Answer:
n =22
Step-by-step explanation:
12-5=7
15-5=10
20-5=15
n-5=17
collect like terms
n=17+5
n=22
Heya!
![\text{First, manipulate the left side.}\\\text{Use the rule:}~a-b=\frac{(a-b)(a-b)}{a+b} = \frac{a^2-b^2}{a+b} \\\text{Use the identity:}~1-sin^2(x)=cos^2(x)\\\frac{1+cos(x)-sin(x)}{1+cos(x)+sin(x)} = \frac{cos(x)+\frac{cos^2(x)}{1+sin(y)}}{1+cos(x)+sin(x)}](https://tex.z-dn.net/?f=%5Ctext%7BFirst%2C%20manipulate%20the%20left%20side.%7D%5C%5C%5Ctext%7BUse%20the%20rule%3A%7D~a-b%3D%5Cfrac%7B%28a-b%29%28a-b%29%7D%7Ba%2Bb%7D%20%3D%20%5Cfrac%7Ba%5E2-b%5E2%7D%7Ba%2Bb%7D%20%5C%5C%5Ctext%7BUse%20the%20identity%3A%7D~1-sin%5E2%28x%29%3Dcos%5E2%28x%29%5C%5C%5Cfrac%7B1%2Bcos%28x%29-sin%28x%29%7D%7B1%2Bcos%28x%29%2Bsin%28x%29%7D%20%20%3D%20%5Cfrac%7Bcos%28x%29%2B%5Cfrac%7Bcos%5E2%28x%29%7D%7B1%2Bsin%28y%29%7D%7D%7B1%2Bcos%28x%29%2Bsin%28x%29%7D)
![\text{Second, simplify the numerator}~cos(x)+\frac{cos^2(x)}{1+sin(x)}\\\text{Convert element to a fraction:}~cos(x)=\frac{cos(x)(1+sin(x))}{1+sin(x)}\\\text{Add:}~cos(x)=\frac{cos(x)(1+sin(x))}{1+sin(x)}+\frac{cos^2(x)}{1+sin(x)}\\\text{The denominators are equal so combine:}~\frac{cos(x)(1+sin(x))+cos^2(x)}{1+sin(x)}\\\text{Simplify:} \frac{\frac{cos(x)(sin(x)+1)+cos^2(x)}{1+sin(x)} }{1+cos(x)+sin(x)}\\ \text{Apply fraction rule:}~\frac{cos(x)(1+sin(x))+cos^2(x)}{1+sin(x)}\\\\](https://tex.z-dn.net/?f=%5Ctext%7BSecond%2C%20simplify%20the%20numerator%7D~cos%28x%29%2B%5Cfrac%7Bcos%5E2%28x%29%7D%7B1%2Bsin%28x%29%7D%5C%5C%5Ctext%7BConvert%20element%20to%20a%20fraction%3A%7D~cos%28x%29%3D%5Cfrac%7Bcos%28x%29%281%2Bsin%28x%29%29%7D%7B1%2Bsin%28x%29%7D%5C%5C%5Ctext%7BAdd%3A%7D~cos%28x%29%3D%5Cfrac%7Bcos%28x%29%281%2Bsin%28x%29%29%7D%7B1%2Bsin%28x%29%7D%2B%5Cfrac%7Bcos%5E2%28x%29%7D%7B1%2Bsin%28x%29%7D%5C%5C%5Ctext%7BThe%20denominators%20are%20equal%20so%20combine%3A%7D~%5Cfrac%7Bcos%28x%29%281%2Bsin%28x%29%29%2Bcos%5E2%28x%29%7D%7B1%2Bsin%28x%29%7D%5C%5C%5Ctext%7BSimplify%3A%7D%20%5Cfrac%7B%5Cfrac%7Bcos%28x%29%28sin%28x%29%2B1%29%2Bcos%5E2%28x%29%7D%7B1%2Bsin%28x%29%7D%20%7D%7B1%2Bcos%28x%29%2Bsin%28x%29%7D%5C%5C%20%5Ctext%7BApply%20fraction%20rule%3A%7D~%5Cfrac%7Bcos%28x%29%281%2Bsin%28x%29%29%2Bcos%5E2%28x%29%7D%7B1%2Bsin%28x%29%7D%5C%5C%5C%5C)
![\text{Factor:}~\frac{cos(x)(1+sin(x)+cos(x))}{(1+sin(x))(1+cos(x)+sin(x))} \\\text{Simplify:}~\frac{cos(x)}{1+sin(x)}](https://tex.z-dn.net/?f=%5Ctext%7BFactor%3A%7D~%5Cfrac%7Bcos%28x%29%281%2Bsin%28x%29%2Bcos%28x%29%29%7D%7B%281%2Bsin%28x%29%29%281%2Bcos%28x%29%2Bsin%28x%29%29%7D%20%5C%5C%5Ctext%7BSimplify%3A%7D~%5Cfrac%7Bcos%28x%29%7D%7B1%2Bsin%28x%29%7D)
