Answer:
![y + x - 6 = 0](https://tex.z-dn.net/?f=y%20%2B%20x%20-%206%20%3D%200)
Step-by-step explanation:
Given
![M(0,6) \ and \ N(6,0)](https://tex.z-dn.net/?f=M%280%2C6%29%20%5C%20and%20%5C%20N%286%2C0%29)
Required
Find the equation of the line
First, the slope of the line has to be calculated using the following formula;
![m = \frac{y_2 - y_1}{x_2 - x_1}](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7By_2%20-%20y_1%7D%7Bx_2%20-%20x_1%7D)
![where\ (x_1,y_1) = (0,6) \ and \ (x_2,y_2) = (6,0)](https://tex.z-dn.net/?f=where%5C%20%20%28x_1%2Cy_1%29%20%3D%20%280%2C6%29%20%5C%20and%20%5C%20%28x_2%2Cy_2%29%20%3D%20%286%2C0%29)
So, the equation becomes
![m = \frac{0 - 6}{6 - 0}](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7B0%20-%206%7D%7B6%20-%200%7D)
![m = \frac{-6}{6}](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7B-6%7D%7B6%7D)
![m = -1](https://tex.z-dn.net/?f=m%20%3D%20-1)
The equation of the line can then be calculated using
![Using \ m = \frac{y - y_1}{x - x_1}](https://tex.z-dn.net/?f=Using%20%5C%20m%20%3D%20%5Cfrac%7By%20-%20y_1%7D%7Bx%20-%20x_1%7D)
![-1 = \frac{y - 6}{x -0}](https://tex.z-dn.net/?f=-1%20%3D%20%5Cfrac%7By%20-%206%7D%7Bx%20-0%7D)
![-1 = \frac{y - 6}{x}](https://tex.z-dn.net/?f=-1%20%3D%20%5Cfrac%7By%20-%206%7D%7Bx%7D)
Multiply both sides by x
![-1 * x = \frac{y - 6}{x} * x](https://tex.z-dn.net/?f=-1%20%2A%20x%20%3D%20%5Cfrac%7By%20-%206%7D%7Bx%7D%20%2A%20x)
![-x = y - 6](https://tex.z-dn.net/?f=-x%20%3D%20y%20-%206)
Add x to both sides
![x -x = y - 6 + x](https://tex.z-dn.net/?f=x%20-x%20%3D%20y%20-%206%20%2B%20x)
![0 = y - 6 + x](https://tex.z-dn.net/?f=0%20%3D%20y%20-%206%20%2B%20x)
Reorder
![y + x- 6 = 0](https://tex.z-dn.net/?f=y%20%2B%20x-%206%20%3D%200)
![Using \ m = \frac{y - y_2}{x - x_2}](https://tex.z-dn.net/?f=Using%20%5C%20m%20%3D%20%5Cfrac%7By%20-%20y_2%7D%7Bx%20-%20x_2%7D)
![-1 = \frac{y - 0}{x - 6}](https://tex.z-dn.net/?f=-1%20%3D%20%5Cfrac%7By%20-%200%7D%7Bx%20-%206%7D)
![-1 = \frac{y}{x - 6}](https://tex.z-dn.net/?f=-1%20%3D%20%5Cfrac%7By%7D%7Bx%20-%206%7D)
Multiply both sides by x - 6
![-1 * (x-6) = \frac{y}{x - 6} * (x-6)](https://tex.z-dn.net/?f=-1%20%2A%20%28x-6%29%20%3D%20%5Cfrac%7By%7D%7Bx%20-%206%7D%20%2A%20%28x-6%29)
![-1 * (x-6) = y](https://tex.z-dn.net/?f=-1%20%2A%20%28x-6%29%20%3D%20y)
![-x+6 = y](https://tex.z-dn.net/?f=-x%2B6%20%3D%20y)
Add x - 6 to both sided
![x - 6 -x+6 = y +x - 6](https://tex.z-dn.net/?f=x%20-%206%20-x%2B6%20%3D%20y%20%2Bx%20-%206)
