1. Consider a new addition for real numbers, denoted by , and defined as a b = 3a + 3b, where is the regular addition for reals. Is commutative? Is associative? If any of your answers are affirmative, argue why it is true for any a and b, if they are negative, construct a concrete counterexample where the property fails. 2. Same questions for ab = 3a + b.

Q: 2. Perform the indicated Integer operations. -2+(-3) = -4-(-5) = 1- (-2) +2 (-3) 2 (2-4) + (-4) 2-8=…

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Q: 3. Simplify the following expressions. A. 2/(x-3) B. (x-3)/5 5x 2x² + 7x +3 x + 3 2x² – 3x - 2 C.…

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Q: Determine whether it is possible to express 1 as a liner combination of 1 = m· 44 + n· 91 ,. for…

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Q: If all variables in the expression 5/x10y – 4x/xy represent nonnegative real numbers, then which of…

A: Given,          The expression is 5x10y9-4xxy9 .

Q: 7. Which of these below is equivalent to 3(x-1)-2(x+3)-x? -3 4x-9 4x+ 3

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Q: I need help with this here

A: The objective of the question is to understand the number of ways a number can be written as a…

Q: 6. Expand and simplify each of the following algebraic expressions. c) 4x(x-3y)2 d) (3x - [6+3x -…

A: Given that: (c)4x(x-3y)2 (d)(3x-[6+3x-(4x+1)+2])

Q: True or False. " The quotient of 0 and a negative number is undefined"

A: FALSE Since we know the property of 0 that when 0 is divided by any nonzero number then its value is…

Q: 6.) If x =3, what is the value of the following expression? 3x + 2

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Q: 4 (ii) 16 | at + 15.

A: Step-1 1)16|a4+15

Q: For all integers x and y, if 6x+y is odd, then x and y are both odd. True False

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Q: Write each of the following in the simplest form or as a√b, where a and b are integers, b>0, and b…

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Q: Express the following statement using N-notation.: 12.5 (3x + 4) for all real numbers x > 2. x + 2

A: In the given question the objective is to express the following statement using notation

Q: Evaluate or indicate that the root is not a real number √(25 - 16) ?

A: Given(25-16)

Q: Evaluate: 0 V|2 − r|+dr -2

A: In this question, the concept of Integration is applied. Integration Integration is a method of…

Q: Use the order of operations to find the value of the following expression. 52 -8 + 22 x4 - 1 .....

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Q: 11. Write each expression in power form axb for rational numbers a and b. 3V5 В. С. 3x4 4

A: B. 3s4=34s12

Q: Let matices

A: Given that, I=1001 ; A=100-1 ; B=-1001 ; C=-100-1 G = {I, A, B, C} Let the binary operation defined…

Q: Part 2) Directions: Consider the followin 4x2 + 8x +3 and 483 2x + 1 21 a. How are these expressions…

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Q: 18. Which of the following expressions is equivalent to (5x - 4y) (3x – 2y)? Select all that are…

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Q: 3. Simplify the following: a. 7-12| b. -|12-7| c. √25 d. √-25 e. -√25

A: Step 1:Step 2: Step 3: Step 4:

Q: the chosen letter on separate aheet of paper. Which of the following expressions correctly applies…

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Q: 1. ? Why or why not? Does x+14 simplify to 14 Choose the correct answer below. O A. No. The first…

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Q: True or false: If a is any integer, then (5a + 2,7a + 3) =1. Justify your answer.

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Q: 130. Explain why the given expressions cannot be simplifiod furiher. a 21+ 3y c. 2Vi + 3Vi

A: Function is the unique relation where each x is mapped to unique y. It can be of many type,…

Q: Evaluate or indicate that the root is not a real number √144 + √25 ?

A: To evaluate: 144+25

Q: The commutative property of addition allows us to simplify expressions by combining like terms.…

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Q: 1.If 10C0+11C1+12C2+...+15C5+16C6 = 17Ck+1 then k = _____.

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Q: 15. Which expression simplifies to 2v3 - 62 a. Vỹ + 8V24 – 3 V6 а. b. V18 – 4V12 –- 3 50 c. V12 +…

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