Answers:
B = 50
a = 10.9
c = 17.0
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Explanation:
This is a right triangle, so the acute angles are complementary, meaning they add to 90
B+40 = 90
B+40-40 = 90-40
B = 50
Also, because this is a right triangle, we can use trig ratios to compute the missing sides
tan(angle) = opposite/adjacent
tan(40) = a/13
a = 13*tan(40)
a = 10.908
a = 10.9
cos(angle) = adjacent/hypotenuse
cos(40) = 13/c
c*cos(40) = 13
c = 13/cos(40)
c = 17.0
note: make sure your calculator is in degree mode
Hello,
Your answer would be:
2=2
Your explanation/work would be:
7(2) - 12 = 8(2) - 14
14 - 12 = 16 - 14
2 = 2
Plz mark me brainliest
Answer:
500 divided by 10 = 50
Step-by-step explanation:
quotient means the answer of a division problem 50 is the quotient of 500 being divided by 10
No solution simply because the expression cannot be solved with rational numbers
Answer:
![(x-1)(2x^2+x+2)](https://tex.z-dn.net/?f=%28x-1%29%282x%5E2%2Bx%2B2%29)
Step-by-step explanation:
Factorize:
![f(x)=2x^3-x^2+x-2](https://tex.z-dn.net/?f=f%28x%29%3D2x%5E3-x%5E2%2Bx-2)
<u>Factor Theorem</u>
If f(a) = 0 for a polynomial then (x - a) is a factor of the polynomial f(x).
Substitute x = 1 into the function:
![\implies f(1)=2(1)^3-1^2+1-2=0](https://tex.z-dn.net/?f=%5Cimplies%20f%281%29%3D2%281%29%5E3-1%5E2%2B1-2%3D0)
Therefore, (x - 1) is a factor.
As the polynomial is cubic:
![\implies f(x)=(x-1)(ax^2+bx+c)](https://tex.z-dn.net/?f=%5Cimplies%20%20f%28x%29%3D%28x-1%29%28ax%5E2%2Bbx%2Bc%29)
Expanding the brackets:
![\implies f(x)=ax^3+bx^2+cx-ax^2-bx-c](https://tex.z-dn.net/?f=%5Cimplies%20%20f%28x%29%3Dax%5E3%2Bbx%5E2%2Bcx-ax%5E2-bx-c)
![\implies f(x)=ax^3+(b-a)x^2+(c-b)x-c](https://tex.z-dn.net/?f=%5Cimplies%20%20f%28x%29%3Dax%5E3%2B%28b-a%29x%5E2%2B%28c-b%29x-c)
Comparing coefficients with the original polynomial:
![\implies ax^3=2x^3 \implies a=2](https://tex.z-dn.net/?f=%5Cimplies%20ax%5E3%3D2x%5E3%20%5Cimplies%20a%3D2)
![\implies (b-a)x^2=-x^2 \implies b-2=-1 \implies b=1](https://tex.z-dn.net/?f=%5Cimplies%20%28b-a%29x%5E2%3D-x%5E2%20%5Cimplies%20b-2%3D-1%20%5Cimplies%20b%3D1)
![\implies -c=-2 \implies c=2](https://tex.z-dn.net/?f=%5Cimplies%20-c%3D-2%20%5Cimplies%20c%3D2)
Therefore:
![\implies f(x)=(x-1)(2x^2+x+2)](https://tex.z-dn.net/?f=%5Cimplies%20%20f%28x%29%3D%28x-1%29%282x%5E2%2Bx%2B2%29)
Cannot be factored any further.