A) I would make the positive integer x and then form an equation.
x + 30 = x^2 - 12
x + 42 = x^2
0 = x^2 - x - 42 this can be factorised
(x - 7) ( x + 6) Therefore x = 7 or x = -6
Since the question asks for a positive integer the answer is 7.
B) two positive numbers x and y.
X - y = 3
x^2 + y^2 = 117
Use these simultaneous equations to figure out each number.
Rearrange the first equation
x = y + 3
Then substitute it into the second equation.
(y+3)^2 + y^2 = 117
y^2 + 6y + 9 + y^2 = 117
2y^2 + 6y - 108 = 0
then factorise this.
(2y - 12) (y + 9)
This means that y = 6 or y = -9 but it’s 6 because that’s the only positive number.
Use y to find x
x = y + 3
x = 6 + 3
x = 9
So the answers are x = 9 and y = 6.
Answer:
State income tax: 
Step-by-step explanation:
Based on the interface, it seems like you have chosen lawyer as a career with the given salary of $115,820.
The chart given for state income tax is broken into two categories:
$21,400-$80,650 => 6.45%
$80,651-$215,400 => 6.65%
Since the chosen career's salary is $115,820, the career falls into the second range of 6.65% state income tax.
The deduction is simply the amount of money taxed. For a 6.65% state income tax, the deduction can be found from:
Answer3:
Step-by-step explanation:
I do not know
