Quadratic functions ! questions attached below

Q 30) x = -3 or x = 12.

Q 31) x = 1 or x = 2.

Q 32) x = -1/2 or x = 8.

Q 33) x = 2/5 or x = 3.

Q 34) x = 1.80424764151 or x = -0.5542476415.

Q 35) x = 1.5 or x = -1/3.

Step-by-step explanation:

Q 30)

x^2 - 9x - 36 = 0.

Solving by factoring:

Multiplying 1 and 36 yields 36. The factors whose difference results in 9 are 12 and 3. Therefore:

x^2 - 12x + 3x - 36 = 0.

x(x - 12) + 3(x - 12) = 0.

(x + 3)(x - 12) = 0.

Either x + 3 = 0 or x - 12 = 0.

Therefore, x = -3 or x = 12.

Q 31)

x^2 - 3x + 2 = 0.

Solving by factoring:

Multiplying 1 and 2 yields 2. The factors whose sum results in 3 are 2 and 1. Therefore:

x^2 - 2x - x + 2 = 0.

x(x - 2) - 1(x - 2) = 0.

(x - 1)(x - 2) = 0.

Either x - 1 = 0 or x - 2 = 0.

Therefore, x = 1 or x = 2.

Q 32)

2x^2 - 15x - 8 = 0.

Solving by factoring:

Multiplying 2 and 8 yields 16. The factors whose difference results in 15 are 16 and 1. Therefore:

2x^2 - 16x + x - 8 = 0.

2x(x - 8) + 1(x - 8) = 0.

(2x + 1)(x - 8) = 0.

Either 2x + 1 = 0 or x - 8 = 0.

Therefore, x = -1/2 or x = 8.

Q 33)

5x^2 - 17x + 6 = 0.

Solving by factoring:

Multiplying 5 and 6 yields 30. The factors whose sum results in 17 are 15 and 2. Therefore:

5x^2 - 15x - 2x + 6 = 0.

5x(x - 3) - 2(x - 3) = 0.

(5x - 2)(x - 3) = 0.

Either 5x - 2 = 0 or x - 3 = 0.

Therefore, x = 2/5 or x = 3.

Q 34)

4x^2 - 5x - 4 = 0.

Solving by completing the square:

4x^2 - 5x = 4.

x^2 - 5x/4 = 1.

(x)^2 - 2*(x)*(5/8) + (5/8)^2 = 1 + (5/8)^2.

(x - 5/8)^2 = 1 + 25/64.

(x - 5/8)^2 = 89/64.

x - 5/8 = ±1.17924764151.

x - 5/8 = 1.17924764151 or x - 5/8 = -1.17924764151.

Therefore, x = 1.80424764151 or x = -0.5542476415.

Q 35)

6x^2 - 7x - 3 = 0.

Solving by quadratic formula:

x = (-b ± √(b^2 - 4ac))/2a.

a = 6, b = -7, and c = -3.

x = (-(-7) ± √((-7)^2 - 4*(6)*(-3)))/2(6).

x = (7 ± √(49 + 72))/12.

x = (7 ± √(121))/12.

x = (7 ± 11)/12.

x = (7 + 11)/12 or x = (7 - 11)/12.

x = 18/12 or x = -4/12.

Therefore, x = 1.5 or x = -1/3.

In summary:

Q 30) x = -3 or x = 12!!!

Q 31) x = 1 or x = 2!!!

Q 32) x = -1/2 or x = 8!!!

Q 33) x = 2/5 or x = 3!!!

Q 34) x = 1.80424764151 or x = -0.5542476415!!!

Q 35) x = 1.5 or x = -1/3!!!

vertical=18cm horizontal=18cm hypotenuse=25.5

step-by-step explanation:

55.44 inches

step-by-step explanation:

part a. assuming a perfectly linear relationship, we can find the slope from the first two data points.

slope = m = (change in rainfall)/(change in years)

= (61.80 -62.33)/(2005 -2004) = -0.53/1 = -0.53

then the point-slope form of the equation of the line can be written as

y = m(x -h) +k . . . . . m = -0.53, (h, k) = (0, 62.33)

y = -0.53x +62.33 . . . x = years after 2004

part b. in 2017, x = 2017 -2004 = 13. then the predicted rainfall is

y = -0.53·13 +62.33 = 55.44 . . inches

the predicted rainfall in 2017 is 55.44 in.