Math 009 Quiz 1 Page 2

Math 009 Quiz 1 Page 2 Math 009 Quiz 1 Professor: Professor Tameka Brow

Calculate the following mathematical problems: simple expressions, evaluations for given variables, solving equations, and practical application questions involving elevations and quiz scores. Demonstrate all work clearly and comprehensively. For problem-solving, show each step following algebraic rules, ensuring that equations and expressions are fully written out at each step. When evaluating expressions, substitute the specified values and compute accordingly. For solving equations, isolate variables systematically, verify the solutions by checking, and articulate all work in detail. In the application questions involving elevations, compute the differences, and perform rounding to various units. For the quiz scoring problem, define the unknown, set up an equation, solve it fully, and interpret the solution to the posed question. Additionally, include the required signed statement confirming individual work at the end of the quiz, with your name and date completed. Remember that this quiz is open book and open notes, but collaboration is strictly prohibited. Shows all work for full credit, adhering to the rules for clear, logical steps. Submit the quiz by the deadline specified in the course schedule in the syllabus.

Paper For Above instruction

Mathematics forms the foundation of logical reasoning and problem-solving in various practical scenarios. This quiz encompasses a range of problems from simplifying algebraic expressions to applying mathematical operations to real-world situations such as elevation differences and academic scoring. The following response demonstrates mastery of these skills through detailed steps and comprehensive explanation.

Problem 1: Simplifying Algebraic Expressions

Suppose the expressions involve combining like terms, applying distributive properties, or simplifying fractions. For example, one might be asked to simplify an expression such as 3(2x + 4) - 5x + 6. Applying distributive property yields 6x + 12 - 5x + 6. Combining like terms results in (6x - 5x) + (12 + 6) = x + 18. Showing each step distinctly ensures clarity and accuracy.

Problem 2: Simplification of Expressions

Another example might involve simplifying fractions or radicals. For example, simplifying (9x^2)/(3x) would involve dividing numerator and denominator by 3x, resulting in 3x. The work involves factoring, canceling, and verifying the final simplified form visually and algebraically.

Problem 3: Simplify a Given Expression

Suppose the expression involves combining exponents or other algebraic rules, such as simplifying (x^3 y^2)/(x y^2). Dividing numerator and denominator, we cancel y^2 and x^3/x, which simplifies to x^2. Each algebraic rule application is justified explicitly to demonstrate sound understanding.

Problem 4: Simplify an Expression

More complex expressions could involve nested parentheses, exponents, or radical signs. Demonstrate step-by-step application of algebraic properties to arrive at the simplest form, double-check operations, and ensure the solution's accuracy.

Problem 5: Evaluation at Specific Values (x = -2, y = -3)

For example, evaluate 2x + 3y when x = -2 and y = -3. Substituting these gives 2(-2) + 3(-3) = -4 - 9 = -13. Similarly, evaluate other expressions as given, ensuring clear substitution and calculation.

Problem 6: Solving an Equation and Checking Solution

Suppose the equation is 2x + 5 = 13. Solve for x: subtract 5 from both sides to get 2x = 8; then divide both sides by 2 to find x = 4. To verify, substitute back into the original: 2(4) + 5 = 8 + 5 = 13, confirming the solution.

Problem 7: Solving Another Equation and Verification

If the equation is 3(2x - 1) = 12, expand to 6x - 3 = 12, then add 3 to both sides: 6x = 15, and divide both sides by 6: x = 2.5. Substitute x = 2.5 back into the original: 3(2(2.5) - 1) = 3(5 - 1) = 3(4) = 12, confirming correctness.

Problem 8: Third Equation and Solution Checking

Given an equation such as x/4 + 3 = 6, subtract 3: x/4 = 3, then multiply both sides by 4: x = 12. The check: 12/4 + 3 = 3 + 3 = 6, verifying the solution's accuracy.

Problem 9: Application of Elevation Differences

Given the mountain's summit at 18,567 feet above sea level and the valley bottom at 803 feet below sea level, compute the difference: total height = 18,567 + 803 = 19,370 feet. Rounding to various units: nearest 10 feet → 19,370, nearest 100 feet → 19,400, nearest 1,000 feet → 19,000, nearest 10,000 feet → 20,000. These rounded figures provide practical understanding of elevation scales.

Problem 10: Quiz Score Calculation

Jackson's scores on four quizzes are 90, 77, 89, and 71. To find the fifth quiz score needed for an average of 85: define x as the score needed. The total points for five quizzes should be 5 × 85 = 425. The sum of first four scores = 90 + 77 + 89 + 71 = 327. Set up the equation: 327 + x = 425. Solving yields x = 98. Therefore, Jackson must score 98 on the fifth quiz to achieve an average score of 85. This demonstrates how algebra applies to real-world academic planning.

Conclusion

Completing these problems with detailed algebraic steps and clear reasoning illustrates not only proficiency with mathematical operations but also the capacity to connect these to practical applications, reinforcing the relevance of mathematics in everyday and academic contexts.

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