Step-by-step explanation:
You can let me know, but i dont think -3x² is supposed to be squared in this question because then it would make it unsolvable.
5x-15
can be simplified to 5(x-3)
x²-3x
can be simplified to x(x-3)
Then u rewrite it (5 + x)(x - 3)
Answer:
y=5x+9 because it has the same slope as the original line.
Step-by-step explanation:
![\bf \qquad \qquad \textit{ratio relations} \\\\ \begin{array}{ccccllll} &\stackrel{ratio~of~the}{Sides}&\stackrel{ratio~of~the}{Areas}&\stackrel{ratio~of~the}{Volumes}\\ &-----&-----&-----\\ \cfrac{\textit{similar shape}}{\textit{similar shape}}&\cfrac{s}{s}&\cfrac{s^2}{s^2}&\cfrac{s^3}{s^3} \end{array}\\\\ \rule{31em}{0.25pt}\\\\ \cfrac{\textit{similar shape}}{\textit{similar shape}}\qquad \cfrac{s}{s}=\cfrac{\sqrt{s^2}}{\sqrt{s^2}}=\cfrac{\sqrt[3]{s^3}}{\sqrt[3]{s^3}}](https://tex.z-dn.net/?f=%20%5Cbf%20%5Cqquad%20%5Cqquad%20%5Ctextit%7Bratio%20relations%7D%20%5C%5C%5C%5C%20%5Cbegin%7Barray%7D%7Bccccllll%7D%20%26%5Cstackrel%7Bratio~of~the%7D%7BSides%7D%26%5Cstackrel%7Bratio~of~the%7D%7BAreas%7D%26%5Cstackrel%7Bratio~of~the%7D%7BVolumes%7D%5C%5C%20%26-----%26-----%26-----%5C%5C%20%5Ccfrac%7B%5Ctextit%7Bsimilar%20shape%7D%7D%7B%5Ctextit%7Bsimilar%20shape%7D%7D%26%5Ccfrac%7Bs%7D%7Bs%7D%26%5Ccfrac%7Bs%5E2%7D%7Bs%5E2%7D%26%5Ccfrac%7Bs%5E3%7D%7Bs%5E3%7D%20%5Cend%7Barray%7D%5C%5C%5C%5C%20%5Crule%7B31em%7D%7B0.25pt%7D%5C%5C%5C%5C%20%5Ccfrac%7B%5Ctextit%7Bsimilar%20shape%7D%7D%7B%5Ctextit%7Bsimilar%20shape%7D%7D%5Cqquad%20%5Ccfrac%7Bs%7D%7Bs%7D%3D%5Ccfrac%7B%5Csqrt%7Bs%5E2%7D%7D%7B%5Csqrt%7Bs%5E2%7D%7D%3D%5Ccfrac%7B%5Csqrt%5B3%5D%7Bs%5E3%7D%7D%7B%5Csqrt%5B3%5D%7Bs%5E3%7D%7D%20)
![\bf \rule{31em}{0.25pt}\\\\ \cfrac{smaller}{larger}\qquad \cfrac{s}{s}=\cfrac{\sqrt{98}}{\sqrt{162}}~~ \begin{cases} 98=2\cdot 7\cdot 7\\ \qquad 2\cdot 7^2\\ 162=2\cdot 9\cdot 9\\ \qquad 2\cdot 9^2 \end{cases}\implies \cfrac{s}{s}=\cfrac{\sqrt{2\cdot 7^2}}{\sqrt{2\cdot 9^2}} \\[2em] \cfrac{s}{s}=\cfrac{7\sqrt{2}}{9\sqrt{2}}\implies \cfrac{s}{s}=\cfrac{7}{9}](https://tex.z-dn.net/?f=%20%5Cbf%20%5Crule%7B31em%7D%7B0.25pt%7D%5C%5C%5C%5C%20%5Ccfrac%7Bsmaller%7D%7Blarger%7D%5Cqquad%20%5Ccfrac%7Bs%7D%7Bs%7D%3D%5Ccfrac%7B%5Csqrt%7B98%7D%7D%7B%5Csqrt%7B162%7D%7D~~%20%5Cbegin%7Bcases%7D%2098%3D2%5Ccdot%207%5Ccdot%207%5C%5C%20%5Cqquad%202%5Ccdot%207%5E2%5C%5C%20162%3D2%5Ccdot%209%5Ccdot%209%5C%5C%20%5Cqquad%202%5Ccdot%209%5E2%20%5Cend%7Bcases%7D%5Cimplies%20%5Ccfrac%7Bs%7D%7Bs%7D%3D%5Ccfrac%7B%5Csqrt%7B2%5Ccdot%207%5E2%7D%7D%7B%5Csqrt%7B2%5Ccdot%209%5E2%7D%7D%20%5C%5C%5B2em%5D%20%5Ccfrac%7Bs%7D%7Bs%7D%3D%5Ccfrac%7B7%5Csqrt%7B2%7D%7D%7B9%5Csqrt%7B2%7D%7D%5Cimplies%20%5Ccfrac%7Bs%7D%7Bs%7D%3D%5Ccfrac%7B7%7D%7B9%7D%20)
bearing in mind that the ratio of the sides, is the same as the ratio of the perimeters.
Answer:
52:49
Step-by-step explanation:
pink:green
The ratio of pink to green marbles is
3k:4k
He removes 5 green marbles and adds 8 pink marbles.
Now the ratio of pink to green marbles is
(3k + 8):(4k - 5)
This rario is equal to 29:23.
(3k + 8)/(4k - 5) = 29/23
29(4k - 5) = 23(3k + 8)
116k - 145 = 69k + 184
47k = 329
k = 7
Original amounts:
3 * k = 3 * 7 = 21 pink
4 * k = 4 * 7 = 28 green
Original total = 21 + 28 = 49
Amounts after replacement:
3k + 8 = 3(7) + 8 = 29 pink
4k - 5 = 4(7) - 5 = 23 green
Total after replacement = 23 + 29 = 52
Answer: The ratio of the total number of marbles in the jar after replacement to the total number of marbles in the jar originally is 52:49.
