170
Because you have to add
120 + 50 = 170
Step-by-step explanation:
Geometry is one of the oldest branches of math. Geometry is mostly about distance, shape, size, and relative position of figures. It is related to measurement, relationships of points, lines, angles, surfaces, and solids. There are 8 types of Geometry and the basic concepts of Geometry are point, line and plane. It isn't possible to exactly define the terms, however, we know it is refers to the mark of the position and has an accurate location.
Hope this helps :)
Answer:
![\large\boxed{1.\ f^{-1}(x)=4\log(x\sqrt[4]2)}\\\\\boxed{2.\ f^{-1}(x)=\log(x^5+5)}\\\\\boxed{3.\ f^{-1}(x)=\sqrt{4^{x-1}}}](https://tex.z-dn.net/?f=%5Clarge%5Cboxed%7B1.%5C%20f%5E%7B-1%7D%28x%29%3D4%5Clog%28x%5Csqrt%5B4%5D2%29%7D%5C%5C%5C%5C%5Cboxed%7B2.%5C%20f%5E%7B-1%7D%28x%29%3D%5Clog%28x%5E5%2B5%29%7D%5C%5C%5C%5C%5Cboxed%7B3.%5C%20f%5E%7B-1%7D%28x%29%3D%5Csqrt%7B4%5E%7Bx-1%7D%7D%7D)
Step-by-step explanation:
![\log_55^{\frac{1}{4}y}=\log_5\left(2^\frac{1}{4}x\right)\qquad\text{use}\ a^\frac{1}{n}=\sqrt[n]{a}\\\\\dfrac{1}{4}y=\log(x\sqrt[4]2)\qquad\text{multiply both sides by 4}\\\\y=4\log(x\sqrt[4]2)](https://tex.z-dn.net/?f=%5Clog_55%5E%7B%5Cfrac%7B1%7D%7B4%7Dy%7D%3D%5Clog_5%5Cleft%282%5E%5Cfrac%7B1%7D%7B4%7Dx%5Cright%29%5Cqquad%5Ctext%7Buse%7D%5C%20a%5E%5Cfrac%7B1%7D%7Bn%7D%3D%5Csqrt%5Bn%5D%7Ba%7D%5C%5C%5C%5C%5Cdfrac%7B1%7D%7B4%7Dy%3D%5Clog%28x%5Csqrt%5B4%5D2%29%5Cqquad%5Ctext%7Bmultiply%20both%20sides%20by%204%7D%5C%5C%5C%5Cy%3D4%5Clog%28x%5Csqrt%5B4%5D2%29)
![--------------------------\\2.\\y=(10^x-5)^\frac{1}{5}\\\\\text{Exchange x and y. Solve for y:}\\\\(10^y-5)^\frac{1}{5}=x\qquad\text{5 power of both sides}\\\\\bigg[(10^y-5)^\frac{1}{5}\bigg]^5=x^5\qquad\text{use}\ (a^n)^m=a^{nm}\\\\(10^y-5)^{\frac{1}{5}\cdot5}=x^5\\\\10^y-5=x^5\qquad\text{add 5 to both sides}\\\\10^y=x^5+5\qquad\log\ \text{of both sides}\\\\\log10^y=\log(x^5+5)\Rightarrow y=\log(x^5+5)](https://tex.z-dn.net/?f=--------------------------%5C%5C2.%5C%5Cy%3D%2810%5Ex-5%29%5E%5Cfrac%7B1%7D%7B5%7D%5C%5C%5C%5C%5Ctext%7BExchange%20x%20and%20y.%20Solve%20for%20y%3A%7D%5C%5C%5C%5C%2810%5Ey-5%29%5E%5Cfrac%7B1%7D%7B5%7D%3Dx%5Cqquad%5Ctext%7B5%20power%20of%20both%20sides%7D%5C%5C%5C%5C%5Cbigg%5B%2810%5Ey-5%29%5E%5Cfrac%7B1%7D%7B5%7D%5Cbigg%5D%5E5%3Dx%5E5%5Cqquad%5Ctext%7Buse%7D%5C%20%28a%5En%29%5Em%3Da%5E%7Bnm%7D%5C%5C%5C%5C%2810%5Ey-5%29%5E%7B%5Cfrac%7B1%7D%7B5%7D%5Ccdot5%7D%3Dx%5E5%5C%5C%5C%5C10%5Ey-5%3Dx%5E5%5Cqquad%5Ctext%7Badd%205%20to%20both%20sides%7D%5C%5C%5C%5C10%5Ey%3Dx%5E5%2B5%5Cqquad%5Clog%5C%20%5Ctext%7Bof%20both%20sides%7D%5C%5C%5C%5C%5Clog10%5Ey%3D%5Clog%28x%5E5%2B5%29%5CRightarrow%20y%3D%5Clog%28x%5E5%2B5%29)
6) 9/4 divided by 5/8
9/4x5/8
9x8/4x5
72/4/5
72/20
18/5
Answer: 18/5
7) 2 1/2 divided by 4 1/2
2x2+1/2 divided by 4 1/2
4+1/2 divided by 4 1/2
5/2 divided by 4 1/2
5/2 divided by 8+1/2
5/2 divided by 9/2
5/2x9/2
5/2x2/9
5x1/9
5/9
Answer: 5/9
Answer:
.
Step-by-step explanation:
The given expression is
We need to simplify the expression such that answer should contain only positive exponents with no fractional exponents in the denominator.
Using properties of exponents, we get
![[\because a^ma^n=a^{m+n}]](https://tex.z-dn.net/?f=%5B%5Cbecause%20a%5Ema%5En%3Da%5E%7Bm%2Bn%7D%5D)
![[\because a^{-n}=\dfrac{1}{a^n}]](https://tex.z-dn.net/?f=%5B%5Cbecause%20a%5E%7B-n%7D%3D%5Cdfrac%7B1%7D%7Ba%5En%7D%5D)
We can not simplify further because on further simplification we get negative exponents in numerator or fractional exponents in the denominator.
Therefore, the required expression is .
