Answer:
<u>Challenge #1:</u>
<u>Different examples:</u>
2x+1=3x+2
4x+3=5x+4
3x+2=4x+3
<u>Challenge #2:</u>
<u>Different examples:</u>
2x+0=4x+1
3x+1=2x+5
6x+5=8x+6
Each container is 50 pounds, forget about the second sentence it's just there to confuse you. One ton is 2,000 pounds, half of that is 1,000 lbs. 1,000 divided by 20 is 50. 50 pounds each.
Answer:
![f(x)=x^2+3x+2](https://tex.z-dn.net/?f=f%28x%29%3Dx%5E2%2B3x%2B2)
Step-by-step explanation:
step 1
we have the points
(-1,0), (-2,0), and (0,2)
Plot the points
using a graphing tool
see the attached figure
The graph of a quadratic function must be a vertical parabola open upward
The vertex is a minimum
The quadratic function in general form is equal to
![f(x)=ax^2+bx+c](https://tex.z-dn.net/?f=f%28x%29%3Dax%5E2%2Bbx%2Bc)
Substitute the value of x and the value of y of each given ordered pair in the general equation and solve for a,b and c
(0,2)
For x=0, y=2
substitute
![2=a(0)^2+b(0)+c](https://tex.z-dn.net/?f=2%3Da%280%29%5E2%2Bb%280%29%2Bc)
(-1,0)
For x=-1, y=0
substitute
![0=a(-1)^2+b(-1)+2](https://tex.z-dn.net/?f=0%3Da%28-1%29%5E2%2Bb%28-1%29%2B2)
---->
----> equation A
(-2,0)
For x=-2, y=0
substitute
![0=a(-2)^2+b(-2)+2](https://tex.z-dn.net/?f=0%3Da%28-2%29%5E2%2Bb%28-2%29%2B2)
----> equation B
we have the system
----> equation A
----> equation B
substitute equation A in equation B
solve for b
![b=3](https://tex.z-dn.net/?f=b%3D3)
Find the value of a
therefore
The quadratic function in general form is equal to
![f(x)=x^2+3x+2](https://tex.z-dn.net/?f=f%28x%29%3Dx%5E2%2B3x%2B2)
see the attached figure N 2 to better understand the problem
<span>we know that cos(a - b) = cos(a) cos(b) + sin(a) sin(b)
given a = π/3 and b = π/5
cos(π/3) cos(π/5) + sin(π/3) sin(π/5) = cos((π/3) - (π/5) = cos(2π/15)
hope it helps
</span>
<h2>
Answer:</h2>
√44
2 Real Roots
<h2>
Step-by-step explanation:</h2>
Looking at the image attached, the discriminant is the value under the square root.
In the equation given:
a = 1
b = -8
c = 5
The discriminant is therefore:
√(b²- 4ac) = √(-8²- (4*1*5)) = √(64-20) = √44
√44 is a positive number. Because it is positive, there must be 2 real roots.
If it were negative, there would be 2 imaginary roots.
If it were zero, there would be 1 real root.