Y = |x| - 2. Nothing too complicated for this transformation
Answer:
i am pretty sure the answer is b
Step-by-step explanation:
hope this helps :)
<h2>
Answer:</h2>
The possible formula for a fourth degree polynomial g is:
![g(x)=\dfrac{1}{4}(x^4-3x^3-12x^2+20x+48)](https://tex.z-dn.net/?f=g%28x%29%3D%5Cdfrac%7B1%7D%7B4%7D%28x%5E4-3x%5E3-12x%5E2%2B20x%2B48%29)
<h2>
Step-by-step explanation:</h2>
We know that if a polynomial has zeros as a,b,c and d then the possible polynomial form is given by:
![f(x)=m(x-a)(x-b)(x-c)(x-d)](https://tex.z-dn.net/?f=f%28x%29%3Dm%28x-a%29%28x-b%29%28x-c%29%28x-d%29)
Here the polynomial g has a double zero at -2, g(4) = 0, g(3) = 0.
This means that the polynomial g(x) is given by:
![g(x)=m(x-(-2))^2(x-4)(x-3)\\\\i.e.\\\\g(x)=m(x+2)^2(x-4)(x-3)\\\\i.e.\\\\g(x)=m(x^2+2^2+2\times 2\times x)(x(x-3)-4(x-3))\\\\i.e.\\\\g(x)=m(x^2+4+4x)(x^2-3x-4x+12)\\\\i.e.\\\\g(x)=m(x^2+4+4x)(x^2-7x+12)\\\\i.e.\\\\g(x)=m[x^2(x^2-7x+12)+4(x^2-7x+12)+4x(x^2-7x+12)]\\\\i.e.\\\\g(x)=m[x^4-7x^3+12x^2+4x^2-28x+48+4x^3-28x^2+48x]\\\\i.e.\\\\g(x)=m[x^4-7x^3+4x^3+12x^2+4x^2-28x^2-28x+48x+48]\\\\i.e.\\\\g(x)=m[x^4-3x^3-12x^2+20x+48]](https://tex.z-dn.net/?f=g%28x%29%3Dm%28x-%28-2%29%29%5E2%28x-4%29%28x-3%29%5C%5C%5C%5Ci.e.%5C%5C%5C%5Cg%28x%29%3Dm%28x%2B2%29%5E2%28x-4%29%28x-3%29%5C%5C%5C%5Ci.e.%5C%5C%5C%5Cg%28x%29%3Dm%28x%5E2%2B2%5E2%2B2%5Ctimes%202%5Ctimes%20x%29%28x%28x-3%29-4%28x-3%29%29%5C%5C%5C%5Ci.e.%5C%5C%5C%5Cg%28x%29%3Dm%28x%5E2%2B4%2B4x%29%28x%5E2-3x-4x%2B12%29%5C%5C%5C%5Ci.e.%5C%5C%5C%5Cg%28x%29%3Dm%28x%5E2%2B4%2B4x%29%28x%5E2-7x%2B12%29%5C%5C%5C%5Ci.e.%5C%5C%5C%5Cg%28x%29%3Dm%5Bx%5E2%28x%5E2-7x%2B12%29%2B4%28x%5E2-7x%2B12%29%2B4x%28x%5E2-7x%2B12%29%5D%5C%5C%5C%5Ci.e.%5C%5C%5C%5Cg%28x%29%3Dm%5Bx%5E4-7x%5E3%2B12x%5E2%2B4x%5E2-28x%2B48%2B4x%5E3-28x%5E2%2B48x%5D%5C%5C%5C%5Ci.e.%5C%5C%5C%5Cg%28x%29%3Dm%5Bx%5E4-7x%5E3%2B4x%5E3%2B12x%5E2%2B4x%5E2-28x%5E2-28x%2B48x%2B48%5D%5C%5C%5C%5Ci.e.%5C%5C%5C%5Cg%28x%29%3Dm%5Bx%5E4-3x%5E3-12x%5E2%2B20x%2B48%5D)
Also,
![g(0)=12](https://tex.z-dn.net/?f=g%280%29%3D12)
i.e.
![48m=12\\\\i.e.\\\\m=\dfrac{12}{48}\\\\i.e.\\\\m=\dfrac{1}{4}](https://tex.z-dn.net/?f=48m%3D12%5C%5C%5C%5Ci.e.%5C%5C%5C%5Cm%3D%5Cdfrac%7B12%7D%7B48%7D%5C%5C%5C%5Ci.e.%5C%5C%5C%5Cm%3D%5Cdfrac%7B1%7D%7B4%7D)
Hence, the polynomial g(x) is given by:
![g(x)=\dfrac{1}{4}(x^4-3x^3-12x^2+20x+48)](https://tex.z-dn.net/?f=g%28x%29%3D%5Cdfrac%7B1%7D%7B4%7D%28x%5E4-3x%5E3-12x%5E2%2B20x%2B48%29)
Answer:
A Rs. 500 note, and four Rs. 100 notes.
Step-by-step explanation:
The cost of the two shoes = Rs.1,300 + Rs. 1,800
= Rs. 3,100
He gave 4 notes of Rs. 1,000 = 4 x Rs. 1,000
= Rs. 4,000
Manoj's expected change = Rs. 4,000 - Rs. 3,100
= Rs. 900
Since he was returned 5 notes in the denominations of Rs. 500 and Rs. 100, then;
Rs. 500 + Rs. 100 + Rs. 100 + Rs. 100 + Rs. 100 = Rs. 900
Therefore, Manaoj was returned a Rs. 500 note, and four Rs. 100 notes.
Answer:
C. 3x^2 +7x -2
Step-by-step explanation:
(x^2 +4x +2) + (2x^2 +3x -4) = x^2+ 2x^2+ 4x+ 3x+ 2- 4
= 3x^2 +7x -2