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:
b = √(c^2 - a²)
Step-by-step explanation:
Start with the given c = √a^2 + b^2. Squaring both sides, we get:
c² = a² + b².
We want to iosolate b² and then b.
So: subtract a² from both sides, resulting in:
c² - a² = b²
Taking the square root of both sides, we get:
√b² = √(c² - a²)
and so:
b = √(c^2 - a²)
Answer:
c = 2
Step-by-step explanation:
6c + 3y = 18
6c + 3(2) = 18
6c + 6 = 18
6c = 12
c = 2
Believe it’s 15° B is correct
