1 Find the integers between which sqrt(33) lies. 1.2 Convert the recurring decimal 0.45 to a common fraction. 2.1 Simplify ((3x)2 (-2xy)1)/(2x3 y4).

Hey 🥹❤️‍🔥M💞🥹Miseketeri, good to see you again. Question 1 1.1 To find the integers between which sqrt(33) lies, we find the perfect squares closest to 33. 5^2 = 25 6^2 = 36 Since 25 < 33 < 36, we can take the square root of all parts: sqrt(25) < sqrt(33) < sqrt(36) 5 < sqrt(33) < 6 The value of sqrt(33) lies between the integers 5 and 6. The integers are 5 and 6. 1.2 Let x = 0.45. This means x = 0.4555... Step 1: Multiply by 10 to move the non-repeating part to the left of the decimal. 10x = 4.555... (1) Step 2: Multiply by 100 to move one full repeating block to the left of the decimal. 100x = 45.555... (2) Step 3: Subtract equation (1) from equation (2). 100x - 10x = 45.555... - 4.555... 90x = 41 Step 4: Solve for x. x = (41)/(90) The common fraction in its simplest form is (41)/(90). Question 2 2.1 Simplify: ((3x)^2 (-2xy)^1)/(2x^3 y^4) Step 1: Expand the terms in the numerator. ((3^2 x^2) (-2xy))/(2x^3 y^4) (9x^2 (-2xy))/(2x^3 y^4) Step 2: Multiply the terms in the numerator. -18x^2+1y2x^3 y^4 (-18x^3y)/(2x^3 y^4) Step 3: Simplify the coefficients and variables. (-18)/(2) · (x^3)/(x^3) · (y)/(y^4) -9 · x^3-3 · y^1-4 -9 · x^0 · y^-3 -9 · 1 · (1)/(y^3) -(9)/(y^3) The simplified expression is -(9)/(y^3). 2.2.1 Factorise completely: 6p + 40 - p^2 Step 1: Rearrange the terms in standard quadratic form. -p^2 + 6p + 40 Step 2: Factor out -1. -(p^2 - 6p - 40) Step 3: Factor the quadratic expression p^2 - 6p - 40. We need two numbers that multiply to -40 and add to -6. These numbers are -10 and 4. -(p-10)(p+4) Alternatively, distribute the negative sign into one of the factors: (10-p)(p+4) The factorised expression is (10-p)(p+4). 2.2.2 Factorise completely: -xy - (y-x)b + b^2 Step 1: Distribute the negative sign and b in the middle term. -xy - yb + xb + b^2 Step 2: Group terms with common factors. (-xy - yb) + (xb + b^2) Step 3: Factor out common terms from each group. -y(x+b) + b(x+b) Step 4: Factor out the common binomial (x+b). (x+b)(-y+b) (x+b)(b-y) The factorised expression is (x+b)(b-y). Question 3 3.1 Solve for x: (x+2)/(x^2-3x-4) = (3)/(x-4) - (1)/(2+2x) Step 1: Factor the denominators. x^2-3x-4 = (x-4)(x+1) 2+2x = 2(1+x) The equation becomes: (x+2)/((x-4)(x+1)) = (3)/(x-4) - (1)/(2(x+1)) Step 2: Identify restrictions on x. The denominators cannot be zero, so x ≠ 4 and x ≠ -1. Step 3: Find the Lowest Common Denominator (LCD), which is 2(x-4)(x+1). Step 4: Multiply every term by the LCD. 2(x-4)(x+1) · (x+2)/((x-4)(x+1)) = 2(x-4)(x+1) · (3)/(x-4) - 2(x-4)(x+1) · (1)/(2(x+1)) Step 5: Simplify and solve for x. 2(x+2) = 2 · 3 · (x+1) - (x-4) · 1 2x+4 = 6(x+1) - (x-4) 2x+4 = 6x+6 - x+4 2x+4 = 5x+10 4-10 = 5x-2x -6 = 3x x = (-6)/(3) x =