Answer:
a. attached graph; zero real: 2
b. p(x) = (x - 2)(x + 3 + 3i)(x + 3 - 3i)
c. the solutions are 2, -3-3i and -3+3i
Step-by-step explanation:
p(x) = x³ + 4x² + 6x - 36
a. Through the graph, we can see that 2 is a real zero of the polynomial p. We can also use the Rational Roots Test.
p(2) = 2³ + 4.2² + 6.2 - 36 = 8 + 16 + 12 - 36 = 0
b. Now, we can use Briott-Ruffini to find the other roots and write p as a product of linear factors.
2 | 1 4 6 -36
1 6 18 0
x² + 6x + 18 = 0
Δ = 6² - 4.1.18 = 36 - 72 = -36 = 36i²
√Δ = 6i
x = -6±6i/2 = 2(-3±3i)/2
x' = -3-3i
x" = -3+3i
p(x) = (x - 2)(x + 3 + 3i)(x + 3 - 3i)
c. the solutions are 2, -3-3i and -3+3i
Answer:
![\large\boxed{x=\dfrac{17}{10}=1.7}](https://tex.z-dn.net/?f=%5Clarge%5Cboxed%7Bx%3D%5Cdfrac%7B17%7D%7B10%7D%3D1.7%7D)
Step-by-step explanation:
![8=2^3\\\\\dfrac{1}{16}=\dfrac{1}{2^4}=2^{-4}\qquad\text{used}\ a^{-n}=\dfrac{1}{a^n}\\\\8^{2x-3}=\left(\dfrac{1}{16}\right)^{x-2}\\\\(2^3)^{2x-3}=(2^{-4})^{x-2}\qquad\text{use}\ (a^n)^m=a^{nm}\\\\2^{3(2x-3)}=2^{-4(x-2)}\iff3(2x-3)=-4(x-2)\\\\\text{use the distributive property}\ a(b+c)=ab+ac\\\\(3)(2x)+(3)(-3)=(-4)(x)+(-4)(-2)\\\\6x-9=-4x+8\qquad\text{add 9 to both sides}\\\\6x=-4x+17\qquad\text{add 4x to both sides}\\\\10x=17\qquad\text{divide both sides by 10}\\\\x=1.7](https://tex.z-dn.net/?f=8%3D2%5E3%5C%5C%5C%5C%5Cdfrac%7B1%7D%7B16%7D%3D%5Cdfrac%7B1%7D%7B2%5E4%7D%3D2%5E%7B-4%7D%5Cqquad%5Ctext%7Bused%7D%5C%20a%5E%7B-n%7D%3D%5Cdfrac%7B1%7D%7Ba%5En%7D%5C%5C%5C%5C8%5E%7B2x-3%7D%3D%5Cleft%28%5Cdfrac%7B1%7D%7B16%7D%5Cright%29%5E%7Bx-2%7D%5C%5C%5C%5C%282%5E3%29%5E%7B2x-3%7D%3D%282%5E%7B-4%7D%29%5E%7Bx-2%7D%5Cqquad%5Ctext%7Buse%7D%5C%20%28a%5En%29%5Em%3Da%5E%7Bnm%7D%5C%5C%5C%5C2%5E%7B3%282x-3%29%7D%3D2%5E%7B-4%28x-2%29%7D%5Ciff3%282x-3%29%3D-4%28x-2%29%5C%5C%5C%5C%5Ctext%7Buse%20the%20distributive%20property%7D%5C%20a%28b%2Bc%29%3Dab%2Bac%5C%5C%5C%5C%283%29%282x%29%2B%283%29%28-3%29%3D%28-4%29%28x%29%2B%28-4%29%28-2%29%5C%5C%5C%5C6x-9%3D-4x%2B8%5Cqquad%5Ctext%7Badd%209%20to%20both%20sides%7D%5C%5C%5C%5C6x%3D-4x%2B17%5Cqquad%5Ctext%7Badd%204x%20to%20both%20sides%7D%5C%5C%5C%5C10x%3D17%5Cqquad%5Ctext%7Bdivide%20both%20sides%20by%2010%7D%5C%5C%5C%5Cx%3D1.7)
Alwyas choose c When your doubting your abilities
Answer:
mark me brainliest
Step-by-step explanation: the answer is ####### good luck !!! :D i have done this before dont worry lol
well, let's split the hours in minutes, so since 1 hr is 60 minutes, so he can walk 2.833 miles in 60 minutes, well, 3 hrs is 3*60 = 180 minutes, then we add 15 minutes, that's 195 minutes.
if he can walk 2.833 miles in 60 minutes, how long will it be for 195 minutes?
![\bf \begin{array}{ccll} miles&minutes\\ \cline{1-2} 2.833&60\\ x&195 \end{array}\implies \cfrac{2.833}{x}=\cfrac{60}{195}\implies \cfrac{2.833}{x}=\cfrac{4}{13} \\\\\\ 36.829=4x\implies \cfrac{36.829}{4}=x\implies 9.20725 = x](https://tex.z-dn.net/?f=%5Cbf%20%5Cbegin%7Barray%7D%7Bccll%7D%20miles%26minutes%5C%5C%20%5Ccline%7B1-2%7D%202.833%2660%5C%5C%20x%26195%20%5Cend%7Barray%7D%5Cimplies%20%5Ccfrac%7B2.833%7D%7Bx%7D%3D%5Ccfrac%7B60%7D%7B195%7D%5Cimplies%20%5Ccfrac%7B2.833%7D%7Bx%7D%3D%5Ccfrac%7B4%7D%7B13%7D%20%5C%5C%5C%5C%5C%5C%2036.829%3D4x%5Cimplies%20%5Ccfrac%7B36.829%7D%7B4%7D%3Dx%5Cimplies%209.20725%20%3D%20x)