Sum/difference:
Let
This means that
Now, assume that 
is rational. The sum/difference of two rational numbers is still rational (so 5-x is rational), and the division by 3 doesn't change this. So, you have that the square root of 8 equals a rational number, which is false. The mistake must have been supposing that was rational, which proves that the sum/difference of the two given terms was irrational
Multiplication/division:
The logic is actually the same: if we multiply the two terms we get
if again we assume x to be rational, we have
But if x is rational, so is -x/15, and again we come to a contradiction: we have the square root of 8 on one side, which is irrational, and -x/15 on the other, which is rational. So, again, x must have been irrational. You can prove the same claim for the division in a totally similar fashion.
Step-by-step explanation:
It is all done I am not sure if it is correct
If A and B are complementary angles, then they add up to 90 degrees.
So A + B = 90 => (x + 24) + (x + 16) = 90 => 2x + 40 = 90 => 2x = 50.
So x = 25, and thus, the measurement of B is (25 + 16) = 41.
The measurement of angle A is (25 + 24) = 49, and indeed they are complementary.
Answer:
the new equation is f(x)=x^2-4
vertex- (0,-4)
zeros- (-2,2)
y-intercept- (-4)
and it has a minimum
Step-by-step explanation:
Y=-3x+4
Gradient, m= -3
Parallel lines have equal gradients;
So, equation II,
y=mx+c
y=-3x+c
Replacing for x and y using point (-4, 6)
6=-3(-4)+c
6=12+c
6-12=c
c=-6
y=-3x-6
