Answer:
4th option
Step-by-step explanation:
The given expression is:
![\frac{1}{1+\sqrt{3}}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B1%2B%5Csqrt%7B3%7D%7D)
In order to simplify this expression we have to multiply and divide it with the conjugate of the denominator i.e multiply and divide the entire expression with
, as shown below:
![\frac{1}{1+\sqrt{3}}\\=\frac{1}{1+\sqrt{3}} \times \frac{1-\sqrt{3}}{1-\sqrt{3}}\\=\frac{1-\sqrt{3}}{(1)^{2}-(\sqrt{3})^{2}}\\\\ =\frac{1-\sqrt{3}}{1-3}\\\\ =\frac{1-\sqrt{3}}{-2}\\\\ =\frac{-1(1-\sqrt{3})}{2}\\\\ =\frac{-1+\sqrt{3}}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B1%2B%5Csqrt%7B3%7D%7D%5C%5C%3D%5Cfrac%7B1%7D%7B1%2B%5Csqrt%7B3%7D%7D%20%5Ctimes%20%5Cfrac%7B1-%5Csqrt%7B3%7D%7D%7B1-%5Csqrt%7B3%7D%7D%5C%5C%3D%5Cfrac%7B1-%5Csqrt%7B3%7D%7D%7B%281%29%5E%7B2%7D-%28%5Csqrt%7B3%7D%29%5E%7B2%7D%7D%5C%5C%5C%5C%20%3D%5Cfrac%7B1-%5Csqrt%7B3%7D%7D%7B1-3%7D%5C%5C%5C%5C%20%3D%5Cfrac%7B1-%5Csqrt%7B3%7D%7D%7B-2%7D%5C%5C%5C%5C%20%3D%5Cfrac%7B-1%281-%5Csqrt%7B3%7D%29%7D%7B2%7D%5C%5C%5C%5C%20%3D%5Cfrac%7B-1%2B%5Csqrt%7B3%7D%7D%7B2%7D)
Thus, 4th option gives the correct answer.
The standard form equation of the line connecting the two points is ![2x + y = -2](https://tex.z-dn.net/?f=2x%20%2B%20%20y%20%3D%20-2)
Linear equation in a standard form is given as ![Ax + By = C](https://tex.z-dn.net/?f=Ax%20%2B%20By%20%3D%20C)
where,
A, B, and C are constants or numbers
x and y are the variables.
To solve this problem, the following steps would be taken:
Step 1: Find the slope of the line connecting points (-3,4) and (2,-6)
![slope (m) = \frac{y_2 - y_1}{x_2 - x_1}](https://tex.z-dn.net/?f=slope%20%28m%29%20%3D%20%5Cfrac%7By_2%20-%20y_1%7D%7Bx_2%20-%20x_1%7D)
where,
![(x_1, y_1) = (-3,4)\\(x_2, y_2) = (2,-6)](https://tex.z-dn.net/?f=%28x_1%2C%20y_1%29%20%3D%20%28-3%2C4%29%5C%5C%28x_2%2C%20y_2%29%20%3D%20%282%2C-6%29)
Substitute
![slope (m) = \frac{-6 - 4}{2 -(-3)} \\m = \frac{-10}{5}\\m = -2](https://tex.z-dn.net/?f=slope%20%28m%29%20%3D%20%5Cfrac%7B-6%20-%204%7D%7B2%20-%28-3%29%7D%20%5C%5Cm%20%3D%20%5Cfrac%7B-10%7D%7B5%7D%5C%5Cm%20%3D%20-2)
Step 2: Find the y-intercept (b) of the line by substituting
and
into
(slope-intercept form)
![4 = -2(-3) + b\\4 = 6 + b\\4 - 6 = 6 + b - 6\\-2 = b\\b = -2](https://tex.z-dn.net/?f=4%20%3D%20-2%28-3%29%20%2B%20b%5C%5C4%20%3D%206%20%2B%20b%5C%5C4%20-%206%20%3D%206%20%2B%20b%20-%206%5C%5C-2%20%3D%20b%5C%5Cb%20%3D%20-2)
Step 3: Write the equation of the line in slope-intercept form by substituting
and
into ![y = mx + b](https://tex.z-dn.net/?f=y%20%3D%20mx%20%2B%20b)
![y = -2x + (-2)\\y = -2x - 2](https://tex.z-dn.net/?f=y%20%3D%20-2x%20%2B%20%28-2%29%5C%5Cy%20%3D%20-2x%20-%202)
Step 4: Rewrite the equation in standard form ![(Ax + By = C)](https://tex.z-dn.net/?f=%28Ax%20%2B%20By%20%3D%20C%29)
![y = -2x - 2\\](https://tex.z-dn.net/?f=y%20%3D%20-2x%20-%202%5C%5C)
Add
to both sides
![2x + y = -2x - 2 + 2x\\2x + y = -2](https://tex.z-dn.net/?f=2x%20%2B%20y%20%3D%20-2x%20-%202%20%2B%202x%5C%5C2x%20%2B%20%20y%20%3D%20-2)
The standard form equation of the points (-3,4) and (2,-6) is ![2x + y = -2](https://tex.z-dn.net/?f=2x%20%2B%20%20y%20%3D%20-2)
Learn more about standard form of two points of a linear equation here:
brainly.com/question/18446164
Answer:
15 (mark me brainliest if you want and lmk if you need more help understanding)
Step-by-step explanation:
perimeter is (l*w)*2
if a pentagon is 5 sided, you do 75/5 which is 15.
each side has 15 cm
Answer:
the answer is 5/9
Step-by-step explanation:
Answer:
option 4
Step-by-step explanation:
fog(x)=(x-5)²+4
=x²-10x+25+4
fog(x)=x²-10x+29