Answer:
38 = D
Step-by-step explanation:
The 3 angles of a triangle equal 180 degrees
<B + <C + <D = 360
7x+ 12 + 2x+13 + 2x+ 12 =180
Combine terms
11x+37 = 180
Subtract 37 from each side
11x+37-37 = 180-37
11x =143
Divide by 11
11x/11 = 143/11
x =13
We want to find angle D
2x+12 = D
2(13) + 12 = D
26+12 = D
38 = D
[-2 3] times [2
1]
comes out to -2(2)+3(1) = -1. Eliminate the first answer choice, due to
the presence of that -7 instead of -1.
[-2 3] times [0
-3]
comes out to - 9. This matches answer choices #2, #3 and #4.
[3,-4][2
1]
comes out to 6-4, or 2. Matches #2, #3, #4.
[3, -4][0
-3]
comes out to +12, which matches answer choice #4.
Answer choice #4 is the correct one.
Review matrix multiplication if need be. Feel free to ask questions here and now if need be.
Answer:
Step-by-step explanation:
A(t) is the amount of salt in the tank at time t.
dA / dt = rate of salt flowing into the tank - rate of salt going out of the tank
dA / dt = (1 g/L)*(5 L/min) - (A(t)/250 g/L) * (5L/min)
dA / dt = 5 g/min - (A(t) / 50) g/min
![\frac{dA}{dt}+\frac{A(t)}{50} = 5\\\\The\ integrating\ factor(IF)= e^{\int\limits \frac{1}{50}dt }=e^{\frac{t}{50} }\\\\Multiplying\ through\ by\ the\ I.F:\\\\\frac{dA}{dt}*e^{\frac{t}{50} }+\frac{A(t)}{50}*e^{\frac{t}{50} } = 5*e^{\frac{t}{50} }\\\\Integrating \ both \ sides:\\\\\int\limits[ \frac{dA}{dt}*e^{\frac{t}{50} }+\frac{A(t)}{50}*e^{\frac{t}{50} }] dt=\int\limits 5e^{\frac{t}{50} } dt\\\\A(t)e^{\frac{t}{50} } =\int\limits 5e^{\frac{t}{50} } dt\\\\](https://tex.z-dn.net/?f=%5Cfrac%7BdA%7D%7Bdt%7D%2B%5Cfrac%7BA%28t%29%7D%7B50%7D%20%3D%205%5C%5C%5C%5CThe%5C%20integrating%5C%20factor%28IF%29%3D%20e%5E%7B%5Cint%5Climits%20%5Cfrac%7B1%7D%7B50%7Ddt%20%7D%3De%5E%7B%5Cfrac%7Bt%7D%7B50%7D%20%7D%5C%5C%5C%5CMultiplying%5C%20through%5C%20by%5C%20the%5C%20I.F%3A%5C%5C%5C%5C%5Cfrac%7BdA%7D%7Bdt%7D%2Ae%5E%7B%5Cfrac%7Bt%7D%7B50%7D%20%7D%2B%5Cfrac%7BA%28t%29%7D%7B50%7D%2Ae%5E%7B%5Cfrac%7Bt%7D%7B50%7D%20%7D%20%3D%205%2Ae%5E%7B%5Cfrac%7Bt%7D%7B50%7D%20%7D%5C%5C%5C%5CIntegrating%20%5C%20both%20%5C%20sides%3A%5C%5C%5C%5C%5Cint%5Climits%5B%20%20%5Cfrac%7BdA%7D%7Bdt%7D%2Ae%5E%7B%5Cfrac%7Bt%7D%7B50%7D%20%7D%2B%5Cfrac%7BA%28t%29%7D%7B50%7D%2Ae%5E%7B%5Cfrac%7Bt%7D%7B50%7D%20%7D%5D%20dt%3D%5Cint%5Climits%20%205e%5E%7B%5Cfrac%7Bt%7D%7B50%7D%20%7D%20dt%5C%5C%5C%5CA%28t%29e%5E%7B%5Cfrac%7Bt%7D%7B50%7D%20%7D%20%3D%5Cint%5Climits%20%205e%5E%7B%5Cfrac%7Bt%7D%7B50%7D%20%7D%20dt%5C%5C%5C%5C)
Answer:
y = 5x - 11
Step-by-step explanation:
The equation is y = mx+b where m is the slope and b is the y intercept
y = 5x + b (now lets substitute the coordinate in to solve for b)
4 = 5(3) + b
4 = 15 +b
b = -11
y = 5x - 11
