We know that a square root is a number that when multiplied by itself, makes a certain number. That sounds vague, but you probably have some intuition about this concept. You may realize that the square root of 9, for example, is 3, because 3 times 3 is 9. But -3 is also a square root of 9. Indeed, -3 times -3 is 9.
Now this is an interesting property. These two numbers both make positive 9. But what about -9? What number multiplied by itself gives -9?
You may recall that the product of two positive numbers is positive, and that the product of two negative numbers is also positive. The square root, by definition, requires that the number times itself equals its square, so we can't have two numbers of different signs. Thus, you can't "really" have the square root of a negative number.
But some clever mathematicians—Euler and Gauss—didn't accept this dogma. They defined our familiar numbers as "real" numbers, denoted ℝ, and made a new set of num
bers. These are called "imaginary" numbers (no joke), whose set of numbers are sometimes denoted ℂ (there's a bit more nuance to this definition). The imaginary numbers allow you to have a square root for a negative number. They are defined such that
, or
. This has opened up an unbelievable number of pathways in mathematics, but I'm sure you'll learn about it in due time. :)
Answer:
y - 2 = 1/3(x - 3)
Step-by-step explanation:
The general equation for a line in point-slope form is:
y₁ - y₂ = m(x₁ - x₂)
In this form, "m" represents the slope, "x₁" and "y₂" represent the values from one point, and "x₂" and "y₂" represent the values from a second point.
You have been given the slope and values from one point. Therefore, you can plug these values into the formula to find the correct equation. Since you were given the values of only one point, the subscripts in the final answer are insignificant.
m = 1/3
x = 3 y = 2
y - 2 = 1/3(x - 3)
(I am not sure why this answer doesn't seem to be one of the options. I even checked with an online calculator. Perhaps while you were copying something over, something was mistyped).
The MAD for City 1 is 24.
The MAD for City 2 is 11 1/3.
The MAD for City 2 is less than the MAD for City 1, which means the average monthly temperatures of City 2 vary less than the average monthly temperatures for City 1.
Answer:
108 children and 115 adults were admitted
Step-by-step explanation:
Create a system of equations where c is the number of children admitted and a is the number of adults admitted:
c + a = 223
3.5c + 6.8a = 1160
Solve by elimination by multiplying the top equation by -3.5:
-3.5c - 3.5a = -780.5
3.5c + 6.8a = 1160
Add the equations together and solve for a:
3.3a = 379.5
a = 115
So, 115 adults were admitted.
Find how many children were admitted by subtracting 115 from 223, the total number of people admitted:
223 - 115
= 108
108 children and 115 adults were admitted.