Answer:
The quadratic mean of 2 real positive numbers is greater than or equal to the arithmetic mean.
Step-by-step explanation:
x and y Quadratic Mean Arithmetic mean
3 and 3 3 3
2 and 3 2.55 2.5
3 and 6 4.74 4.5
2 and 5 3.8 3.5
2 and 17 12.1 9.5
18 and 28 23.5 23
10 and 48 34.7 29
The quadratic mean is always greater than the arithmetic mean except when x and y are the same.
When the difference between the pairs is small the difference in the means is also small. As that difference increases the difference in the means also increases.
So we conjecture that the quadratic mean is always greater than or equal to the arithmetic mean.
Proof.
Suppose it is true then:
√(x^2 + y^2) / 2) ≥ (x + y)/2 Squaring both sides:
(x ^2 + y^2) / 2 ≥ (x + y)^2 / 4 Multiply through by 4:
2x^2 +2y^2 ≥ (x + y)^2
2x^2 +2y^2 >= x^2 + 2xy + y^2
x^2 + y^2 >= 2xy.
x^2 - 2xy + y^2 ≥ 0
(x - y)^2 ≥ 0
This is true because the square of any real number is positive so the original inequality must also be true.
Answer:
a.ABCD is reflected over both axes.
Step-by-step explanation:
Reflection over x-axis transforms point (x, y) into (x, -y)
Reflection over y-axis transforms point (x, y) into (-x, y)
Then, reflection over both axes transforms point (x, y) into (-x, -y). Applying this rule to figure ABCD:
A (-2, 2) -> (2, -2) which corresponds to point A'
B (-1, 2) -> (1, -2) which corresponds to point B'
C (-1, 1) -> (1, -1) which corresponds to point C'
D (-3, 1) -> (3, -1) which corresponds to point D'
Answer:
5/39
Step-by-step explanation:
<u>Step 1: Find the probability</u>
Cross country / total
10 / 78
(10/2) / (78/2)
5 / 39
Answer: 5/39
Answer:
50.5
Step-by-step explanation:
Sooo first we calculate edf. 11/2= 5.5, 5.5x5=27.5
And then we do the other part.9/5=4, and 4x11.5=46, and we need to cut that in half cuz it’s a triangle 46/2=23. We add up the rectangle and the triangle: 27.5+23=50.5
The slope of GH is 1, so any line parallel to GH will have the same slope.
Since this other line passes through (-5,6), you can use the point-slope formula:

so you are correct.