let's firstly convert the mixed fractions to improper fractions, and then subtract.
![\bf \stackrel{mixed}{10\frac{1}{3}}\implies \cfrac{10\cdot 3+1}{3}\implies \stackrel{improper}{\cfrac{31}{3}}~\hfill \stackrel{mixed}{13\frac{1}{2}}\implies \cfrac{13\cdot 2+1}{2}\implies \stackrel{improper}{\cfrac{27}{2}} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \cfrac{27}{2}-\cfrac{31}{3}\implies \stackrel{\textit{using the LCD of 6}}{\cfrac{(3)27~~-~~(2)31}{6}}\implies \cfrac{81~~-~~62}{6}\implies \cfrac{19}{6}\implies 3\frac{1}{6}](https://tex.z-dn.net/?f=%5Cbf%20%5Cstackrel%7Bmixed%7D%7B10%5Cfrac%7B1%7D%7B3%7D%7D%5Cimplies%20%5Ccfrac%7B10%5Ccdot%203%2B1%7D%7B3%7D%5Cimplies%20%5Cstackrel%7Bimproper%7D%7B%5Ccfrac%7B31%7D%7B3%7D%7D~%5Chfill%20%5Cstackrel%7Bmixed%7D%7B13%5Cfrac%7B1%7D%7B2%7D%7D%5Cimplies%20%5Ccfrac%7B13%5Ccdot%202%2B1%7D%7B2%7D%5Cimplies%20%5Cstackrel%7Bimproper%7D%7B%5Ccfrac%7B27%7D%7B2%7D%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20%5Crule%7B34em%7D%7B0.25pt%7D%5C%5C%5C%5C%20%5Ccfrac%7B27%7D%7B2%7D-%5Ccfrac%7B31%7D%7B3%7D%5Cimplies%20%5Cstackrel%7B%5Ctextit%7Busing%20the%20LCD%20of%206%7D%7D%7B%5Ccfrac%7B%283%2927~~-~~%282%2931%7D%7B6%7D%7D%5Cimplies%20%5Ccfrac%7B81~~-~~62%7D%7B6%7D%5Cimplies%20%5Ccfrac%7B19%7D%7B6%7D%5Cimplies%203%5Cfrac%7B1%7D%7B6%7D)
(2p + 3)2 - (2p - 3)2 = 4p+6-4p+6=12
Answer:
C.
If the line doesn't pass through the origin, the easiest point to pick is the origin (0,0). Substitute into your inequality.
y > 5x + 1
0 > 5(0) + 1
0 > 1 which is a false statement.
So, you shade the side of the line on which (0,0) doesn't lie.
If the statement would have be true, you shade the side of the line on which (0,0) lies.
1. SSS 2. SAS 3. HL 4. AAS 5. HL 6. AAS 7. NP 8. SSS 9. ASA 10. NP
idk i'm probably wrong
Using the two points we can find the slope of the line using (y2-y1)/(x2-x1):
(-5-1)/(5-(-10))=-6/15=-3/5. Then we can use the formula y-y1=m(x-x1). Out of the 5 variables, we have 4 of them: y=-3, y1=1, m=-3/5, and x1=-10. Now we just solve for x: -3-1=(-3/5)(x-(-10)).
-4=(-3/5)(x+10)
-4(-5/3)=x+10
20/3-10=x, so the x coordinate is -10/3.
