Answer:
That guy is correct a because its both greater than and equal to 8
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:
17
Step-by-step explanation:
We have two congruent triangles here. Thus, b must be 17.
Answer:
7. 49
8. 10.4
Step-by-step explanation:
7) our hypotenuse is 8, and the side opposite the base of ladder and ground angle is 6, therefore we can use Sin
sin = opposite/hypotenuse
sin(x) = 6/8 = 3/4
sin-1(3/4) = 49
8) using the theorem that alternate exterior angles are congruent
the angle opposite side x is 30
tan = opposite/adjacent
tan(30) = x/18
x = 18tan(30) = 6√(3) = 10.4
you can also use 30-60-90 special right triangles.
the side opposite 30 is x
side opposite 60 is x√(3)
and side opposite 90 is 2x
Answer:
16 year olds had the higher ratio of black belts to brown belts.
Step-by-step explanation:
15 year olds: 8/28 students had black belts
8/28 = 28.6% had black belts
16 year olds: 10/27 students had bald belts
10/27 = 37.0% had black belts