Answer: See the graph attached.
Step-by-step explanation:
The standard form of a quadratic function is:
![f(x)=a(x-h)+k](https://tex.z-dn.net/?f=f%28x%29%3Da%28x-h%29%2Bk)
Where (h,k) is the vertex of the parabola.
If
is negative, then the parabola opens down.
Then, for the function:
![f(x)=-(x-2)^2+4](https://tex.z-dn.net/?f=f%28x%29%3D-%28x-2%29%5E2%2B4)
You can identify:
![h=2\\k=4](https://tex.z-dn.net/?f=h%3D2%5C%5Ck%3D4)
Then the vertex of the parabola is at (2,4)
Note that
, therefore the parabola opens down.
Find the intersection with the x-axis. Substitute
and solve for x:
![0=-(x-2)^2+4\\0=x^2-4x\\0=x(x-4)\\\\x_1=0\\x_2=4](https://tex.z-dn.net/?f=0%3D-%28x-2%29%5E2%2B4%5C%5C0%3Dx%5E2-4x%5C%5C0%3Dx%28x-4%29%5C%5C%5C%5Cx_1%3D0%5C%5Cx_2%3D4)
Knowing that the vertex is at (2,4), the parabola opens down and it intersects the x-axis at x=0 and x=4, you can graph the function, as you observe in the figure attached.
Well we set the perimeter to 120 feet.
This means that 2x+2y=120
Now we know the area of a rectangle is xy so we have to solve for both x and y in the perimeter equation.
2x=120-2y
x=60-y
2y=120-2x
y=60-x
Now we plug these values into our area equation A=xy to get:
A=(60-y)(60-x)
Answer:
The ninth term? That would be 98.
Step-by-step explanation:
Notice how the numbers add 10 every time. If we keep doing that pattern until we get the ninth number, then we get this:
8, 18, 28, 38, 48, 58, 68, 78, 88, 98
Therefore, the answer is 98.
Answer:77 cents Clara found 77 cents bc you just need to add up the cents and you have it
For simplicity sake, let's call Train A "A" and Train B "B".
A + B = 192
A > B
A - B = 120
192 ÷ 2 = 96
96 ± 120 ÷ 2 = 96 ± 60 = 156, 36
Train A weighs 156 tons and Train B weighs 36 tons :)