X^2 + y^2 = 25
2x + y = -5.....y = -2x - 5
x^2 + (-2x - 5)^2 = 25
x^2 + (-2x - 5)(-2x - 5) = 25
x^2 + (4x^2 + 20x + 25) = 25
5x^2 + 20x + 25 = 25
5x^2 + 20x = 0
5x(x + 4) = 0
5x = 0 2(0) + y = -5
x = 0 y = -5
x + 4 = 0 2(-4) + y = -5
x = -4 -8 + y = -5
y = 3
solutions are : x = 0, y = -5.....and x = -4, y = 3
Answer:
You'll have a <u>closed circle at x = 2</u>, and <u>shading to the left</u>
See the diagram below
=========================================================
Explanation:
The fractions here are 3/7 and 21/2. The denominators of which are 7 and 2 respectively. The LCD is 7*2 = 14.
If we multiply both sides by 14, then this will clear out the denominators and make the fractions go away.
- 14*(3/7) = (14*3)/7 = 42/7 = 8
- 14*(21/2) = (14*21)/2 = 294/2 = 147
So if we multiplied both sides by 14, then we have these steps
![\frac{3}{7}(35x-14) \le \frac{21x}{2}+3\\\\14*\frac{3}{7}(35x-14) \le 14*\left(\frac{21x}{2}+3\right)\\\\14*\frac{3}{7}(35x-14) \le 14*\left(\frac{21x}{2}\right)+14*\left(3\right)\\\\6(35x-14) \le 147x+42\\\\](https://tex.z-dn.net/?f=%5Cfrac%7B3%7D%7B7%7D%2835x-14%29%20%5Cle%20%5Cfrac%7B21x%7D%7B2%7D%2B3%5C%5C%5C%5C14%2A%5Cfrac%7B3%7D%7B7%7D%2835x-14%29%20%5Cle%2014%2A%5Cleft%28%5Cfrac%7B21x%7D%7B2%7D%2B3%5Cright%29%5C%5C%5C%5C14%2A%5Cfrac%7B3%7D%7B7%7D%2835x-14%29%20%5Cle%2014%2A%5Cleft%28%5Cfrac%7B21x%7D%7B2%7D%5Cright%29%2B14%2A%5Cleft%283%5Cright%29%5C%5C%5C%5C6%2835x-14%29%20%5Cle%20147x%2B42%5C%5C%5C%5C)
--------------------------
Let's isolate x
![6(35x-14) \le 147x+42\\\\6(35x)+6(-14) \le 147x+42\\\\210x-84 \le 147x+42\\\\210x-147x \le 42+84\\\\63x \le 126\\\\x \le 126/63\\\\x \le 2\\\\](https://tex.z-dn.net/?f=6%2835x-14%29%20%5Cle%20147x%2B42%5C%5C%5C%5C6%2835x%29%2B6%28-14%29%20%5Cle%20147x%2B42%5C%5C%5C%5C210x-84%20%5Cle%20147x%2B42%5C%5C%5C%5C210x-147x%20%5Cle%2042%2B84%5C%5C%5C%5C63x%20%5Cle%20126%5C%5C%5C%5Cx%20%5Cle%20126%2F63%5C%5C%5C%5Cx%20%5Cle%202%5C%5C%5C%5C)
The graph of this will consist of a closed or filled in circle at x = 2. We shade to the left to represent numbers smaller than 2.
So either x = 2 or x < 2.
If we used an open hole at 2, then we wouldn't be including 2 (but we want to include this endpoint).
See the diagram below.
Hi Kimberlys969pdrfzz,
Question:
Find the mean
Mean - "The mean is the average of the numbers: a calculated "central" value of a set of numbers. To calculate it: add up all the numbers, then divide by how many numbers there are."
Solution:
![\frac{10 + 12 + 17 + 14 + 20 + 27 + 24 + 28 + 28}{9} = \frac{180}{9} = 20](https://tex.z-dn.net/?f=%5Cfrac%7B10%20%2B%2012%20%2B%2017%20%2B%2014%20%2B%2020%20%2B%2027%20%2B%2024%20%2B%2028%20%2B%2028%7D%7B9%7D%20%3D%20%5Cfrac%7B180%7D%7B9%7D%20%3D%2020)
Answer:
Mean = 20
Hope This Helps!
The first answer is that the system represents 2 lines. They are two parallel lines.
For the second question, it just represents 1 line. In this case, the two lines are right on top of each other. This is because they are the same equation, just in different forms.