Answer:
see attached
Step-by-step explanation:
To find the inverse function, solve ...
x = f(y)
x = (y^7)/7 -4 . . . . . . . use the definition of f(x)
x +4 = (y^7)/7 . . . . . . add 4
7(x +4) = y^7 . . . . . . multiply by 7
(7(x +4))^(1/7) = y . . take the 7th root
The inverse function is the one shown in the attachment.
Answer:
![1. \quad\dfrac{1}{k^{\frac{2}{3}}}\\\\2. \quad\sqrt[7]{x^5}\\\\3. \quad\dfrac{1}{\sqrt[5]{y^2}}](https://tex.z-dn.net/?f=1.%20%5Cquad%5Cdfrac%7B1%7D%7Bk%5E%7B%5Cfrac%7B2%7D%7B3%7D%7D%7D%5C%5C%5C%5C2.%20%5Cquad%5Csqrt%5B7%5D%7Bx%5E5%7D%5C%5C%5C%5C3.%20%5Cquad%5Cdfrac%7B1%7D%7B%5Csqrt%5B5%5D%7By%5E2%7D%7D)
Step-by-step explanation:
The applicable rule is ...
![x^{\frac{m}{n}}=\sqrt[n]{x^m}](https://tex.z-dn.net/?f=x%5E%7B%5Cfrac%7Bm%7D%7Bn%7D%7D%3D%5Csqrt%5Bn%5D%7Bx%5Em%7D)
It works both ways, going from radicals to frational exponents and vice versa.
The particular power or root involved can be in either the numerator or the denominator. The transformation applies to the portion of the expression that is the power or root.
Step-by-step explanation:
because VW || YZ, the 2 triangles are similar.
this is given by the rules of equal angles of intersecting lines with parallel lines. Z to V and Y to W would be such intersecting lines.
and therefore, the angle at W is the angle at Y, the angle at V is the angle at Z. and therefore both angles at A are equal.
so, for similar triangles the scaling factor between corresponding pairs of sides is the same for all sides.
e.g. the same scaling factor that converts 7.2 to 12, converts then also x to x+4.
7.2 × f = 12
f = 12/7.2 = 12/ 72/10 = 120/72 = 10/6 = 5/3
x × 5/3 = x + 4
5x = 3x + 12
2x = 12
x = 6
A to Y = x = 6
W to A = x + 4 = 6 + 4 = 10
Answer: There are 3.25 or 3 1/4 gallons in one cooler
Step-by-step explanation:
If one liter is appx .26 gallons we need to multiply the number of liters there are. So 12.5 times .26 to get the answer 3.25
The slope is calculated through the formula:
dy/dx.
If you apply this to your question you get:
(4-2)/(4-1) = 2/3 or 0.667
Hope this helps!
