Answer:
11 ; 13
Step-by-step explanation:
Let the numbers be :
x and x + 2
x * (x + 2) = 6(x + x + 2) - 1
x² + 2x = 6(2x + 2) - 1
x² + 2x = 12x + 12 - 1
x² + 2x = 12x + 11
x² + 2x - 12x - 11 = 0
x² - 10x + 11 = 0
x² - 11x + x + 11 = 0
x(x - 11) + 1(x - 11) = 0
(x - 11) = 0 or (x + 1) = 0
x = 11 or x = - 1
X cannot be negative
x = 11
x + 2 = 11 +2 = 13
If x is a real number such that x3 + 4x = 0 then x is 0”.Let q: x is a real number such that x3 + 4x = 0 r: x is 0.i To show that statement p is true we assume that q is true and then show that r is true.Therefore let statement q be true.∴ x2 + 4x = 0 x x2 + 4 = 0⇒ x = 0 or x2+ 4 = 0However since x is real it is 0.Thus statement r is true.Therefore the given statement is true.ii To show statement p to be true by contradiction we assume that p is not true.Let x be a real number such that x3 + 4x = 0 and let x is not 0.Therefore x3 + 4x = 0 x x2+ 4 = 0 x = 0 or x2 + 4 = 0 x = 0 orx2 = – 4However x is real. Therefore x = 0 which is a contradiction since we have assumed that x is not 0.Thus the given statement p is true.iii To prove statement p to be true by contrapositive method we assume that r is false and prove that q must be false.Here r is false implies that it is required to consider the negation of statement r.This obtains the following statement.∼r: x is not 0.It can be seen that x2 + 4 will always be positive.x ≠ 0 implies that the product of any positive real number with x is not zero.Let us consider the product of x with x2 + 4.∴ x x2 + 4 ≠ 0⇒ x3 + 4x ≠ 0This shows that statement q is not true.Thus it has been proved that∼r ⇒∼qTherefore the given statement p is true.
15*1.04=15.6
Her new hourly wage will be $15.60
