Answer: Irrational
I'm going to write 'x' in place of "square root of 2" just to save time. Let's consider the possibility that 7-x is rational. I'm going to show there's a contradiction which ultimately concludes that the expression is irrational.
If 7-x was rational, then 7-x = p/q for some integers p,q with q being nonzero. Solve for x to get
7-x = p/q
-x = (pq) - 7
x = -(p/q) + 7
x = 7 - (p/q)
x = (7q/q) - (p/q)
x = (7q-p)/q
So if 7-x were rational, then this forces x to be rational because 7q-p is an integer over q (also an integer). The format is rational = integer/integer. But this is where the contradiction lies. Remember that x is standing in place for "square root of 2", which is an irrational number. There is no way to write sqrt(2) as a ratio of two integers. So x cannot be both rational and irrational at the same time.
Therefore, 7-x must be irrational making 7-sqrt(2) to be irrational as well.
note: sqrt is shorthand for "square root"
another note: adding any rational number to an irrational number will always result in an irrational number.
Answer:
The relationship between a distance in yards (y) and the same distance in miles (m) is described by the equation y = 1760m.
Step-by-step explanation:
Supplementary angles mean that two angles equal to 180°.
Let us assume the 2 angles are angle A and angle B.
Angle A is 4 times bigger than Angle B, the supplement.
Let Angle B be represented by x.
Angle A is 4x ; Angle B is x.
4x + x = 180°
5x = 180°
x = 180°/5
x = 36° This is the measure of angle B.
4x = 4(36°) = 144° This is the measure of angle A.
4x + x = 180°
144° + 36° = 180°
180° = 180°
18
you just multiply 6 by 3 because 4 is being multiplied by 3 as well to get $12
Answer:
4Ф64÷6→β44
Step-by-step explanation:
