Please: Use "^" to denote exponentiation: <span>2x^2 + 8x - 12 = 0
Reduce this by div. every term by 2: </span><span>x^2 + 4x - 6 = 0
Here a=1, b=4 and c = -6. Square half of b, obtaining (4/2)^2 = 4, and add, and then subtract, this 4 to x^2 + 4x - 6:
</span> x^2 + 4x +4 - 4 - 6 = 0. Rewrite the square as (x+2)^2, obtaining new equation
(x+2)^2 = 10. Take the sqrt of both sides: x+2 = plus or minus sqrt(10).
Finally, solve for x: x = -2 plus or minus sqrt(10).
Answer: 30° and 330°
<u>Step-by-step explanation:</u>
sec θ = 
sec θ = 
=
cos θ = 
cos θ = 
cos θ = 
cos θ = 
Look at the Unit Circle to see that cos = at 30° and 330° ( which is equivalent to π/6 and 11π/6)
Answer:
Step-by-step explanation:
Andrew made a mistake at last step.
<u>It should be:</u>
- -11.8 + 9.8 = 9.8 - 11.8 = -2 but not -21.6
Angle Q and angle S equal 61
Step-by-step explanation:
![\bold{40.}\\\\A+B=\left[\begin{array}{ccc}3&1\\5&7\end{array}\right] +\left[\begin{array}{ccc}4&1\\6&0\end{array}\right] =\left[\begin{array}{ccc}3+4&1+1\\5+6&7+0\end{array}\right]=\left[\begin{array}{ccc}7&1\\11&7\end{array}\right]](https://tex.z-dn.net/?f=%5Cbold%7B40.%7D%5C%5C%5C%5CA%2BB%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D3%261%5C%5C5%267%5Cend%7Barray%7D%5Cright%5D%20%2B%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D4%261%5C%5C6%260%5Cend%7Barray%7D%5Cright%5D%20%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D3%2B4%261%2B1%5C%5C5%2B6%267%2B0%5Cend%7Barray%7D%5Cright%5D%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D7%261%5C%5C11%267%5Cend%7Barray%7D%5Cright%5D)
![\bold{41.}\\\\B-A=\left[\begin{array}{ccc}4&1\\6&0\end{array}\right]-\left[\begin{array}{ccc}3&1\\5&7\end{array}\right]=\left[\begin{array}{ccc}4-3&1-1\\6-5&0-7\end{array}\right]=\left[\begin{array}{ccc}1&0\\1&-7\end{array}\right]](https://tex.z-dn.net/?f=%5Cbold%7B41.%7D%5C%5C%5C%5CB-A%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D4%261%5C%5C6%260%5Cend%7Barray%7D%5Cright%5D-%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D3%261%5C%5C5%267%5Cend%7Barray%7D%5Cright%5D%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D4-3%261-1%5C%5C6-5%260-7%5Cend%7Barray%7D%5Cright%5D%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%260%5C%5C1%26-7%5Cend%7Barray%7D%5Cright%5D)
![\bold{42.}\\\\3C=3\left[\begin{array}{ccc}-2&3&1\\-1&0&4\end{array}\right]=\left[\begin{array}{ccc}(3)(-2)&(3)(3)&(3)(1)\\(3)(-1)&(3)(0)&(3)(4)\end{array}\right]=\left[\begin{array}{ccc}-6&9&3\\-3&0&12\end{array}\right]](https://tex.z-dn.net/?f=%5Cbold%7B42.%7D%5C%5C%5C%5C3C%3D3%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-2%263%261%5C%5C-1%260%264%5Cend%7Barray%7D%5Cright%5D%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D%283%29%28-2%29%26%283%29%283%29%26%283%29%281%29%5C%5C%283%29%28-1%29%26%283%29%280%29%26%283%29%284%29%5Cend%7Barray%7D%5Cright%5D%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-6%269%263%5C%5C-3%260%2612%5Cend%7Barray%7D%5Cright%5D)
