A) one of the roots of the equation 10x^2−33x+c=0 is 5.3. find the other root and the coefficient c.
b)the difference between the roots of the quadratic equation x^2−12x+q=0 is 2. find q.
c)the difference between the roots of the quadratic equation x^2+x+c=0 is 6. find c.

a) The other root is -2

   The coefficient c = -106

b) q = 35

c) c = -8.75

Step-by-step explanation:

* Lets study the general form of the quadratic equation

* ax² + bx + c = 0

- Their roots are x1 and and x2

- The sum of them = -b/a ⇒ x1 + x2 = -b/a

- The product of them = c/a ⇒ (x1)(x2) = c/a

a) * Assume that the roots of the equation 10x² - 33x + c = 0

     are m and n

∵ m + n = -b/a

∵ a = 10 and b = -33

∴ m + n = -(-33)/10 = 3.3

∵ m = 5.3

∴ 5.3 + n = 3.3 ⇒ n = 3.3 - 5.5 = -2

∴ n = -2

* The other root is -2

∵ m × n = c/a

∵ m = 5.3 , n = -2 , a = 10

∴ (5.3)(-2) = c/10

∴ -10.6 = c/10 ⇒ Multiply both sides by 10

∴ c = -106

* The coefficient c = -106

b) * Assume that the roots of the equation x² - 12x + q = 0

     are m and n

∵ The difference between the roots is 2

∴ m - n = 2 ⇒ (1)

∵ From the equation m + n = -b/a

∵ a = 1 , b = -12

∴ m + n = -(-12)/1 = 12

∴ m + n = 12 ⇒ (2)

* Lets solve the two equation

- Add the two equation to eliminate n

∴ 2m = 14 ⇒ divide both sides by 2

∴ m = 7

* Substitute the value of m in (1) or (2)

∴ 7 - n = 2 ⇒ 7 - 2 = n ⇒ 5 = n

∴ n = 5

∵ mn = c/a

∵ c = q , a = 1

∴ mn = q/1 = q

∴ q = 7 × 5 = 35

* q = 35

c) * Assume that the roots of the equation x² + x + c = 0

     are m and n

∵ The difference between the roots is 6

∴ m - n = 6 ⇒ (1)

∵ From the equation m + n = -b/a

∵ a = 1 , b = 1

∴ m + n = -(1)/1 = -1

∴ m + n = -1 ⇒ (2)

* Lets solve the two equation

- Add the two equation to eliminate n

∴ 2m = 5 ⇒ divide both sides by 2

∴ m = 2.5

* Substitute the value of m in (1) or (2)

∴ 2.5 + n = -1 ⇒ n = -1 - 2.5 = -3.5

∴ n = -3.5

∵ mn = c/a

∵ c = c , a = 1

∴ mn = c/1 = c

∴ c = 2.5 × (-3.5) = -8.75

* c = -8.75

a. 74 degrees

step-by-step explanation:

because the lines through the side and the box in the corners shows that these are congruent triangles and since they are mirrored the 37 degrees is also mirrored so the answer is 37 * 2 which is 74.