![\text{Third, manipulate the right side.}\\\text{Use the basic trigonometric identity:}~sec(x)=\frac{1}{cos(x)} \\\text{Use the basic trigonometric identity:}~tan(x)=\frac{sin(x)}{cos(x)} \\\text{Put the expression back together:}~\frac{1}{cos(x)}-\frac{sin(x)}{cos(x)}\\\text{Simplify:}~\frac{\frac{cos^2(x)}{1+sin(x)} }{cos(x)}](https://tex.z-dn.net/?f=%5Ctext%7BThird%2C%20manipulate%20the%20right%20side.%7D%5C%5C%5Ctext%7BUse%20the%20basic%20trigonometric%20identity%3A%7D~sec%28x%29%3D%5Cfrac%7B1%7D%7Bcos%28x%29%7D%20%5C%5C%5Ctext%7BUse%20the%20basic%20trigonometric%20identity%3A%7D~tan%28x%29%3D%5Cfrac%7Bsin%28x%29%7D%7Bcos%28x%29%7D%20%5C%5C%5Ctext%7BPut%20the%20expression%20back%20together%3A%7D~%5Cfrac%7B1%7D%7Bcos%28x%29%7D-%5Cfrac%7Bsin%28x%29%7D%7Bcos%28x%29%7D%5C%5C%5Ctext%7BSimplify%3A%7D~%5Cfrac%7B%5Cfrac%7Bcos%5E2%28x%29%7D%7B1%2Bsin%28x%29%7D%20%7D%7Bcos%28x%29%7D)
![\text{Fourth, simplify.}\\\text{Apply the fraction rule:}~\frac{cos^2(x)}{(1+sin(x))cos(x)} \\\text{Cancel out the common factor:}~\frac{cos(x)}{1+sin(x)}](https://tex.z-dn.net/?f=%5Ctext%7BFourth%2C%20simplify.%7D%5C%5C%5Ctext%7BApply%20the%20fraction%20rule%3A%7D~%5Cfrac%7Bcos%5E2%28x%29%7D%7B%281%2Bsin%28x%29%29cos%28x%29%7D%20%5C%5C%5Ctext%7BCancel%20out%20the%20common%20factor%3A%7D~%5Cfrac%7Bcos%28x%29%7D%7B1%2Bsin%28x%29%7D)
Therefore, the expression is TRUE.
Best of Luck!
Answer:
![p(x,y) = (-2.6 ,2.4)](https://tex.z-dn.net/?f=p%28x%2Cy%29%20%3D%20%28-2.6%20%2C2.4%29)
Step-by-step explanation:
Given
a(-5,4) and b(7,-4)
Required
Partition P
Given that the segment ab is divided into ratio;
The coordinates of point p can be calculated using ratio formula given below
![p(x,y) = (\frac{mx_2 + nx_1}{m+n} ,\frac{my_2 + ny_1}{m+n})](https://tex.z-dn.net/?f=p%28x%2Cy%29%20%3D%20%28%5Cfrac%7Bmx_2%20%2B%20nx_1%7D%7Bm%2Bn%7D%20%2C%5Cfrac%7Bmy_2%20%2B%20ny_1%7D%7Bm%2Bn%7D%29)
Where m and n are the ratio; m = 1 and n = 4
![(x_1, y_1) = (-5,4); \\(x_2, y_2) = (7,-4)](https://tex.z-dn.net/?f=%28x_1%2C%20y_1%29%20%3D%20%28-5%2C4%29%3B%20%5C%5C%28x_2%2C%20y_2%29%20%3D%20%287%2C-4%29)
So,
becomes
![p(x,y) = (\frac{1 *7 + 4 * -5}{1+4} ,\frac{1 * -4 + 4 * 4}{1+4})](https://tex.z-dn.net/?f=p%28x%2Cy%29%20%3D%20%28%5Cfrac%7B1%20%2A7%20%2B%204%20%2A%20-5%7D%7B1%2B4%7D%20%2C%5Cfrac%7B1%20%2A%20-4%20%2B%204%20%2A%204%7D%7B1%2B4%7D%29)
![p(x,y) = (\frac{7 + -20}{5} ,\frac{-4 + 16}{5})](https://tex.z-dn.net/?f=p%28x%2Cy%29%20%3D%20%28%5Cfrac%7B7%20%2B%20-20%7D%7B5%7D%20%2C%5Cfrac%7B-4%20%2B%2016%7D%7B5%7D%29)
![p(x,y) = (\frac{-13}{5} ,\frac{12}{5})](https://tex.z-dn.net/?f=p%28x%2Cy%29%20%3D%20%28%5Cfrac%7B-13%7D%7B5%7D%20%2C%5Cfrac%7B12%7D%7B5%7D%29)
![p(x,y) = (-2.6 ,2.4)](https://tex.z-dn.net/?f=p%28x%2Cy%29%20%3D%20%28-2.6%20%2C2.4%29)
Hence, the coordinates of p are (-2.6,2.4)
Answer: You need to count how many squares are shaded(at least half of it), therefore the area is 32 square units.