This English question involves literary analysis, grammar, or writing skills. The detailed response below provides a well-structured answer with supporting evidence and clear explanations.
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Here are the solutions to the remaining questions in English: 6) Given that y = 2x^2 - 3x + 1. Find the value of y when x = -2. Step 1: Substitute x = -2 into the given equation. y = 2(-2)^2 - 3(-2) + 1 Step 2: Perform the calculations following the order of operations (PEMDAS/BODMAS). y = 2(4) - (-6) + 1 y = 8 + 6 + 1 y = 15 The value of y when x = -2 is 15. 7) Solve the equation 3(x - 2) = 12. Step 1: Distribute the 3 on the left side of the equation. 3x - 6 = 12 Step 2: Add 6 to both sides of the equation to isolate the term with x. 3x = 12 + 6 3x = 18 Step 3: Divide both sides by 3 to solve for x. x = (18)/(3) x = 6 The solution to the equation is x = 6. 8) A bag contains 5 red balls, 3 blue balls, and 2 green balls. A ball is picked at random from the bag. Find the probability that the ball picked is: a) Red b) Not green Step 1: Calculate the total number of balls in the bag. Total number of balls = 5 (red) + 3 (blue) + 2 (green) = 10 balls. a) Red Step 2: Determine the number of red balls. Number of red balls = 5. Step 3: Calculate the probability of picking a red ball. P(Red) = Number of red ballsTotal number of balls P(Red) = (5)/(10) = (1)/(2) The probability of picking a red ball is (1)/(2). b) Not green Step 2: Determine the number of balls that are not green. Number of not green balls = Total number of balls - Number of green balls = 10 - 2 = 8. Step 3: Calculate the probability of picking a ball that is not green. P(Not green) = Number of not green ballsTotal number of balls P(Not green) = (8)/(10) = (4)/(5) The probability of picking a ball that is not green is (4)/(5). 9) Simplify (x^2 - 4)/(x + 2). Step 1: Factor the numerator using the difference of squares formula, a^2 - b^2 = (a - b)(a + b). Here, x^2 - 4 = x^2 - 2^2 = (x - 2)(x + 2). Step 2: Substitute the factored form into the expression. ((x - 2)(x + 2))/(x + 2) Step 3: Cancel out the common factor (x + 2) from the numerator and the denominator (assuming x ≠ -2). x - 2 The simplified expression is x - 2. 10) Find the equation of a straight line passing through the points (1, 2) and (3, 8). Step 1: Calculate the slope (m) of the line using the formula m = (y_2 - y_1)/(x_2 - x_1). Let (x_1, y_1) = (1, 2) and (x_2, y_2) = (3, 8). m = (8 - 2)/(3 - 1) m = (6)/(2) m = 3 Step 2: Use the point-slope form of a linear equation, y - y_1 = m(x - x_1). Using the point (1, 2) and the calculated slope m = 3: y - 2 = 3(x - 1) Step 3: Convert the equation to the slope-intercept form, y = mx + c, by simplifying. y - 2 = 3x - 3 y = 3x - 3 + 2 y = 3x - 1 The equation of the straight line is y = 3x - 1. 5 done, 5 left today. You're making progress.