Math Problem Statement

The image contains a set of mathematical problems involving various topics such as arithmetic operations, factorization, functions, and geometry.

Solution

The image contains a set of mathematical problems involving various topics such as arithmetic operations, factorization, functions, and geometry. Here is a breakdown of the problems:

1. Izračunaj (Calculate):

  • a) Two expressions with fractions and basic arithmetic.
  • b) A product involving a set of brackets with fractions and decimals.

2. Zapiši u obliku potencije s bazom 3 sljedeće brojeve (Write the following numbers as powers with base 3):

  • a) 632936 \cdot 3^2 \cdot 9^3
  • b) 294+15311+22742 \cdot 9^4 + 15 - 3^{11} + 2 \cdot 27^4

3. Provedi kvadriranje (Perform squaring):

  • a) (8a+3)2(8a + 3)^2
  • b) (815b512)2\left(\frac{8}{15} b - \frac{5}{12}\right)^2

4. Rastavi na faktore sljedeće višelčane izraze (Factorize the following expressions):

  • a) 2a1(3a+2)+2a1(2a+3)2a - 1(3a + 2) + 2a - 1(2a + 3)
  • b) Complex factorization with multiple variables aa, bb, cc, xx, etc.

5. Izračunaj (Calculate):

  • a) Two fractions added and simplified.
  • b) More fraction operations involving aa, bb, and constants.

6. Nacrataj graf linearne funkcije (Draw the graph of the linear function):

  • A function is provided, and the task is to graph it and calculate the slope.

7. Sustav jednadžbi riješi uvođenjem novih nepoznanica (Solve the system of equations by introducing new unknowns):

  • A system of three linear equations is given.

8. Duljine stranica trokuta (Lengths of triangle sides):

  • Problems involving the calculation of triangle side lengths, including special cases like right triangles and using trigonometry (sine).

9. Duljina druge katete (Length of the second leg of a right triangle):

  • Given one leg and the hypotenuse, calculate the other leg.

10. Odredi koordinatu četvrtog vrha paralelograma (Determine the coordinate of the fourth vertex of the parallelogram):

  • Given three coordinates, find the fourth vertex.

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Math Problem Analysis

Mathematical Concepts

Arithmetic Operations
Algebraic Factorization
Linear Functions
Geometry
Trigonometry
System of Equations

Formulas

Quadratic Formula
Factorization Formulas
Slope of a Line: m = (y2 - y1) / (x2 - x1)
Pythagorean Theorem: a^2 + b^2 = c^2
Trigonometric Ratios

Theorems

Pythagorean Theorem
Basic Principles of Linear Functions
Trigonometric Ratios for Right Triangles

Suitable Grade Level

Grades 9-12