Answer:
- 4x² + 6x - 3 remainder -12
Step-by-step explanation:
<u>Given:</u>
- (x) = 8x³ + 16x² − 15
- g(x) = 2x + 1
<u>To find:</u>
<u>Use long division:</u>
- (8x³ + 16x² − 15) / (2x + 1)
2x + 1 | (8x³ + 16x² − 15
<u>| 8x³ + 4x²</u>
12x² + 0x - 15
<u>12x² + 6x</u>
-6x - 15
<u>-6x - 3</u>
-12
4x² + 6x - 3 remainder -12
Answer:
Step-by-step explanation:
1)
------- ( 1 )
![= 4^2 + (2\sqrt6)^2\\\\=16 + (4 \times 6)\\\\= 16 + 24\\\\= 40](https://tex.z-dn.net/?f=%3D%204%5E2%20%2B%20%282%5Csqrt6%29%5E2%5C%5C%5C%5C%3D16%20%2B%20%284%20%5Ctimes%206%29%5C%5C%5C%5C%3D%2016%20%2B%2024%5C%5C%5C%5C%3D%2040)
![AB = \sqrt {40} = \sqrt {4 \times 10} = 2\sqrt{10}](https://tex.z-dn.net/?f=AB%20%3D%20%5Csqrt%20%7B40%7D%20%3D%20%5Csqrt%20%7B4%20%5Ctimes%2010%7D%20%3D%202%5Csqrt%7B10%7D)
2)
--------------( 2 )
![=(2 \sqrt6)^2 + 6^2 \\\\= 24 + 36\\\\=60](https://tex.z-dn.net/?f=%3D%282%20%5Csqrt6%29%5E2%20%2B%206%5E2%20%5C%5C%5C%5C%3D%2024%20%2B%2036%5C%5C%5C%5C%3D60)
![AC= \sqrt{60} = \sqrt{4 \times 15} = 2 \sqrt{15}](https://tex.z-dn.net/?f=AC%3D%20%5Csqrt%7B60%7D%20%3D%20%5Csqrt%7B4%20%5Ctimes%2015%7D%20%3D%202%20%5Csqrt%7B15%7D)
3)
BC² = AB² + AC²
(4 + 6)² = 40 + 60
100 = 100
Satisfies Pythagoras Theorem, therefore triangle ABC is right angles triangle.
Answer: (d)
Step-by-step explanation:
Given
Annual profit is given by
![P=10x^2-280x+1600](https://tex.z-dn.net/?f=P%3D10x%5E2-280x%2B1600)
When it is factored then,
![\Rightarrow 10x^2-280x+1600=0\\\Rightarrow 10\left( x^2-28x+160\right)=0\\\Rightarrow x^2-20x-8x+160=0\\\Rightarrow x(x-20)-8(x-20)=0\\\Rightarrow (x-8)(x-20)=0\\\Rightarrow x=8,20](https://tex.z-dn.net/?f=%5CRightarrow%2010x%5E2-280x%2B1600%3D0%5C%5C%5CRightarrow%2010%5Cleft%28%20x%5E2-28x%2B160%5Cright%29%3D0%5C%5C%5CRightarrow%20x%5E2-20x-8x%2B160%3D0%5C%5C%5CRightarrow%20x%28x-20%29-8%28x-20%29%3D0%5C%5C%5CRightarrow%20%28x-8%29%28x-20%29%3D0%5C%5C%5CRightarrow%20x%3D8%2C20)
On factorization, we get that annual profit is zero at a whole prize of $8 and $20.
First you divide 380 by 100 to get what 1% is, (3.8) and then you multiply by 18 to give you 18%. The answer is 68.4, so add that to 380 and you'll have the final answer of 448.4.