1. Since 12 took both, subtract 12 from 20 and 25.
Now we have 8 taking only chemistry, 13 taking only biology, and 12 taking both. Add all those together to get 33.
Subtract 33 from 50 to get 17, which is the number of students taking neither.
2. He had 3 nickels, 1 quarter, and 6 dimes.
This is an equation that represented his coins:
3n + 1q + 6d = 1.00
3 x .5 = .15 1 x .25 = .25 6 x .10 = .60 .60 + .25 = .85 .85 + .15 = 1.00
3. Add together 7 and 11 to get the 5th and 6th graders: 18 students.
The remaining 4th graders make up 1/3 of the team, so 18 is 2/3 of the team.
Find 1/3 by dividing 18 by 2 to get 9.
There are 9 4th graders.
Hope this helps!
Answer:
a) We get ![\mathbf{A+B=x^2-2x+1}](https://tex.z-dn.net/?f=%5Cmathbf%7BA%2BB%3Dx%5E2-2x%2B1%7D)
So, Is the result of A+B is a polynomial:Yes
b) We get ![\mathbf{A-B=6x^3-7x^2+2x-1}](https://tex.z-dn.net/?f=%5Cmathbf%7BA-B%3D6x%5E3-7x%5E2%2B2x-1%7D)
So, Is the result of A-B is a polynomial:Yes
c) We get ![\mathbf{A.B=9x^6+21x^5-18x^4+9x^3-3x^2}](https://tex.z-dn.net/?f=%5Cmathbf%7BA.B%3D9x%5E6%2B21x%5E5-18x%5E4%2B9x%5E3-3x%5E2%7D)
So, Is the result of A.B is a polynomial:Yes
Step-by-step explanation:
We are giving the polynomial equations:
![A= 3x^2(x-1)\\B=-3x^3+4x^2-2x+1](https://tex.z-dn.net/?f=A%3D%203x%5E2%28x-1%29%5C%5CB%3D-3x%5E3%2B4x%5E2-2x%2B1)
We need to find
a) A+B
![A+B=3x^2(x-1)+(-3x^3+4x^2-2x+1)\\A+B=3x^3-3x^2-3x^3+4x^2-2x+1\\A+B=3x^3-3x^3-3x^2+4x^2-2x+1\\A+B=x^2-2x+1\\](https://tex.z-dn.net/?f=A%2BB%3D3x%5E2%28x-1%29%2B%28-3x%5E3%2B4x%5E2-2x%2B1%29%5C%5CA%2BB%3D3x%5E3-3x%5E2-3x%5E3%2B4x%5E2-2x%2B1%5C%5CA%2BB%3D3x%5E3-3x%5E3-3x%5E2%2B4x%5E2-2x%2B1%5C%5CA%2BB%3Dx%5E2-2x%2B1%5C%5C)
So, we get ![\mathbf{A+B=x^2-2x+1}](https://tex.z-dn.net/?f=%5Cmathbf%7BA%2BB%3Dx%5E2-2x%2B1%7D)
So, Is the result of A+B is a polynomial:Yes
b) A-B
![A-B=3x^2(x-1)-(-3x^3+4x^2-2x+1)\\A-B=3x^3-3x^2+3x^3-4x^2+2x-1\\A-B=3x^3+3x^3-3x^2-4x^2+2x-1\\A-B=6x^3-7x^2+2x-1\\](https://tex.z-dn.net/?f=A-B%3D3x%5E2%28x-1%29-%28-3x%5E3%2B4x%5E2-2x%2B1%29%5C%5CA-B%3D3x%5E3-3x%5E2%2B3x%5E3-4x%5E2%2B2x-1%5C%5CA-B%3D3x%5E3%2B3x%5E3-3x%5E2-4x%5E2%2B2x-1%5C%5CA-B%3D6x%5E3-7x%5E2%2B2x-1%5C%5C)
So, we get ![\mathbf{A-B=6x^3-7x^2+2x-1}](https://tex.z-dn.net/?f=%5Cmathbf%7BA-B%3D6x%5E3-7x%5E2%2B2x-1%7D)
So, Is the result of A-B is a polynomial:Yes
c) A . B
![A.B=3x^3(-3x^3+4x^2-2x+1)-3x^2(-3x^3+4x^2-2x+1)\\A.B=9x^6+12x^5-6x^4+3x^3+9x^5-12x^4+6x^3-3x^2\\A.B=9x^6+12x^5+9x^5-6x^4-12x^4+3x^3+6x^3-3x^2\\A.B=9x^6+21x^5-18x^4+9x^3-3x^2](https://tex.z-dn.net/?f=A.B%3D3x%5E3%28-3x%5E3%2B4x%5E2-2x%2B1%29-3x%5E2%28-3x%5E3%2B4x%5E2-2x%2B1%29%5C%5CA.B%3D9x%5E6%2B12x%5E5-6x%5E4%2B3x%5E3%2B9x%5E5-12x%5E4%2B6x%5E3-3x%5E2%5C%5CA.B%3D9x%5E6%2B12x%5E5%2B9x%5E5-6x%5E4-12x%5E4%2B3x%5E3%2B6x%5E3-3x%5E2%5C%5CA.B%3D9x%5E6%2B21x%5E5-18x%5E4%2B9x%5E3-3x%5E2)
So, we get ![\mathbf{A.B=9x^6+21x^5-18x^4+9x^3-3x^2}](https://tex.z-dn.net/?f=%5Cmathbf%7BA.B%3D9x%5E6%2B21x%5E5-18x%5E4%2B9x%5E3-3x%5E2%7D)
So, Is the result of A.B is a polynomial:Yes
10 is not a perfect square however 100 is. This is because a square is defined as numbers that are the product of another whole number when multiplied by itself. So, 10x10=100, making 100 a perfect square. However, no number multiplied by itself equals 10, meaning 10 is NOT a perfect square.
Answer:
The area is 6.5 square meters
Step-by-step explanation
Hope this helps!