3s is 3 times sydneys age. so the equation would be 3s-5
Answer: LAST OPTION.
Step-by-step explanation:
1. You have the following equation:
![6x^{2}=54](https://tex.z-dn.net/?f=6x%5E%7B2%7D%3D54)
2. Then you must solve for x, as following:
![x^{2}=54/6\\x^{2}=9\\x=\sqrt{9}\\x=+/-3](https://tex.z-dn.net/?f=x%5E%7B2%7D%3D54%2F6%5C%5Cx%5E%7B2%7D%3D9%5C%5Cx%3D%5Csqrt%7B9%7D%5C%5Cx%3D%2B%2F-3)
Therefore, as you can see above, the answer for the exercise is the last option.
Answer:
Tan x= 3/4 Cos x= 4/5 Sin x=3/5
Step-by-step explanation:
"soh-cah-toa"
Just an easy way to remember how Sine, Cosine and Tangent work:
Soh...
Sine = Opposite / Hypotenuse
...cah...
Cosine = Adjacent / Hypotenuse
...toa
Tangent = Opposite / Adjacent
Answer:
Error of Andrew: Made incorrect factors from the roots
Step-by-step explanation:
Roots of the polynomial are: 3, 2 + 2i, 2 - 2i. According to the factor theorem, if a is a root of the polynomial P(x), then (x - a) is a factor of P(x). According to this definition:
(x - 3) , (x - (2 + 2i)) , (x - (2 - 2i)) are factors of the required polynomial.
Simplifying the brackets, we get:
(x - 3), (x - 2 - 2i), (x - 2 + 2i) are factors of the required polynomial.
This is the step where Andrew made the error. The factors will always be of the form (x - a) , not (x + a). Andrew wrote the complex factors in form of (x + a) which resulted in the wrong answer.
So, the polynomial would be:
![(x - 3)(x - 2 - 2i)(x - 2+2i)=0\\\\ (x-3)(x^{2}-2x+2xi-2x+4-4i-2xi+4i-4i^{2})=0\\\\ (x-3)(x^{2}-4x+4+4)=0\\\\ (x-3)(x^{2}-4x+8)=0\\\\ x^{3}-4x^{2}+8x-3x^{2}+12x-24=0\\\\ x^{3}-7x^{2}+20x-24=0](https://tex.z-dn.net/?f=%28x%20-%203%29%28x%20-%202%20-%202i%29%28x%20-%202%2B2i%29%3D0%5C%5C%5C%5C%20%28x-3%29%28x%5E%7B2%7D-2x%2B2xi-2x%2B4-4i-2xi%2B4i-4i%5E%7B2%7D%29%3D0%5C%5C%5C%5C%20%28x-3%29%28x%5E%7B2%7D-4x%2B4%2B4%29%3D0%5C%5C%5C%5C%20%28x-3%29%28x%5E%7B2%7D-4x%2B8%29%3D0%5C%5C%5C%5C%20x%5E%7B3%7D-4x%5E%7B2%7D%2B8x-3x%5E%7B2%7D%2B12x-24%3D0%5C%5C%5C%5C%20x%5E%7B3%7D-7x%5E%7B2%7D%2B20x-24%3D0)
You know that 3 times 2 is 6 so 30'times 20 equals 60