Solve each equation by factoring or by using the quadratic

Question

1. Perform the indicated operations-

(a) 3(-2r² + 3r -1)-4(3r² + 4r - 2)

(b) (3k - 4)(2k + 1)           

2. Factor each polynomial-

(a) 3(x² - 8x +12)

(b) 9m² - 16

(c) 8m³ + 27

3. Solve each equation-

(a) -5x + 1 = 2x -3

(b) 2a + 2 - 5(a+2) = -4(2a - 1) +3a

4. Evaluate each expression-

(a) (2³ · 3²)³

(b) (27/64)^-(1/3)

(c) 4^-2 · 2⁴

(d) (9/16)^1/2

5. Simplify

(a) (x⁴ · x^-3)²

(b) [(x²)²]^1/4

(c) (w²w⁶)^-3/w³w⁴

6. Rational the denominator of each expression-

(a) 3/√5

(b)1/(2-√3)

7. Find the slope of the line determined by each pair of points-

(a) (-2, 1) and (-2, 3)

(b) (3, -4) and (2, 1)

(c) (0, 5) and (3, 0)

8. For each equation, find the slope m and y-intercept b and draw the graph-

(a) 4x + 2y = 12 

(b) 3x+9= -6y

(c)  y - 2= 1/3(x + 4)

9. Write an equation of the line in the form y = mx + b satisfying the following conditions-

(a)  Slope -1/2 and passing through the point (-2, 4)

(b)  Vertical and passing through the point (1/3, 2/3)

(c)  Passing through the points (3, 2) and (4, 3)

(d)  Perpendicular to the line defined by 2x +3y = 18 and passing through the point (-2, 3)

10. Graph each function below by finding the x and y intercepts-

(a) f(x) = -2x - 3

(b) f(x) = 2/3x + 2

11. Solve each equation by factoring or by using the Quadratic Formula-

(a) x² - 9x = -18

(b) 2x² + 3x -1 = 0

(c) 2y² - 24 = -8y

Answer 1

As given few questions which is based on mathematics. Give the solution of all question. 1. Execute the designated operations- (i) 3(-2r2 + 3r -1)-4(3r2 + 4r - 2) (ii) (3k - 4)(2k + 1) 2. Factor each polynomial- (i) 3(x2 - 8x +12) (ii) 9m2 - 16 (iii) 8m3 + 27 3. Explain each equation- (i) -5x + 1 = 2x -3 (ii) 2a + 2 - 5(a+2) = -4(2a - 1) +3a