Math Problem Statement
Solution
I see you've uploaded an image containing a set of math problems. I'll help you by addressing the solutions to these questions.
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Question 4: The decimal representation of is a non-terminating non-recurring decimal.
Answer: (c) -
Question 5: The coefficient of in .
Expanding gives terms where the coefficient of is 12.
Answer: (c) -
Question 6: The zero of the polynomial is found by solving .
Solving gives .
Answer: (b) -
Question 7: Solving gives . Which of Euclid's axioms is used to solve it?
This uses the axiom: If equals are subtracted from equals, the remainders are equal.
Answer: (d) -
Question 8: The point that lies on the line representing .
Substituting each option in , only (2, 6) satisfies the equation.
Answer: (a) -
Question 9: The distance between points A (4, 0) and B (0, 3) is given by the distance formula:
Answer: (a) -
Question 10: "A terminated line can be produced indefinitely" is a postulate.
Answer: (d) -
Question 11: If the measure of an angle is 5 times its complement, let the angle be and its complement be .
Solving this gives .
Answer: (d) -
Question 12: In the given figure, if , the angle can be found using the parallel line properties. The answer is 75°.
Answer: (d)
Would you like more detailed solutions or explanations? Here are 5 questions for further practice:
- How do you expand and simplify binomial expressions?
- What is the method for solving polynomials for their zeros?
- How do you determine the distance between two points in a coordinate plane?
- What are Euclid's five axioms in geometry?
- How do complementary angles work in geometry?
Tip: Always verify results by substituting your solution back into the original equation, especially when solving polynomials or algebraic equations!
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Math Problem Analysis
Mathematical Concepts
Decimal Representation
Algebraic Equations
Polynomials
Euclidean Geometry
Distance Formula
Angles and Complementary Angles
Formulas
Distance formula: d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Complementary angles: x + y = 90°
Theorems
Euclid's Axioms
Postulates on Lines
Properties of Parallel Lines
Suitable Grade Level
Grades 8-10
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