Answer:
29.71
Step-by-step explanation:
8+6+5pi
14+15.71
29.71
15.71 is approx 5pi
9514 1404 393
Answer:
Step-by-step explanation:
If we let x represent one of the numbers, then you want ...
x(58 -x) = 201.25
x² -58x +201.25 = 0 . . . . . put in standard form
(x² -58x +29²) +201.25 -29² = 0 . . . . complete the square
(x -29)² -639.75 = 0
x -29 = ±√639.75 . . . . . add 639.75 and take the square root
x = 29 ±√639.75 . . . . . . add 29
The two numbers of interest are ...
29 +√639.75 ≈ 54.2933
29 -√639.75 ≈ 3.7067
Answer:
-3.2
Step-by-step explanation:
Answer:
y = - x - 2
Step-by-step explanation:
y=mx+b
m refers to slope
b refers to y intercept
y = (-1)x + (-2)
y = - x - 2
(a) ![x^{-5}](https://tex.z-dn.net/?f=x%5E%7B-5%7D)
(b) ![3x^{-7}](https://tex.z-dn.net/?f=3x%5E%7B-7%7D)
(c) ![$\frac{4}{3}x^4](https://tex.z-dn.net/?f=%24%5Cfrac%7B4%7D%7B3%7Dx%5E4)
Solution:
To write each of the given expression in the form
:
(a) ![\frac{x^3}{x^8}](https://tex.z-dn.net/?f=%5Cfrac%7Bx%5E3%7D%7Bx%5E8%7D)
Using exponential rule: ![\frac{a^x}{a^y}=a^{x-y}](https://tex.z-dn.net/?f=%5Cfrac%7Ba%5Ex%7D%7Ba%5Ey%7D%3Da%5E%7Bx-y%7D)
![$\frac{x^3}{x^8}=x^{3-8}](https://tex.z-dn.net/?f=%24%5Cfrac%7Bx%5E3%7D%7Bx%5E8%7D%3Dx%5E%7B3-8%7D)
![$\frac{x^3}{x^8}=x^{-5}](https://tex.z-dn.net/?f=%24%5Cfrac%7Bx%5E3%7D%7Bx%5E8%7D%3Dx%5E%7B-5%7D)
(b) ![\frac{6x}{2x^8}](https://tex.z-dn.net/?f=%5Cfrac%7B6x%7D%7B2x%5E8%7D)
Divide numerator and denominator by the common factor 2, we get
![$\frac{6x}{2x^8}=\frac{3x}{x^8}](https://tex.z-dn.net/?f=%24%5Cfrac%7B6x%7D%7B2x%5E8%7D%3D%5Cfrac%7B3x%7D%7Bx%5E8%7D)
Using exponential rule: ![\frac{a^x}{a^y}=a^{x-y}](https://tex.z-dn.net/?f=%5Cfrac%7Ba%5Ex%7D%7Ba%5Ey%7D%3Da%5E%7Bx-y%7D)
![$=3x^{1-8}](https://tex.z-dn.net/?f=%24%3D3x%5E%7B1-8%7D)
![$\frac{6x}{2x^8} =3x^{-7}](https://tex.z-dn.net/?f=%24%5Cfrac%7B6x%7D%7B2x%5E8%7D%20%3D3x%5E%7B-7%7D)
(c) ![\frac{28x^6}{21x^2}](https://tex.z-dn.net/?f=%5Cfrac%7B28x%5E6%7D%7B21x%5E2%7D)
Divide numerator and denominator by the common factor 7, we get
![$\frac{28x^6}{21x^2}=\frac{4x^6}{3x^2}](https://tex.z-dn.net/?f=%24%5Cfrac%7B28x%5E6%7D%7B21x%5E2%7D%3D%5Cfrac%7B4x%5E6%7D%7B3x%5E2%7D)
Using exponential rule: ![\frac{a^x}{a^y}=a^{x-y}](https://tex.z-dn.net/?f=%5Cfrac%7Ba%5Ex%7D%7Ba%5Ey%7D%3Da%5E%7Bx-y%7D)
![$=\frac{4}{3}x^{6-2}](https://tex.z-dn.net/?f=%24%3D%5Cfrac%7B4%7D%7B3%7Dx%5E%7B6-2%7D)
![$\frac{28x^6}{21x^2}=\frac{4}{3}x^4](https://tex.z-dn.net/?f=%24%5Cfrac%7B28x%5E6%7D%7B21x%5E2%7D%3D%5Cfrac%7B4%7D%7B3%7Dx%5E4)