Answer is A because the number line is going by 2
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.
Simplifying
5x(4y + 3x) = 5x(3x + 4y)
Reorder the terms:
5x(3x + 4y) = 5x(3x + 4y)
(3x * 5x + 4y * 5x) = 5x(3x + 4y)
Reorder the terms:
(20xy + 15x2) = 5x(3x + 4y)
(20xy + 15x2) = 5x(3x + 4y)
20xy + 15x2 = (3x * 5x + 4y * 5x)
Reorder the terms:
20xy + 15x2 = (20xy + 15x2)
20xy + 15x2 = (20xy + 15x2)
Add '-20xy' to each side of the equation.
20xy + -20xy + 15x2 = 20xy + -20xy + 15x2
Combine like terms: 20xy + -20xy = 0
0 + 15x2 = 20xy + -20xy + 15x2
15x2 = 20xy + -20xy + 15x2
Combine like terms: 20xy + -20xy = 0
15x2 = 0 + 15x2
15x2 = 15x2
Add '-15x2' to each side of the equation.
15x2 + -15x2 = 15x2 + -15x2
Combine like terms: 15x2 + -15x2 = 0
0 = 15x2 + -15x2
Combine like terms: 15x2 + -15x2 = 0
0 = 0
Solving
0 = 0
Couldn't find a variable to solve for.
This equation is an identity, all real numbers are solutions.
Using BIDMAS (Brackets, Indices, Division, Multiplication, Addition, Subtraction)
32/4 + 4x8
8+32
40
B. Do you see how there is a pi symbol next to 308, that means you don't have to multiply by pi so 967.61 but divided by