4x+20 = 3x - 28
x + 20 = -28
x = - 48
can you subscribe to this channel and leave a like on the only video there is? It would mean the world to me since im a newbie to yt!
h t t p s : / / w w w . y o u t u b e . c o m / w a t c h ? v = Y B u y R P r W 6 Q g & t = 1 0 s
Answer:
The cost of hardbook is $9 and cost of paperback is $5.
Step-by-step explanation:
Let x be the price for hardback book and y be the price for paperback book.
Mr. Yamamoto purchased 42 new hardcover books and 64 new paperback books, which cost a total of $698.
We can write the equation as:
![42x + 64y = 698](https://tex.z-dn.net/?f=42x%20%2B%2064y%20%3D%20698)
He also purchased 42 new hardcover books and 58 new paperback books, which cost a total of $668.
We can write the equation as:
![42x + 58y = 668](https://tex.z-dn.net/?f=42x%20%2B%2058y%20%3D%20668)
We have to use the elimination method to solve the two equations.
We eliminate x by subtracting the two equations.
![42x + 64y-(42x + 58y) = 698 - 668\\\Rightarrow 6y = 30\\\Rightarrow y = 5\\42x + 64(5) = 698\\\\\Rightarrow x = \displaystyle\frac{698 - 64(5)}{42}\\\\\Rightarrow x = 9](https://tex.z-dn.net/?f=42x%20%2B%2064y-%2842x%20%2B%2058y%29%20%3D%20698%20-%20668%5C%5C%5CRightarrow%206y%20%3D%2030%5C%5C%5CRightarrow%20y%20%3D%205%5C%5C42x%20%2B%2064%285%29%20%3D%20698%5C%5C%5C%5C%5CRightarrow%20x%20%3D%20%5Cdisplaystyle%5Cfrac%7B698%20-%2064%285%29%7D%7B42%7D%5C%5C%5C%5C%5CRightarrow%20x%20%3D%209)
Thus, the cost of hardbook is $9 and cost of paperback is $5.
Answer:
The scale factor of a dilation from ABCD to RSTU is ![\frac{1}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D)
Step-by-step explanation:
We know that the rectangle ABCD is similar to rectangle RSTU.
Given that in rectangle ABCD the longest sides are DC and AB and in the rectangle RSTU the longest sides are UT and RS ⇒ The scale factor of a dilation will transform the sides DC and AB into UT and RS
Working with the lengths of the sides :
DC.(Scale factor) = UT
AB.(Scale factor) = RS
Replacing with the values of the lengths (Scale factor : SF) :
![DC.SF=UT\\(90ft).(SF)=45ft\\SF=\frac{45ft}{90ft} \\SF=\frac{1}{2}](https://tex.z-dn.net/?f=DC.SF%3DUT%5C%5C%2890ft%29.%28SF%29%3D45ft%5C%5CSF%3D%5Cfrac%7B45ft%7D%7B90ft%7D%20%5C%5CSF%3D%5Cfrac%7B1%7D%7B2%7D)
![AB.SF=RS\\(90ft).(SF)=45ft\\SF=\frac{45ft}{90ft} \\SF=\frac{1}{2}](https://tex.z-dn.net/?f=AB.SF%3DRS%5C%5C%2890ft%29.%28SF%29%3D45ft%5C%5CSF%3D%5Cfrac%7B45ft%7D%7B90ft%7D%20%5C%5CSF%3D%5Cfrac%7B1%7D%7B2%7D)
Notice that the scale factor is dimensionless.
We can verify this result with the sides AD and BC :
![AD.SF=UR\\50ft.(\frac{1}{2})=25ft\\ 25ft=25ft](https://tex.z-dn.net/?f=AD.SF%3DUR%5C%5C50ft.%28%5Cfrac%7B1%7D%7B2%7D%29%3D25ft%5C%5C%2025ft%3D25ft)
![BC.SF=TS\\50ft.(\frac{1}{2})=25ft\\ 25ft=25ft](https://tex.z-dn.net/?f=BC.SF%3DTS%5C%5C50ft.%28%5Cfrac%7B1%7D%7B2%7D%29%3D25ft%5C%5C%2025ft%3D25ft)
The scale factor (SF) is ![\frac{1}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D)