![\bold{43.}\\\\CD=\left[\begin{array}{ccc}-2&3&1\\-1&0&4\end{array}\right]\left[\begin{array}{ccc}-2&3&4\\0&-2&1\\3&4&-1\end{array}\right]\\\\=\left[\begin{array}{ccc}(-2)(-2)+(3)(0)+(1)(3)&(-2)(3)+(3)(-2)+(1)(4)&(-2)(4)+(3)(1)+(1)(-1)\\(-1)(-2)+(0)(0)+(4)(3)&(-1)(3)+(0)(-2)+(4)(4)&(-1)(4)+(0)(1)+(4)(-1)\end{array}\right]\\\\=\left[\begin{array}{ccc}4+0+1&-6-6+4&-8+3-1\\2+0+12&-3+0+16&-4+0-4\end{array}\right]\\\\=\left[\begin{array}{ccc}5&-8&-6\\14&13&-8\end{array}\right]](https://tex.z-dn.net/?f=%5Cbold%7B43.%7D%5C%5C%5C%5CCD%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-2%263%261%5C%5C-1%260%264%5Cend%7Barray%7D%5Cright%5D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-2%263%264%5C%5C0%26-2%261%5C%5C3%264%26-1%5Cend%7Barray%7D%5Cright%5D%5C%5C%5C%5C%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D%28-2%29%28-2%29%2B%283%29%280%29%2B%281%29%283%29%26%28-2%29%283%29%2B%283%29%28-2%29%2B%281%29%284%29%26%28-2%29%284%29%2B%283%29%281%29%2B%281%29%28-1%29%5C%5C%28-1%29%28-2%29%2B%280%29%280%29%2B%284%29%283%29%26%28-1%29%283%29%2B%280%29%28-2%29%2B%284%29%284%29%26%28-1%29%284%29%2B%280%29%281%29%2B%284%29%28-1%29%5Cend%7Barray%7D%5Cright%5D%5C%5C%5C%5C%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D4%2B0%2B1%26-6-6%2B4%26-8%2B3-1%5C%5C2%2B0%2B12%26-3%2B0%2B16%26-4%2B0-4%5Cend%7Barray%7D%5Cright%5D%5C%5C%5C%5C%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D5%26-8%26-6%5C%5C14%2613%26-8%5Cend%7Barray%7D%5Cright%5D)
![\bold{44.}\\\\2D+3C=2\left[\begin{array}{ccc}-2&3&4\\0&-2&1\\3&4&-1\end{array}\right]+3\left[\begin{array}{ccc}-2&3&1\\-1&0&4\end{array}\right]\\\\=\left[\begin{array}{ccc}(2)(-2)&(2)(3)&(2)(4)\\(2)(0)&(2)(-2)&(2)(1)\\(2)(3)&(2)(4)&(2)(-1)\end{array}\right]+\left[\begin{array}{ccc}(3)(-2)&(3)(3)&(3)(1)\\(3)(-1)&(3)(0)&(3)(4)\end{array}\right]\\\\=\left[\begin{array}{ccc}-4&6&8\\0&-4&2\\6&8&-2\end{array}\right]+\left[\begin{array}{ccc}-6&9&3\\-3&0&12\end{array}\right]](https://tex.z-dn.net/?f=%5Cbold%7B44.%7D%5C%5C%5C%5C2D%2B3C%3D2%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-2%263%264%5C%5C0%26-2%261%5C%5C3%264%26-1%5Cend%7Barray%7D%5Cright%5D%2B3%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-2%263%261%5C%5C-1%260%264%5Cend%7Barray%7D%5Cright%5D%5C%5C%5C%5C%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D%282%29%28-2%29%26%282%29%283%29%26%282%29%284%29%5C%5C%282%29%280%29%26%282%29%28-2%29%26%282%29%281%29%5C%5C%282%29%283%29%26%282%29%284%29%26%282%29%28-1%29%5Cend%7Barray%7D%5Cright%5D%2B%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D%283%29%28-2%29%26%283%29%283%29%26%283%29%281%29%5C%5C%283%29%28-1%29%26%283%29%280%29%26%283%29%284%29%5Cend%7Barray%7D%5Cright%5D%5C%5C%5C%5C%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-4%266%268%5C%5C0%26-4%262%5C%5C6%268%26-2%5Cend%7Barray%7D%5Cright%5D%2B%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-6%269%263%5C%5C-3%260%2612%5Cend%7Barray%7D%5Cright%5D)
