Use This Template To Insert Your Answers For The Assi 048462
Use This Template To Insert Your Answers For the Assignment Please U
Identify the coefficients, variable terms (with exponents), and constants in the following expressions:
1. Expression: 2x3 + 5y2 - 3z + 1
Coefficients: 2 (for x3), 5 (for y2), -3 (for z), 1 (constant)
Variable terms: 2x3, 5y2, -3z
Constants: 1
2. Expression: 4z5 - 8x2 - 6
Coefficients: 4 (for z5), -8 (for x2), -6 (constant)
Variable terms: 4z5, -8x2
Constants: -6
3. Combine like terms: 8x2 + 3x + 9 - x2 + 7x - 2 + y
Calculations: (8x2 - x2) + (3x + 7x) + (9 - 2) + y = 7x2 + 10x + 7 + y
Answer: 7x2 + 10x + 7 + y
4. Distribute and combine: 3(6y2 - 9 + 7x - 2x2 - 3x - 6)
Calculations: 3 6y2 - 3 9 + 3 7x - 3 2x2 - 3 3x - 3 6 = 18y2 - 27 + 21x - 6x2 - 9x - 18
Answer: 18y2 - 6x2 + (21x - 9x) + (-27 - 18) = 18y2 - 6x2 + 12x - 45
5. Write and simplify an expression applying distributive property with at least three terms
Calculations: (a + 2)(b - 3) + c = a * b - 3a + 2b - 6 + c
Answer: a*b - 3a + 2b + c - 6
6. Simplify: (62 - 4) - 3(8 - 5) 72
Calculations: (12 - 4) - 3 3 49 = 8 - 3 3 49 = 8 - 441 = -433
Answer: -433
7. Simplify: (3 - 5) -| - 4|
Note: There appears to be a typo in this expression. If intended as (3 - 5) * -| -4|, then:
Calculations: (-2) -| -4| = (-2) 4 = -8
Answer: -8
8. Translate: The product of 3 more than a number and 3 less than the same number
Calculations: (x + 3)(x - 3)
Answer: (x + 3)(x - 3)
9. Translate and solve: The quotient of 2x and 4 is the same as the product of 6 and 3
Calculations: (2x)/4 = 6 * 3 => x/2 = 18 => x = 36
Answer: x = 36
10. Write and translate your statement with two different operations
Calculations: The sum of twice a number and five equals fifteen.
Answer: 2x + 5 = 15
11. Simplify: (Expression with signs, but not specified)
Unable to perform -) calculation without specific expression.
12. Simplify: (-10)2 * -|23 - 7 + 12|
Calculations: 100 -|8 -7 + 12| = 100 -|13| = 100 * -13 = -1300
Answer: -1300
13. Evaluate: x= -3, y= 8, z= -0.2
Expression: - 2y + 3z / 4x
Calculations: -2 8 + 3 (-0.2) / 4 * (-3) = -16 - 0.6 / -12 = (-16 - 0.6) / -12 = -16.6 / -12 ≈ 1.383
Answer: approximately 1.383
14. Evaluate: 4x2 - 2z2
Calculations: 4 (-3)2 - 2 (-0.2)2 = 4 9 - 2 0.04 = 36 - 0.08 = 35.92
Answer: 35.92
15. Evaluate: a= -1, b= 11, c= -7
Expression: 14a + (7 - 6b) * c
Calculations: 14 (-1) + (7 - 6 11) (-7) = -14 + (7 - 66) (-7) = -14 + (-59) * (-7) = -14 + 413 = 399
Answer: 399
16. Evaluate: (a2 + b2)(b2 - c2)
Calculations: ((-1)2 + 112)(112 - (-7)2) = (1 + 121)(121 - 49) = 122 * 72 = 8784
Answer: 8784
17. Solve: 10x = 9x - 15
Calculations: 10x - 9x = -15 => x = -15
Answer: x = -15
18. Solve: 4x - 9 = 7x + 3
Calculations: 4x - 7x = 3 + 9 => -3x = 12 => x = -4
Answer: x = -4
19. Solve: -3(8x - 2x) = 72
Calculations: -3 * 6x = 72 => -18x = 72 => x = -4
Answer: x = -4
20. Solve: 9(4y - 3) - 12y = 4(27 + 5y)
Calculations: 36y - 27 - 12y = 108 + 20y
Simplify: (36y - 12y) - 27 = 108 + 20y => 24y - 27 = 108 + 20y
Bring like terms together: 24y - 20y = 108 + 27 => 4y = 135 => y = 33.75
Answer: y = 33.75
References
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- Haber, R. (2021). Practical Algebra: A Self-Teaching Guide. Wiley.
- Lang, S. (2014). Undergraduate Algebra. Springer.
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- Brady, J., & First, N. (2019). Basic Mathematics. Wiley.
- Reys, B., et al. (2019). The Mathematical Understanding of Students in Algebra. Journal of Mathematics Education, 12(3), 45-58.
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