Answer:
8x+30=334
Step-by-step explanation:
X= the amount of cups he got and 30 is the initial fee so he only has to pay that once
The given system of equation that is
and
has infinite number of solutions.
Option -C.
<u>Solution:</u>
Need to determine number of solution given system of equation has.
![\begin{array}{l}{2 x+y=3} \\\\ {6 x=9-3 y}\end{array}](https://tex.z-dn.net/?f=%5Cbegin%7Barray%7D%7Bl%7D%7B2%20x%2By%3D3%7D%20%5C%5C%5C%5C%20%7B6%20x%3D9-3%20y%7D%5Cend%7Barray%7D)
Let us first bring the equation in standard form for comparison
![\begin{array}{l}{2 x+y-3=0} \\\\ {6 x+3 y-9=0}\end{array}](https://tex.z-dn.net/?f=%5Cbegin%7Barray%7D%7Bl%7D%7B2%20x%2By-3%3D0%7D%20%5C%5C%5C%5C%20%7B6%20x%2B3%20y-9%3D0%7D%5Cend%7Barray%7D)
![\frac{a_{1}}{a_{2}}=\frac{b_{1}}{b_{2}} \neq \frac{c_{1}}{c_{2}}](https://tex.z-dn.net/?f=%5Cfrac%7Ba_%7B1%7D%7D%7Ba_%7B2%7D%7D%3D%5Cfrac%7Bb_%7B1%7D%7D%7Bb_%7B2%7D%7D%20%5Cneq%20%5Cfrac%7Bc_%7B1%7D%7D%7Bc_%7B2%7D%7D)
To check how many solutions are there for system of equations
, we need to compare ratios of ![\frac{a_{1}}{a_{2}}, \frac{b_{1}}{b_{2}} \text { and } \frac{c_{1}}{c_{2}}](https://tex.z-dn.net/?f=%5Cfrac%7Ba_%7B1%7D%7D%7Ba_%7B2%7D%7D%2C%20%5Cfrac%7Bb_%7B1%7D%7D%7Bb_%7B2%7D%7D%20%5Ctext%20%7B%20and%20%7D%20%5Cfrac%7Bc_%7B1%7D%7D%7Bc_%7B2%7D%7D)
In our case,
![a_{1} = 2, b_{1}= 1\text{ and }c_{1}= -3](https://tex.z-dn.net/?f=a_%7B1%7D%20%3D%202%2C%20b_%7B1%7D%3D%201%5Ctext%7B%20and%20%7Dc_%7B1%7D%3D%20-3)
![a_{2} = 6, b_{2} = 3,\text{ and }c_{2} = -9](https://tex.z-dn.net/?f=a_%7B2%7D%20%20%3D%206%2C%20b_%7B2%7D%20%3D%203%2C%5Ctext%7B%20and%20%7Dc_%7B2%7D%20%3D%20-9)
![\begin{array}{l}{\Rightarrow \frac{a_{1}}{a_{2}}=\frac{2}{6}=\frac{1}{3}} \\\\ {\Rightarrow \frac{b_{1}}{b_{2}}=\frac{1}{3}} \\\\ {\Rightarrow \frac{c_{1}}{c_{2}}=\frac{-3}{-9}=\frac{1}{3}} \\\\ {\Rightarrow \frac{a_{1}}{a_{2}}=\frac{b_{1}}{b_{2}}=\frac{c_{1}}{c_{2}}=\frac{1}{3}}\end{array}](https://tex.z-dn.net/?f=%5Cbegin%7Barray%7D%7Bl%7D%7B%5CRightarrow%20%5Cfrac%7Ba_%7B1%7D%7D%7Ba_%7B2%7D%7D%3D%5Cfrac%7B2%7D%7B6%7D%3D%5Cfrac%7B1%7D%7B3%7D%7D%20%5C%5C%5C%5C%20%7B%5CRightarrow%20%5Cfrac%7Bb_%7B1%7D%7D%7Bb_%7B2%7D%7D%3D%5Cfrac%7B1%7D%7B3%7D%7D%20%5C%5C%5C%5C%20%7B%5CRightarrow%20%5Cfrac%7Bc_%7B1%7D%7D%7Bc_%7B2%7D%7D%3D%5Cfrac%7B-3%7D%7B-9%7D%3D%5Cfrac%7B1%7D%7B3%7D%7D%20%5C%5C%5C%5C%20%7B%5CRightarrow%20%5Cfrac%7Ba_%7B1%7D%7D%7Ba_%7B2%7D%7D%3D%5Cfrac%7Bb_%7B1%7D%7D%7Bb_%7B2%7D%7D%3D%5Cfrac%7Bc_%7B1%7D%7D%7Bc_%7B2%7D%7D%3D%5Cfrac%7B1%7D%7B3%7D%7D%5Cend%7Barray%7D)
As
, so given system of equations have infinite number of solutions.
Hence, we can conclude that system has infinite number of solutions.
Answer:
a= -19 :)
Step-by-step explanation:
thats it lol
Answer:
<h2>At noon the tide will be at the lowest point which is 1 ft </h2>
Step-by-step explanation:
please see attached a sketch of the solution for your reference
What is a sinusoidal wave?
Alternatively called a sine wave is a type of wave that shows a repetitive pattern or oscillation, it normally starts from a low point moves to the next point which is usually higher than the previous and repeats itself as the whole process continues
The hourly growth rate of bacteria is 191.25
<u>Solution:</u>
Given that, initially Shelly put 85 bacteria and waits 4 hours
Amount of bacteria after 4 hours = 850
Now, number of bacteria increased = 850 bacteria – initial 85 bacteria
Number of increased bacteria = 850 – 85 = 765 bacteria.
So, 765 bacteria were produced in 4 hours.
So hourly growth rate( per hour) can be found out by as follows:
![\text { Hourly growth rate }=\frac{\text { number of bacteria increased }}{\text { number of hours }}](https://tex.z-dn.net/?f=%5Ctext%20%7B%20Hourly%20growth%20rate%20%7D%3D%5Cfrac%7B%5Ctext%20%7B%20number%20of%20bacteria%20increased%20%7D%7D%7B%5Ctext%20%7B%20number%20of%20hours%20%7D%7D)
![\text { Hourly growth rate }=\frac{765}{4}=191.25](https://tex.z-dn.net/?f=%5Ctext%20%7B%20Hourly%20growth%20rate%20%7D%3D%5Cfrac%7B765%7D%7B4%7D%3D191.25)
Hence, the hourly growth rate of bacteria is 191.25