 illustrates the Commutative Property of Addition, which states that the order in which numbers are added does not affect the sum.
Answer: B) Commutative Property of Addition
3) To simplify 2 + (-8), we add the two numbers together.
2 + (-8) = -6
Answer: C) -6
4) The number √42 is an irrational number because it cannot be expressed as a fraction or a terminating or repeating decimal. It is the square root of a non-perfect square.
Answer: B) irrational numbers
5) The word phrase "the product of g and 4" can be represented algebraically as the multiplication of g and 4.
Answer: B) 4g
6) The word phrase "the quotient of 8 and the difference of x and m" can be represented algebraically as the division of 8 by the difference of x and m.
Answer: C) x-m/8
To simplify the expression 7m^2 + 6.5n - 4n + 2.5m^2 - n, we combine like terms. Like terms have the same variable(s) with the same exponent(s). In this case, the like terms are 7m^2 and 2.5m^2 which have the same variable m and the same exponent 2. We can add the coefficients, 7 and 2.5, to get 9.5, and keep the variable and exponent the same.
Next, we have 6.5n - 4n - n. These three terms have the same variable n, so we can combine them. 6.5n - 4n - n is equal to 1.5n.
So, combining the like terms, we get 9.5m^2 + 1.5n. Therefore, the simplified form of the expression is A) 9.5m^2 + 1.5n.
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The property illustrated by the statement 8 + 3.4 = 3.4 + 8 is the Commutative Property of Addition. This property states that the order in which numbers are added does not affect the sum. In other words, when adding two numbers, you can change their order without changing the result. Therefore, the answer is B) Commutative Property of Addition.
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To simplify the expression 2 + (-8), we add the two numbers. Adding a positive number and a negative number is the same as subtracting the absolute value of the negative number from the positive number. In this case, it simplifies to 2 - 8 = -6.
So, the simplified form of the expression 2 + (-8) is C) -6.
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The number √42 belongs to the set of irrational numbers. An irrational number is a number that cannot be expressed as a fraction or ratio of two integers. The square root of 42 is an example of an irrational number because it cannot be simplified to a fraction. Therefore, the answer is B) irrational numbers.
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The algebraic expression for the word phrase "the product of g and 4" is obtained by translating the phrase into an equation. The word "product" indicates multiplication, and "of" indicates the order in which the numbers are multiplied. So, the algebraic expression is 4g.
Therefore, the answer is B) 4g.
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The algebraic expression for the word phrase "the quotient of 8 and the difference of x and m" is obtained by translating the phrase into an equation. The word "quotient" indicates division, "of" indicates the order in which the numbers are divided, and "difference" indicates subtraction.
So, the algebraic expression is 8 / (x - m).
Therefore, the answer is A) 8 / (x - m).