Answer:
x = -1 ± √6
Step-by-step explanation:
![x^{2} +2x - 5 = 0](https://tex.z-dn.net/?f=x%5E%7B2%7D%20%2B2x%20-%205%20%3D%200)
Lets use the quadratic formula → ![x = \frac{-b + \sqrt{b^{2} - 4ac} }{2a} \:or \frac{-b - \sqrt{b^{2}- 4ac } }{2a}](https://tex.z-dn.net/?f=x%20%3D%20%5Cfrac%7B-b%20%2B%20%5Csqrt%7Bb%5E%7B2%7D%20-%204ac%7D%20%7D%7B2a%7D%20%5C%3Aor%20%5Cfrac%7B-b%20-%20%5Csqrt%7Bb%5E%7B2%7D-%204ac%20%7D%20%7D%7B2a%7D)
So ,
![x = \frac{(-2) + \sqrt{(2)^{2} - (4\times1\times-5) } }{2\times1} \:or \frac{(-2) - \sqrt{(2)^{2} - (4\times1\times-5) }}{2\times1}](https://tex.z-dn.net/?f=x%20%3D%20%5Cfrac%7B%28-2%29%20%2B%20%5Csqrt%7B%282%29%5E%7B2%7D%20-%20%284%5Ctimes1%5Ctimes-5%29%20%7D%20%7D%7B2%5Ctimes1%7D%20%5C%3Aor%20%5Cfrac%7B%28-2%29%20-%20%5Csqrt%7B%282%29%5E%7B2%7D%20-%20%284%5Ctimes1%5Ctimes-5%29%20%7D%7D%7B2%5Ctimes1%7D)
![=> x = \frac{-2 + \sqrt{24} }{2} \:or \frac{-2-\sqrt{24} }{2}](https://tex.z-dn.net/?f=%3D%3E%20x%20%3D%20%5Cfrac%7B-2%20%2B%20%5Csqrt%7B24%7D%20%7D%7B2%7D%20%5C%3Aor%20%5Cfrac%7B-2-%5Csqrt%7B24%7D%20%7D%7B2%7D)
![=> x = \frac{-2 + 2\sqrt{6} }{2} \:or \frac{-2 - 2\sqrt{6} }{2}](https://tex.z-dn.net/?f=%3D%3E%20x%20%3D%20%5Cfrac%7B-2%20%2B%202%5Csqrt%7B6%7D%20%7D%7B2%7D%20%5C%3Aor%20%5Cfrac%7B-2%20-%202%5Csqrt%7B6%7D%20%7D%7B2%7D)
Lets take 2 common from numerator.
![=> x = \frac{2(-1 + \sqrt{6}) }{2} \:or \frac{2(-1-\sqrt{6}) }{2}](https://tex.z-dn.net/?f=%3D%3E%20x%20%3D%20%5Cfrac%7B2%28-1%20%2B%20%5Csqrt%7B6%7D%29%20%7D%7B2%7D%20%5C%3Aor%20%5Cfrac%7B2%28-1-%5Csqrt%7B6%7D%29%20%7D%7B2%7D)
Cancelling 2 from numerator & denominator gives
![x = (-1+\sqrt{6} ) \: or (-1 - \sqrt{6} )](https://tex.z-dn.net/?f=x%20%3D%20%28-1%2B%5Csqrt%7B6%7D%20%29%20%5C%3A%20or%20%28-1%20-%20%5Csqrt%7B6%7D%20%29)
Answer:
A) f(x) = |x|
B) f(x) = -|x+3| + 3
Step-by-step explanation:
Absolute value functions
The general form of an absolute value function is f(x) = a|x-b| +c
a indicates the 'amplitude' or multiplier
b indicates horizontal shift
c indicates vertical shift
The turning point of f(x) = |x| is (0, 0)
a = y/x when b = 0 and c = 0
A) f(x) = |x|
Since the turning point is still (0, 0) there is no horizontal nor vertical shift, meaning b = 0 and c = 0
We have the point (2, 2), thus a = 2/2 = 1
f(x) = a|x-b| + c
f(x) = |x|
B) f(x) = -|x+3| + 3
The turning point is at (-3, 3) b = -3 and c = +3
We have the point (3, -3), thus a = y/x = -3/3 = -1
f(x) = a|x-b| + c
f(x) = (-1) (|x-(-3)|) + (+3)
f(x) = -|x+3| + 3
Answer:
There are no options
Step-by-step explanation:
We can factorize the equation given:
<span>5 • 20 + 5 • 3
= 5(20 + 3)
= 5(23)
= 115</span>
Solution
For this case we need to do the following division:
714 /41
Then the answer for this case is:
17 R 17