Math Problem Statement

Evaluate each expression using the given values. (Image provided contains 12 algebraic expressions with variables assigned specific values.)

Solution

I see the math worksheet you uploaded. Let's solve the expressions based on the given values for each problem.

1) n2mn^2 - m; use m=7m = 7, and n=8n = 8

n2m=827=647=57n^2 - m = 8^2 - 7 = 64 - 7 = 57

2) 8(xy)8(x - y); use x=5x = 5, and y=2y = 2

8(xy)=8(52)=8(3)=248(x - y) = 8(5 - 2) = 8(3) = 24

3) yx÷2yx \div 2; use x=7x = 7, and y=2y = 2

yx÷2=(2×7)÷2=14÷2=7yx \div 2 = (2 \times 7) \div 2 = 14 \div 2 = 7

4) mn÷4m - n \div 4; use m=5m = 5, and n=8n = 8

mn÷4=5(8÷4)=52=3m - n \div 4 = 5 - (8 \div 4) = 5 - 2 = 3

5) xy+6x - y + 6; use x=6x = 6, and y=1y = 1

xy+6=61+6=11x - y + 6 = 6 - 1 + 6 = 11

6) z+3x2z + 3x^2; use x=1x = 1, and z=19z = 19

z+3x2=19+3(12)=19+3(1)=19+3=22z + 3x^2 = 19 + 3(1^2) = 19 + 3(1) = 19 + 3 = 22

7) y+yxy + yx; use x=15x = 15, and y=8y = 8

y+yx=8+(8×15)=8+120=128y + yx = 8 + (8 \times 15) = 8 + 120 = 128

8) q÷6+pq \div 6 + p; use p=10p = 10, and q=12q = 12

q÷6+p=(12÷6)+10=2+10=12q \div 6 + p = (12 \div 6) + 10 = 2 + 10 = 12

9) x+8yx + 8 - y; use x=20x = 20, and y=17y = 17

x+8y=20+817=2817=11x + 8 - y = 20 + 8 - 17 = 28 - 17 = 11

10) 15(m+p)15 - (m + p); use m=3m = 3, and p=10p = 10

15(m+p)=15(3+10)=1513=215 - (m + p) = 15 - (3 + 10) = 15 - 13 = 2

11) 10x+y+210 - x + y + 2; use x=5x = 5, and y=2y = 2

10x+y+2=105+2+2=7+2+2=1110 - x + y + 2 = 10 - 5 + 2 + 2 = 7 + 2 + 2 = 11

12) p2+qpp - 2 + qp; use p=7p = 7, and q=4q = 4

p2+qp=72+(4×7)=5+28=33p - 2 + qp = 7 - 2 + (4 \times 7) = 5 + 28 = 33


Let me know if you'd like more details on any of these solutions!

Five relative questions:

  1. What happens to the value of an expression if the variables are negative?
  2. Can you explain how to handle parentheses in expressions?
  3. How do powers (exponents) affect the result in an expression?
  4. What is the order of operations when multiple operations are in the same expression?
  5. How can you solve an expression with a fraction or division involved?

Tip:

Always remember to follow the order of operations: PEMDAS (Parentheses, Exponents, Multiplication/Division (left to right), Addition/Subtraction (left to right)).

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Math Problem Analysis

Mathematical Concepts

Algebra
Basic Arithmetic Operations
Exponents
Order of Operations

Formulas

Basic arithmetic operations (addition, subtraction, multiplication, division)
Exponentiation formula
Order of operations (PEMDAS)

Theorems

Distributive Property
Order of Operations

Suitable Grade Level

Grades 6-8