B. (n + 15) x 3--- That seems to be the correct answer. I hope I helped!
Answer:
Part 1) ![x^{2} -2x-2=(x-1-\sqrt{3})(x-1+\sqrt{3})](https://tex.z-dn.net/?f=x%5E%7B2%7D%20-2x-2%3D%28x-1-%5Csqrt%7B3%7D%29%28x-1%2B%5Csqrt%7B3%7D%29)
Part 2) ![x^{2} -6x+4=(x-3-\sqrt{5})(x-3+\sqrt{5})](https://tex.z-dn.net/?f=x%5E%7B2%7D%20-6x%2B4%3D%28x-3-%5Csqrt%7B5%7D%29%28x-3%2B%5Csqrt%7B5%7D%29)
Step-by-step explanation:
we know that
The formula to solve a quadratic equation of the form
![ax^{2} +bx+c=0](https://tex.z-dn.net/?f=ax%5E%7B2%7D%20%2Bbx%2Bc%3D0)
is equal to
![x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-b%28%2B%2F-%29%5Csqrt%7Bb%5E%7B2%7D-4ac%7D%7D%20%7B2a%7D)
Part 1)
in this problem we have
![x^{2} -2x-2=0](https://tex.z-dn.net/?f=x%5E%7B2%7D%20-2x-2%3D0)
so
![a=1\\b=-2\\c=-2](https://tex.z-dn.net/?f=a%3D1%5C%5Cb%3D-2%5C%5Cc%3D-2)
substitute in the formula
![x=\frac{-(-2)(+/-)\sqrt{-2^{2}-4(1)(-2)}} {2(1)}\\\\x=\frac{2(+/-)\sqrt{12}} {2}\\\\x=\frac{2(+/-)2\sqrt{3}} {2}\\\\x_1=\frac{2(+)2\sqrt{3}} {2}=1+\sqrt{3}\\\\x_2=\frac{2(-)2\sqrt{3}} {2}=1-\sqrt{3}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-%28-2%29%28%2B%2F-%29%5Csqrt%7B-2%5E%7B2%7D-4%281%29%28-2%29%7D%7D%20%7B2%281%29%7D%5C%5C%5C%5Cx%3D%5Cfrac%7B2%28%2B%2F-%29%5Csqrt%7B12%7D%7D%20%7B2%7D%5C%5C%5C%5Cx%3D%5Cfrac%7B2%28%2B%2F-%292%5Csqrt%7B3%7D%7D%20%7B2%7D%5C%5C%5C%5Cx_1%3D%5Cfrac%7B2%28%2B%292%5Csqrt%7B3%7D%7D%20%7B2%7D%3D1%2B%5Csqrt%7B3%7D%5C%5C%5C%5Cx_2%3D%5Cfrac%7B2%28-%292%5Csqrt%7B3%7D%7D%20%7B2%7D%3D1-%5Csqrt%7B3%7D)
therefore
![x^{2} -2x-2=(x-(1+\sqrt{3}))(x-(1-\sqrt{3}))](https://tex.z-dn.net/?f=x%5E%7B2%7D%20-2x-2%3D%28x-%281%2B%5Csqrt%7B3%7D%29%29%28x-%281-%5Csqrt%7B3%7D%29%29)
![x^{2} -2x-2=(x-1-\sqrt{3})(x-1+\sqrt{3})](https://tex.z-dn.net/?f=x%5E%7B2%7D%20-2x-2%3D%28x-1-%5Csqrt%7B3%7D%29%28x-1%2B%5Csqrt%7B3%7D%29)
Part 2)
in this problem we have
![x^{2} -6x+4=0](https://tex.z-dn.net/?f=x%5E%7B2%7D%20-6x%2B4%3D0)
so
![a=1\\b=-6\\c=4](https://tex.z-dn.net/?f=a%3D1%5C%5Cb%3D-6%5C%5Cc%3D4)
substitute in the formula
![x=\frac{-(-6)(+/-)\sqrt{-6^{2}-4(1)(4)}} {2(1)}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-%28-6%29%28%2B%2F-%29%5Csqrt%7B-6%5E%7B2%7D-4%281%29%284%29%7D%7D%20%7B2%281%29%7D)
![x=\frac{6(+/-)\sqrt{20}} {2}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B6%28%2B%2F-%29%5Csqrt%7B20%7D%7D%20%7B2%7D)
![x=\frac{6(+/-)2\sqrt{5}} {2}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B6%28%2B%2F-%292%5Csqrt%7B5%7D%7D%20%7B2%7D)
![x_1=\frac{6(+)2\sqrt{5}}{2}=3+\sqrt{5}](https://tex.z-dn.net/?f=x_1%3D%5Cfrac%7B6%28%2B%292%5Csqrt%7B5%7D%7D%7B2%7D%3D3%2B%5Csqrt%7B5%7D)
![x_2=\frac{6(-)2\sqrt{5}}{2}=3-\sqrt{5}](https://tex.z-dn.net/?f=x_2%3D%5Cfrac%7B6%28-%292%5Csqrt%7B5%7D%7D%7B2%7D%3D3-%5Csqrt%7B5%7D)
therefore
![x^{2} -6x+4=(x-(3+\sqrt{5}))(x-(3-\sqrt{5}))](https://tex.z-dn.net/?f=x%5E%7B2%7D%20-6x%2B4%3D%28x-%283%2B%5Csqrt%7B5%7D%29%29%28x-%283-%5Csqrt%7B5%7D%29%29)
![x^{2} -6x+4=(x-3-\sqrt{5})(x-3+\sqrt{5})](https://tex.z-dn.net/?f=x%5E%7B2%7D%20-6x%2B4%3D%28x-3-%5Csqrt%7B5%7D%29%28x-3%2B%5Csqrt%7B5%7D%29)
Answer:
no solution
Step-by-step explanation:
ya gotta use your eyes and brain huney. it aint that hard. kk? but ill still explain for you.
since x+y=6 and x+y=4. then 4=6. but that is false so no solution.
YOUR WELCOME!
The price of the laptop = $299.99
Given, sales tax = 6%
To find the amount for sales tax we have to find 6% of $299.99.
So the amount of sales tax =
6% of $299.99 = 299.99×(6/100) = (299.99×6)/100
= 1799.94/100 = 17.9994
So we have got sales tax = $17.9994
Therefore, the total cost for laptop including sales tax is selling price of laptop + sales tax.
Total cost for laptop = $299.99+$17.9994 = $317.9894
We have got the required answer.
Total cost for laptop is $317.9894
Answer:
The distance between the given points (2,10) and (-6, 4) on the coordinate plane is 10units
Therefore distance s=10 units
Step-by-step explanation:
Given points are (2,10) and (-6, 4) on the coordinate plane
To distance between the given points :
The distance formula is
units
Let
,
be the given points (2,10) and (-6, 4) respectively
Now substituting the values in the distance formula we get
![=\sqrt{8^2+6^2}](https://tex.z-dn.net/?f=%3D%5Csqrt%7B8%5E2%2B6%5E2%7D)
![=\sqrt{64+36}](https://tex.z-dn.net/?f=%3D%5Csqrt%7B64%2B36%7D)
![=\sqrt{100}](https://tex.z-dn.net/?f=%3D%5Csqrt%7B100%7D)
![=10](https://tex.z-dn.net/?f=%3D10)
Therefore s=10 units
The distance between the given points (2,10) and (-6, 4) on the coordinate plane is 10units