we know that
A quadratic equation is a polynomial with an order of two. Its general form is
![ax^{2} + bx + c = 0](https://tex.z-dn.net/?f=%20ax%5E%7B2%7D%20%2B%20bx%20%2B%20c%20%3D%200%20%20%20)
case a) ![6(x + 2)^{2} + 8x + 2 + 1 = 0](https://tex.z-dn.net/?f=%206%28x%20%2B%202%29%5E%7B2%7D%20%2B%208x%20%2B%202%20%2B%201%20%3D%200%20)
![6(x + 2)^{2} + 8x + 2 + 1 = 0 \\ 6(x^{2} +4x+4)+8x+3=0\\ 6x^{2} +24x+24+8x+3=0\\ 6x^{2} +32x+27=0\\\\ a=6\\ b=32\\ c=27](https://tex.z-dn.net/?f=%206%28x%20%2B%202%29%5E%7B2%7D%20%2B%208x%20%2B%202%20%2B%201%20%3D%200%20%5C%5C%206%28x%5E%7B2%7D%20%2B4x%2B4%29%2B8x%2B3%3D0%5C%5C%206x%5E%7B2%7D%20%2B24x%2B24%2B8x%2B3%3D0%5C%5C%206x%5E%7B2%7D%20%2B32x%2B27%3D0%5C%5C%5C%5C%20a%3D6%5C%5C%20%20b%3D32%5C%5C%20c%3D27%20)
<u>The case a) is a quadratic equation</u>
case b) ![6x^{4} + 7x^{2} - 3 = 0](https://tex.z-dn.net/?f=%206x%5E%7B4%7D%20%2B%207x%5E%7B2%7D%20-%203%20%3D%200%20%20%20)
<u>The case b) is a grade
polynomial</u>
case c) ![5x^{6} + x^{4} + 12 = 0](https://tex.z-dn.net/?f=%205x%5E%7B6%7D%20%2B%20x%5E%7B4%7D%20%2B%2012%20%3D%200%20%20%20)
<u>The case c) is a grade
polynomial</u>
case d) ![x^{9} + x^{3} - 10 = 0](https://tex.z-dn.net/?f=%20x%5E%7B9%7D%20%2B%20x%5E%7B3%7D%20-%2010%20%3D%200%20%20%20)
<u>The case d) is a grade
polynomial</u>
therefore
the answer is
![6(x + 2)^{2} + 8x + 2 + 1 = 0](https://tex.z-dn.net/?f=%206%28x%20%2B%202%29%5E%7B2%7D%20%2B%208x%20%2B%202%20%2B%201%20%3D%200%20)
The climber used 9 rope lengths to complete her descent.
To solve this, simply divide the length of the rope by the distance to the base of the cliff. The resulting number will be the number of rope lengths she used.
585 / 65 = 9
Hope this helps. Good luck! :)
Answer:
The answer is: Volume = 320
Step-by-step explanation:
5 × 8 × 8 = 320
![\sum\limits_{i=3}^{10}\big i^2](https://tex.z-dn.net/?f=%5Csum%5Climits_%7Bi%3D3%7D%5E%7B10%7D%5Cbig%20i%5E2)
or:
![\sum\limits_{i=1}^{8}\left(2+i\right)^2](https://tex.z-dn.net/?f=%5Csum%5Climits_%7Bi%3D1%7D%5E%7B8%7D%5Cleft%282%2Bi%5Cright%29%5E2)
or:
x₁=3, x₂=4, x₃=5, .... x₈=10
![\sum\limits_{i=1}^{8}\big x_i^2](https://tex.z-dn.net/?f=%5Csum%5Climits_%7Bi%3D1%7D%5E%7B8%7D%5Cbig%20x_i%5E2)
Answer:
100
Step-by-step explanation:
2:3:5
20:30:50
20 + 30 + 50 = 50 + 50 = 100