Explanation: An equation is a statement that two expressions are equal, containing an equals sign. x=2 is an equation. x²+xy-y is an expression, not an equation. 3x-4=20y^2 is an equation. 13y=y+1 is an equation. x/5=9 is an equation. Therefore, the equations are A, C, D, and E.

Explanation: The expression has three terms: 5x², 2x, and -2. The term -2 is a constant. Option A is incorrect because there are three terms and one is a constant. Option B is wrong as there are three terms. Option D is incorrect because not all terms are constants; 5x² and 2x are variable terms.

Explanation: Coefficients are the numerical factors of the terms. For 12x³, the coefficient is 12; for 7x², it is 7; for 24x, it is 24. So the coefficients are 12, 7, and 24. Option A lists digits from the exponents. Option B misses 24. Option D includes digits that are not coefficients.

Explanation: To find the sum of the lengths of the sides of the polygon, we first identify the given side lengths: AB = 10- 2x, BC = x+3, CD=4x-5, DE = 6x-7, EF = 62-5, and FA = 42 +2. Next, we add these expressions together: (10-2)+(x+3)+(4x-5)+(6x-7)+(6x-5)+(4x+2). Combining like terms, we group all coefficients of a and constant values: (-2x+x+4x+6x+6x+ 4x)+(10+3-5-7-5+2). Simplifying further, the coefficient of adds up to 192, while the constants simplify to -2. Therefore, the total sum of the lengths of all the sides of the polygon is 19 - 2. This expression represents the perimeter of the polygon in terms of 2.

Explanation: The figure shows a number line with shading to the left of 4, indicating that the solution set includes all values of x less than 4 but not equal to 4, as shown by the open circle. To determine which inequality matches this, we test the options. Starting with 3x−1<2x+3, subtract 2x from both sides to get x−1<3. Adding 1 to both sides yields x<4, which exactly matches the shaded region in the figure. The open circle confirms that 4 is not included in the solution set, meaning the inequality is strict (≤). Therefore, the inequality represented by the figure is 3x−1<2x+3, which corresponds to the third option in the list.