Answer:
![y(t) = 3e^{-4t}+7](https://tex.z-dn.net/?f=y%28t%29%20%3D%203e%5E%7B-4t%7D%2B7)
Step-by-step explanation:
![y(t) = Ce^{-4t}+7](https://tex.z-dn.net/?f=y%28t%29%20%3D%20Ce%5E%7B-4t%7D%2B7)
At <em>y</em>(0) = 10, when <em>t</em> = 0, <em>y</em> = 10.
![y(0) = 10 = Ce^{-4\times0}+7](https://tex.z-dn.net/?f=y%280%29%20%3D%2010%20%3D%20Ce%5E%7B-4%5Ctimes0%7D%2B7)
![10 = C+7](https://tex.z-dn.net/?f=10%20%3D%20C%2B7)
![C = 3](https://tex.z-dn.net/?f=C%20%3D%203)
Hence, the solution is
![y(t) = 3e^{-4t}+7](https://tex.z-dn.net/?f=y%28t%29%20%3D%203e%5E%7B-4t%7D%2B7)
Answer:
Yes;Each side of triangle PQR is the same length as the corresponding side of triangle STU
Step-by-step explanation:
You can observe the sides of both triangles to see if this property holds
Lets check the length of AB
A(0,3) and B(0,-1)
![AB=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\\\\\\\AB=\sqrt{(0-0)^2+(-1-3)^2} \\\\\\\\AB=\sqrt{0^2+-4^2} \\\\\\AB=\sqrt{16} =4units](https://tex.z-dn.net/?f=AB%3D%5Csqrt%7B%28x_2-x_1%29%5E2%2B%28y_2-y_1%29%5E2%7D%20%5C%5C%5C%5C%5C%5C%5C%5CAB%3D%5Csqrt%7B%280-0%29%5E2%2B%28-1-3%29%5E2%7D%20%5C%5C%5C%5C%5C%5C%5C%5CAB%3D%5Csqrt%7B0%5E2%2B-4%5E2%7D%20%5C%5C%5C%5C%5C%5CAB%3D%5Csqrt%7B16%7D%20%3D4units)
Now check the length of the corresponding side DE
D(1,2) and E(1,-2)
![DE=\sqrt{(1-1)^2+(-2-2)^2} \\\\\\DE=\sqrt{0^2+-4^2} \\\\\\DE=\sqrt{16} =4units](https://tex.z-dn.net/?f=DE%3D%5Csqrt%7B%281-1%29%5E2%2B%28-2-2%29%5E2%7D%20%5C%5C%5C%5C%5C%5CDE%3D%5Csqrt%7B0%5E2%2B-4%5E2%7D%20%5C%5C%5C%5C%5C%5CDE%3D%5Csqrt%7B16%7D%20%3D4units)
The side AB has the same length as side DE.This is also true for the remaining corresponding sides.
Answer:
Step-by-step explanation:
Multiplying a(x) and b(x) together results in a quadratic equation (a trinomial). This trinomial looks like (a·b)(x) = (2)(x - 2)(x + 2). Note that this is a "special product;" (2)(x^2 - 4); there is no middle term.
Ànswer is 64 , 80, and 96
First you would have to multiply $18 (The cost for each month) and 12 (the number of months in a year) and the answer would be 216
So she deducts 216 a year, so the answer would have to be negative
The final answer is -216