Math Problem Statement

Various math questions on topics such as decimal representation, coefficients, polynomials, Euclidean axioms, distance between points, and complementary angles.

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.

  1. Question 4: The decimal representation of 5+25 + \sqrt{2} is a non-terminating non-recurring decimal.
    Answer: (c)

  2. Question 5: The coefficient of x2x^2 in (x2+2)3(x^2 + 2)^3.
    Expanding (x2+2)3(x^2 + 2)^3 gives terms where the coefficient of x2x^2 is 12.
    Answer: (c)

  3. Question 6: The zero of the polynomial 7+3x7 + 3x is found by solving 7+3x=07 + 3x = 0.
    Solving gives x=73x = -\frac{7}{3}.
    Answer: (b)

  4. Question 7: Solving x15=25x - 15 = 25 gives x=40x = 40. 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)

  5. Question 8: The point that lies on the line representing y=3xy = 3x.
    Substituting each option in y=3xy = 3x, only (2, 6) satisfies the equation.
    Answer: (a)

  6. Question 9: The distance between points A (4, 0) and B (0, 3) is given by the distance formula:
    d=(40)2+(03)2=16+9=25=5d = \sqrt{(4-0)^2 + (0-3)^2} = \sqrt{16 + 9} = \sqrt{25} = 5
    Answer: (a)

  7. Question 10: "A terminated line can be produced indefinitely" is a postulate.
    Answer: (d)

  8. Question 11: If the measure of an angle is 5 times its complement, let the angle be xx and its complement be 90x90^\circ - x.
    x=5(90x)x = 5(90^\circ - x)
    Solving this gives x=75x = 75^\circ.
    Answer: (d)

  9. Question 12: In the given figure, if ABDEAB \parallel DE, the angle xx 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:

  1. How do you expand and simplify binomial expressions?
  2. What is the method for solving polynomials for their zeros?
  3. How do you determine the distance between two points in a coordinate plane?
  4. What are Euclid's five axioms in geometry?
  5. 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