Find the slope of the line passing throught the points (2, 2) and (4, 3).
The formula of a slope:
![m=\dfrac{y_2-y_1}{x_2-x_1}](https://tex.z-dn.net/?f=m%3D%5Cdfrac%7By_2-y_1%7D%7Bx_2-x_1%7D)
Substitute:
![m=\dfrac{3-2}{4-2}=\dfrac{1}{2}](https://tex.z-dn.net/?f=m%3D%5Cdfrac%7B3-2%7D%7B4-2%7D%3D%5Cdfrac%7B1%7D%7B2%7D)
If the point (x, -1) lie on the same line, then the slope of line passing through the points (2, 2) and (x, -1) the same:
Substitute:
![m=\dfrac{-1-2}{x-2}=\dfrac{-3}{x-2}](https://tex.z-dn.net/?f=m%3D%5Cdfrac%7B-1-2%7D%7Bx-2%7D%3D%5Cdfrac%7B-3%7D%7Bx-2%7D)
We have the equation:
<em>cross multiply</em>
![(1)(x-2)=(-3)(2)](https://tex.z-dn.net/?f=%281%29%28x-2%29%3D%28-3%29%282%29)
<em>add 2 to both sides</em>
![x=-4](https://tex.z-dn.net/?f=x%3D-4)
<h3>Answer: x = -4.</h3>
Answer:
38.56
Step-by-step explanation:
Answer: The number is 15
Step-by-step explanation: basically the equation you should solve is
(x)+(2x)+(2x+7)=82
5x+7=82
5x= -7+82
5x=75
5/5x=75/5
x=15
Answer:
26 Members Voted
Step-by-step explanation:
50 % is 50/100
Voted = ![(50/100) X 52 = 52/2 = 26](https://tex.z-dn.net/?f=%2850%2F100%29%20X%2052%20%3D%2052%2F2%20%3D%2026)
The two values of roots of the polynomial
are ![\frac{11+\sqrt{61}}{2} \text { or } \frac{11-\sqrt{61}}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B11%2B%5Csqrt%7B61%7D%7D%7B2%7D%20%5Ctext%20%7B%20or%20%7D%20%5Cfrac%7B11-%5Csqrt%7B61%7D%7D%7B2%7D)
<u>Solution:</u>
Given, polynomial expression is ![x^{2}-11 x+15](https://tex.z-dn.net/?f=x%5E%7B2%7D-11%20x%2B15)
We have to find the roots of the given expression.
In order to find roots, now let us use quadratic formula.
![x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-b%20%5Cpm%20%5Csqrt%7Bb%5E%7B2%7D-4%20a%20c%7D%7D%7B2%20a%7D)
Given that
Here a = 1, b = -11 and c = 15
On substituting the values we get,
![x=\frac{-(-11) \pm \sqrt{(-11)^{2}-4 \times 1 \times 15}}{2 \times 1}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-%28-11%29%20%5Cpm%20%5Csqrt%7B%28-11%29%5E%7B2%7D-4%20%5Ctimes%201%20%5Ctimes%2015%7D%7D%7B2%20%5Ctimes%201%7D)
![\begin{array}{l}{x=\frac{11 \pm \sqrt{121-60}}{2}} \\\\ {x=\frac{11 \pm \sqrt{61}}{2}} \\\\ {x=\frac{11+\sqrt{61}}{2} \text { or } \frac{11-\sqrt{61}}{2}}\end{array}](https://tex.z-dn.net/?f=%5Cbegin%7Barray%7D%7Bl%7D%7Bx%3D%5Cfrac%7B11%20%5Cpm%20%5Csqrt%7B121-60%7D%7D%7B2%7D%7D%20%5C%5C%5C%5C%20%7Bx%3D%5Cfrac%7B11%20%5Cpm%20%5Csqrt%7B61%7D%7D%7B2%7D%7D%20%5C%5C%5C%5C%20%7Bx%3D%5Cfrac%7B11%2B%5Csqrt%7B61%7D%7D%7B2%7D%20%5Ctext%20%7B%20or%20%7D%20%5Cfrac%7B11-%5Csqrt%7B61%7D%7D%7B2%7D%7D%5Cend%7Barray%7D)
Hence, the roots of given polynomial are ![\frac{11+\sqrt{61}}{2} \text { or } \frac{11-\sqrt{61}}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B11%2B%5Csqrt%7B61%7D%7D%7B2%7D%20%5Ctext%20%7B%20or%20%7D%20%5Cfrac%7B11-%5Csqrt%7B61%7D%7D%7B2%7D)