1) f(x)=2x
when x=3 then f(x) =3×2=<em><u>6</u></em>
when x=4 then f(x)=4×2=<em><u>8</u></em>
2)At y=35(no. of mangoes),x corresponds to y=60(amount)
so$<em><u>6</u></em><em><u>0</u></em><em><u>,</u></em><em><u> </u></em><em><u>amount</u></em><em><u> </u></em><em><u>he</u></em><em><u> </u></em><em><u>need</u></em><em><u> </u></em><em><u>to</u></em><em><u> </u></em><em><u>spend</u></em><em><u>!</u></em>
3) f(x)= x+2
for x=1, f(x)=1+2=<em><u>3</u></em>
for x=2,f(x)=2+2=<em><u>4</u></em>
✌️:)
Answer: 27/50
Explanation
If
, then by rationalizing the denominator we can rewrite
![b = \dfrac1{\sqrt3-\sqrt{11}} \times \dfrac{\sqrt3+\sqrt{11}}{\sqrt3+\sqrt{11}} = \dfrac{\sqrt3+\sqrt{11}}{\left(\sqrt3\right)^2-\left(\sqrt{11}\right)^2} = -\dfrac{\sqrt3+\sqrt{11}}8](https://tex.z-dn.net/?f=b%20%3D%20%5Cdfrac1%7B%5Csqrt3-%5Csqrt%7B11%7D%7D%20%5Ctimes%20%5Cdfrac%7B%5Csqrt3%2B%5Csqrt%7B11%7D%7D%7B%5Csqrt3%2B%5Csqrt%7B11%7D%7D%20%3D%20%5Cdfrac%7B%5Csqrt3%2B%5Csqrt%7B11%7D%7D%7B%5Cleft%28%5Csqrt3%5Cright%29%5E2-%5Cleft%28%5Csqrt%7B11%7D%5Cright%29%5E2%7D%20%3D%20-%5Cdfrac%7B%5Csqrt3%2B%5Csqrt%7B11%7D%7D8)
Now,
![a^2 - b^2 = (a-b) (a+b)](https://tex.z-dn.net/?f=a%5E2%20-%20b%5E2%20%3D%20%28a-b%29%20%28a%2Bb%29)
and
![a - b = \sqrt3 - \sqrt{11} + \dfrac{\sqrt3 + \sqrt{11}}8 = \dfrac{9\sqrt3 - 7\sqrt{11}}8](https://tex.z-dn.net/?f=a%20-%20b%20%3D%20%5Csqrt3%20-%20%5Csqrt%7B11%7D%20%2B%20%5Cdfrac%7B%5Csqrt3%20%2B%20%5Csqrt%7B11%7D%7D8%20%3D%20%5Cdfrac%7B9%5Csqrt3%20-%207%5Csqrt%7B11%7D%7D8)
![a + b = \sqrt3 - \sqrt{11} - \dfrac{\sqrt3 + \sqrt{11}}8 = \dfrac{7\sqrt3 - 9\sqrt{11}}8](https://tex.z-dn.net/?f=a%20%2B%20b%20%3D%20%5Csqrt3%20-%20%5Csqrt%7B11%7D%20-%20%5Cdfrac%7B%5Csqrt3%20%2B%20%5Csqrt%7B11%7D%7D8%20%3D%20%5Cdfrac%7B7%5Csqrt3%20-%209%5Csqrt%7B11%7D%7D8)
![\implies a^2 - b^2 = \dfrac{\left(9\sqrt3 - 7\sqrt{11}\right) \left(7\sqrt3 - 9\sqrt{11}\right)}{64} = \boxed{\dfrac{441 - 65\sqrt{33}}{32}}](https://tex.z-dn.net/?f=%5Cimplies%20a%5E2%20-%20b%5E2%20%3D%20%5Cdfrac%7B%5Cleft%289%5Csqrt3%20-%207%5Csqrt%7B11%7D%5Cright%29%20%5Cleft%287%5Csqrt3%20-%209%5Csqrt%7B11%7D%5Cright%29%7D%7B64%7D%20%3D%20%5Cboxed%7B%5Cdfrac%7B441%20-%2065%5Csqrt%7B33%7D%7D%7B32%7D%7D)
Answer:
![36xy^2 + 8x^2 + 27y^2 + 6x](https://tex.z-dn.net/?f=36xy%5E2%20%2B%208x%5E2%20%2B%2027y%5E2%20%2B%206x)
Step-by-step explanation:
Use the FOIL method of multiplying binomials.
First term in each binomial: ![-2x * -4x = 8x^2](https://tex.z-dn.net/?f=-2x%20%2A%20-4x%20%3D%208x%5E2)
Outside terms: ![-2x * -3 = 6x](https://tex.z-dn.net/?f=-2x%20%2A%20-3%20%3D%206x)
Inside terms: ![-9y^2 * -4x = 36xy^2](https://tex.z-dn.net/?f=-9y%5E2%20%2A%20-4x%20%3D%2036xy%5E2)
Last term in each binomial: ![-9y^2 * -3 = 27y^2](https://tex.z-dn.net/?f=-9y%5E2%20%2A%20-3%20%3D%2027y%5E2)
Now, rearrange the terms correctly. ![36xy^2 + 8x^2 + 27y^2 + 6x](https://tex.z-dn.net/?f=36xy%5E2%20%2B%208x%5E2%20%2B%2027y%5E2%20%2B%206x)
This is our final answer, since it can not be simplified any more.