Answer:
Given system of equations:
![\begin{cases}f(x)=-x^2+2x+3\\g(x)=-2x+3\end{cases}](https://tex.z-dn.net/?f=%5Cbegin%7Bcases%7Df%28x%29%3D-x%5E2%2B2x%2B3%5C%5Cg%28x%29%3D-2x%2B3%5Cend%7Bcases%7D)
To solve by substitution, equate the equations and solve for x:
![\begin{aligned}f(x) & = g(x)\\\implies -x^2+2x+3 & = -2x+3\\-x^2+4x & = 0\\x^2-4x & = 0\\x(x-4) & = 0\\\implies x & = 0\\\implies x-4 & = 0 \implies x=4\end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7Df%28x%29%20%26%20%3D%20g%28x%29%5C%5C%5Cimplies%20-x%5E2%2B2x%2B3%20%26%20%3D%20-2x%2B3%5C%5C-x%5E2%2B4x%20%26%20%3D%200%5C%5Cx%5E2-4x%20%26%20%3D%200%5C%5Cx%28x-4%29%20%26%20%3D%200%5C%5C%5Cimplies%20x%20%26%20%3D%200%5C%5C%5Cimplies%20x-4%20%26%20%3D%200%20%5Cimplies%20x%3D4%5Cend%7Baligned%7D)
Therefore, the x-values of the solution are
and
.
To find the y-values of the solution, substitute the found values of x into the functions:
![f(0)=-(0)^2+2(0)+3=3](https://tex.z-dn.net/?f=f%280%29%3D-%280%29%5E2%2B2%280%29%2B3%3D3)
![g(0)=-2(0)+3=3](https://tex.z-dn.net/?f=g%280%29%3D-2%280%29%2B3%3D3)
![f(4)=-(4)^2+2(4)+3=-5](https://tex.z-dn.net/?f=f%284%29%3D-%284%29%5E2%2B2%284%29%2B3%3D-5)
![g(4)=-2(4)+3=-5](https://tex.z-dn.net/?f=g%284%29%3D-2%284%29%2B3%3D-5)
Therefore, the solutions to the given system of equations are:
and ![(4, -5)](https://tex.z-dn.net/?f=%284%2C%20-5%29)
Answer:
True
Step-by-step explanation:
The whole point of units conversion is to take a value expressed in one set of units (parts per hour) and translate it to a different set of units (parts per week). The rate does not have to involve time.
The statement is TRUE.
<span>0.827 = 0.827 / 1
Numerator = 0.827 × 10 × 10 × 10 = 827
Denominator = 1 × 10 × 10 × 10 = 1000
Numerator / Denominator = 827 / 1000
Simplifying our fraction
= 827/1000
= 827/1000</span>
Answer:
77.6m (3 s.f.)
Step-by-step explanation:
Please see the attached pictures for full solution.