Given 4k + 3r2 = 10, make r2 the subject of the formula. Also, for functions f(x) = (2x-7)/3 and g(x) = x - 2/3, find f(1/2) and solve x when f(x) = g(x). Lastly, solve x2 + x = 132.

Here's the solution for the questions in the image. Question (d) Step 1: Start with the given equation. 4k + 3r^2 = 10 Step 2: Subtract 4k from both sides to isolate the term with r^2. 3r^2 = 10 - 4k Step 3: Divide both sides by 3 to make r^2 the subject. r^2 = (10 - 4k)/(3) r^2 = (10 - 4k)/(3) Question 8 (a) (i) Step 1: Substitute x = (1)/(2) into the function f(x) = (2x-7)/(3). f((1)/(2)) = (2(1)/(2)) - 73 Step 2: Simplify the numerator. f((1)/(2)) = (1 - 7)/(3) f((1)/(2)) = (-6)/(3) Step 3: Perform the division. f((1)/(2)) = -2 -2 Question 8 (a) (ii) Step 1: Set f(x) equal to g(x). (2x-7)/(3) = x - (2)/(3) Step 2: Multiply the entire equation by 3 to eliminate the denominators. 3 · ((2x-7)/(3)) = 3 · (x - (2)/(3)) 2x - 7 = 3x - 2 Step 3: Rearrange the equation to solve for x. Subtract 2x from both sides. -7 = 3x - 2x - 2 -7 = x - 2 Step 4: Add 2 to both sides. -7 + 2 = x x = -5 x = -5 Question 8 (b) Step 1: Rearrange the quadratic equation into standard form ax^2 + bx + c = 0. x^2 + x = 132 x^2 + x - 132 = 0 Step 2: Factor the quadratic expression. We need two numbers that multiply to -132 and add to 1. These numbers are 12 and -11. (x + 12)(x - 11) = 0 Step 3: Set each factor equal to zero and solve for x. x + 12 = 0 or x - 11 = 0 x = -12 or x = 11 x = -12 or x = 11 3 done, 2 left today. You're making progress.