![0 = y + x - 6](https://tex.z-dn.net/?f=0%20%3D%20y%20%2B%20x%20-%206)
![y + x - 6 = 0](https://tex.z-dn.net/?f=y%20%2B%20x%20-%206%20%3D%200)
Hence, the equation of the line is ![y + x - 6 = 0](https://tex.z-dn.net/?f=y%20%2B%20x%20-%206%20%3D%200)
<u>Answer-</u>
<em>The values of x, which are the roots of the polynomial are </em>
![\dfrac{11+ \sqrt{69}}{2},\ \dfrac{11- \sqrt{69}}{2}](https://tex.z-dn.net/?f=%5Cdfrac%7B11%2B%20%5Csqrt%7B69%7D%7D%7B2%7D%2C%5C%20%5Cdfrac%7B11-%20%5Csqrt%7B69%7D%7D%7B2%7D)
<u>Solution-</u>
The given polynomial,
![=x^2 - 11x + 13](https://tex.z-dn.net/?f=%3Dx%5E2%20-%2011x%20%2B%2013)
We know that,
![x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}](https://tex.z-dn.net/?f=x%3D%5Cdfrac%7B-b%5Cpm%20%5Csqrt%7Bb%5E2-4ac%7D%7D%7B2a%7D)
Here,
a = 1, b = -11, c = 13
Putting the values,
![x=\dfrac{-(-11)\pm \sqrt{(-11)^2-4\times 1\times 13}}{2\times 1}](https://tex.z-dn.net/?f=x%3D%5Cdfrac%7B-%28-11%29%5Cpm%20%5Csqrt%7B%28-11%29%5E2-4%5Ctimes%201%5Ctimes%2013%7D%7D%7B2%5Ctimes%201%7D)
![=\dfrac{11\pm \sqrt{121-52}}{2}](https://tex.z-dn.net/?f=%3D%5Cdfrac%7B11%5Cpm%20%5Csqrt%7B121-52%7D%7D%7B2%7D)
![=\dfrac{11\pm \sqrt{69}}{2}](https://tex.z-dn.net/?f=%3D%5Cdfrac%7B11%5Cpm%20%5Csqrt%7B69%7D%7D%7B2%7D)
![\therefore x=\dfrac{11+ \sqrt{69}}{2},\ \dfrac{11- \sqrt{69}}{2}](https://tex.z-dn.net/?f=%5Ctherefore%20x%3D%5Cdfrac%7B11%2B%20%5Csqrt%7B69%7D%7D%7B2%7D%2C%5C%20%5Cdfrac%7B11-%20%5Csqrt%7B69%7D%7D%7B2%7D)
The equation of the new function is f'(x) = -|x|
<h3>How to determine the
equation of the
new function?</h3>
The function is given as:
f(x) = |x|
The rule of flipping the graph over the x-axis
(x, y) = (x, -y)
So, we have:
f'(x) = -f(x)
Substitute f(x) = |x|
f'(x) = -|x|
Hence, the equation of the new function is f'(x) = -|x|
Read more about function transformation at:
brainly.com/question/13810353
#SPJ1
Answer:
I hope i tried best....
Step-by-step explanation:
Photo 1. I believe it is.... 1,500
Photo 2. 6,936.00
Photo 3. Sorry do not know. :(
Photo 4. 170 = 15% off. 180 = 20$ off. 160 = 1/5 Discount
Photo 5. Sorry do not know. :(
Answer:
2x^3 +7x^2+3x-2
Step-by-step explanation:
3x^3 +7x^2 -x
- ( x^3 -4x +2)
------------------------
The first step is to line up the variables by degree
3x^3 +7x^2 -x
- ( x^3 -4x +2)
----------------------------
Then distribute the minus sign
3x^3 +7x^2 -x
- x^3 +4x -2
----------------------------
2x^3 +7x^2+3x-2