Determine if each equation will have 0, 1, or 2 solutions. Equation A: x(x−3)=0 This equation has solutions because... Equation B: x2=−81 This equation has solutions because... Equation C: (x−1)(x−1)=0 This equation has solutions because...

See below

Step-by-step explanation:

Given the expression

x(x-3) = 0

This can be written as x = 0 and x - 3 = 0

x = 0 and x = 0+3

x = 0 and x = 3

Hence the equation has 2 solutions since it is a quadratic equation

B) Given x^2 = -81

Take the square root of both sides

√x² = ±√-81

x =±√-81

Note that √-1 = i

x = ±9i

x = 9i and -9i

Hence this equation has 2 solutions because of its quadratic nature

C) (x−1)(x−1)=0

x - 1 = 0 and x = 1 = 0

x = 1 twice

Hence this equation has 1 solution because of its repitition of root

(sin 42)/31. = sinx)/37

sinx = 37 (sin42)/31

= 37× 0.66/31 = 0.787

x= 51.9

other angle opposite to y = 180-51.9-42

= 180- 93.9 =86.1

so

sin42)/31 = sin 86.1)/y

0.021 = 0.997 /y

y= 0.997/0.021 =47.47