Answer:
![\displaystyle (-3, 6)](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%28-3%2C%206%29)
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
<u>Algebra I</u>
- Coordinates (x, y)
- Midpoint Formula:
![\displaystyle (\frac{x_1 + x_1}{2}, \frac{y_1 + y_2}{2})](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%28%5Cfrac%7Bx_1%20%2B%20x_1%7D%7B2%7D%2C%20%5Cfrac%7By_1%20%2B%20y_2%7D%7B2%7D%29)
Step-by-step explanation:
<u>Step 1: Define</u>
Point A(-2, 5)
Point B(-4, 7)
<u>Step 2: Find Midpoint</u>
- Substitute in points [Midpoint Formula]:
![\displaystyle (\frac{-2 + -4}{2}, \frac{5 + 7}{2})](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%28%5Cfrac%7B-2%20%2B%20-4%7D%7B2%7D%2C%20%5Cfrac%7B5%20%2B%207%7D%7B2%7D%29)
- Add:
![\displaystyle (\frac{-6}{2}, \frac{12}{2})](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%28%5Cfrac%7B-6%7D%7B2%7D%2C%20%5Cfrac%7B12%7D%7B2%7D%29)
- Divide:
![\displaystyle (-3, 6)](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%28-3%2C%206%29)
Answer:
P=5
Step-by-step explanation:
-6(2p + 1) = -7p - 31
Expand -6(2p+1)
Apply distributive law;
a=-6, b=2p, c=1
=-6*2p+(-6)*1
=-6*2p-6*1
Simplify; -6*2p-6*1
=-12p-6
-12p-6=-7p-31
Add 6 to both sides;
-12p-6+6=-7p-31+6
simplify;
-12p=-7p-25
Add 7p to both sides;
-12p+7p=-7p-25+7p
Simplify;
-5p=-25
Divide both sides by -5
-5p/-5=-25/-5
Simplify:
p=5
Answered by the <u><em>One</em></u> and <u><em>Only #DrippQueenMo</em></u>
Answer:
the amount of time until 23 pounds of salt remain in the tank is 0.088 minutes.
Step-by-step explanation:
The variation of the concentration of salt can be expressed as:
![\frac{dC}{dt}=Ci*Qi-Co*Qo](https://tex.z-dn.net/?f=%5Cfrac%7BdC%7D%7Bdt%7D%3DCi%2AQi-Co%2AQo)
being
C1: the concentration of salt in the inflow
Qi: the flow entering the tank
C2: the concentration leaving the tank (the same concentration that is in every part of the tank at that moment)
Qo: the flow going out of the tank.
With no salt in the inflow (C1=0), the equation can be reduced to
![\frac{dC}{dt}=-Co*Qo](https://tex.z-dn.net/?f=%5Cfrac%7BdC%7D%7Bdt%7D%3D-Co%2AQo)
Rearranging the equation, it becomes
![\frac{dC}{C}=-Qo*dt](https://tex.z-dn.net/?f=%5Cfrac%7BdC%7D%7BC%7D%3D-Qo%2Adt)
Integrating both sides
![\int\frac{dC}{C}=\int-Qo*dt\\ln(\abs{C})+x1=-Qo*t+x2\\ln(\abs{C})=-Qo*t+x\\C=exp^{-Qo*t+x}](https://tex.z-dn.net/?f=%5Cint%5Cfrac%7BdC%7D%7BC%7D%3D%5Cint-Qo%2Adt%5C%5Cln%28%5Cabs%7BC%7D%29%2Bx1%3D-Qo%2At%2Bx2%5C%5Cln%28%5Cabs%7BC%7D%29%3D-Qo%2At%2Bx%5C%5CC%3Dexp%5E%7B-Qo%2At%2Bx%7D)
It is known that the concentration at t=0 is 30 pounds in 60 gallons, so C(0) is 0.5 pounds/gallon.
![C(0)=exp^{-Qo*0+x}=0.5\\exp^{x} =0.5\\x=ln(0.5)=-0.693\\](https://tex.z-dn.net/?f=C%280%29%3Dexp%5E%7B-Qo%2A0%2Bx%7D%3D0.5%5C%5Cexp%5E%7Bx%7D%20%3D0.5%5C%5Cx%3Dln%280.5%29%3D-0.693%5C%5C)
The final equation for the concentration of salt at any given time is
![C=exp^{-3*t-0.693}](https://tex.z-dn.net/?f=C%3Dexp%5E%7B-3%2At-0.693%7D)
To answer how long it will be until there are 23 pounds of salt in the tank, we can use the last equation:
![C=exp^{-3*t-0.693}\\(23/60)=exp^{-3*t-0.693}\\ln(23/60)=-3*t-0.693\\t=-\frac{ln(23/60)+0.693}{3}=-\frac{-0.959+0.693}{3}= -\frac{-0.266}{3}=0.088](https://tex.z-dn.net/?f=C%3Dexp%5E%7B-3%2At-0.693%7D%5C%5C%2823%2F60%29%3Dexp%5E%7B-3%2At-0.693%7D%5C%5Cln%2823%2F60%29%3D-3%2At-0.693%5C%5Ct%3D-%5Cfrac%7Bln%2823%2F60%29%2B0.693%7D%7B3%7D%3D-%5Cfrac%7B-0.959%2B0.693%7D%7B3%7D%3D%20%20-%5Cfrac%7B-0.266%7D%7B3%7D%3D0.088)
I believe it’s 245 I believe I did this before I don’t know
Answer:2p + 3q
Step-by-step explanation:
hope this helped!