Answer:
134.62
Step-by-step explanation:
Answer:
7.722cm^2, x=129
Step-by-step explanation:
12*12=144- area of the whole square
the diameter for the circle is 12
radius is 6
Area for circle= pi* r²
3.142*6^2=113.112
144-113.112=30.888
30.888/4=7.722
The answer is $654.06.
5.5% of $575 is $31.63. 575 x 0.055 = 31.63
This means that in one year he earns $31.63. In two years it will be $63.25 (31.63 x 2 = 63.25)
Then in half a year it will be $15.81 (31.63/2 = 15.81)
Finally add 15.81 and 63.25 to get $79.06 which you then add to the initial $575 to get the total amount earned in 2 1/2 years which is $654.06.
Answer:
5 × 1.6 = 8. The answer is 8 pounds.
Step-by-step explanation:
If you multiply 5 and 1.6, you get 8.
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!