Answer:
See explanation
Step-by-step explanation:
<u>Step 1.</u> Substitute for d to solve for n:
From the first equation:

Then substitute it into the second equation:

<u>Step 2:</u> Substitute for n to solve for d:

There are 40 dimes and 30 nikels in the piggy bank
Angle B= 45 degrees
Angle A = 45 degrees
A and B are congruent since they are alternate exterior angles
5x-15 = 2x +21
5x = 2x +36
3x=36
X=12
B)
2x12+21 = 45
A)
5x12-15 =45
Answer:
6 because it is the only number that occurs more then once
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)