4 laps because a mile is 1,760 yards and the 440 laps need to be divided into 1,760 so 1,760/440 is 4 so four laps are needed to complete a mile
I'm sure there's an easier way of solving it than the way I did, but I'm not sure what it could be. Never dealt with a problem like this before.
Anyway, I just plugged in and tested. Chose random values for a, b, c, and d, which follow the rule 0 < a < b < c < d:
a = 1
b = 2
c = 3
d = 4


Simplify into standard form:



Use the quadratic formula to solve:

For functions in the form of

. So in this case:
a = 1
b = -4
c = 2
Plug them in:

Solve for 'x':




So the answer would be A.
Answer:

Step-by-step explanation:
we know that
To find the inverse of a function, exchange variables x for y and y for x. Then clear the y-variable to get the inverse function.
we will proceed to verify each case to determine the solution of the problem
<u>case A)</u> 
Find the inverse of f(x)
Let
y=f(x)
Exchange variables x for y and y for x
Isolate the variable y


Let


therefore
f(x) and g(x) are inverse functions
<u>case B)</u> 
Find the inverse of f(x)
Let
y=f(x)
Exchange variables x for y and y for x
Isolate the variable y


Let


therefore
f(x) and g(x) are inverse functions
<u>case C)</u> ![f(x)=x^{5}, g(x)=\sqrt[5]{x}](https://tex.z-dn.net/?f=f%28x%29%3Dx%5E%7B5%7D%2C%20g%28x%29%3D%5Csqrt%5B5%5D%7Bx%7D)
Find the inverse of f(x)
Let
y=f(x)
Exchange variables x for y and y for x
Isolate the variable y
fifth root both members
![y=\sqrt[5]{x}](https://tex.z-dn.net/?f=y%3D%5Csqrt%5B5%5D%7Bx%7D)
Let

![f^{-1}(x)=\sqrt[5]{x}](https://tex.z-dn.net/?f=f%5E%7B-1%7D%28x%29%3D%5Csqrt%5B5%5D%7Bx%7D)
therefore
f(x) and g(x) are inverse functions
<u>case D)</u> 
Find the inverse of f(x)
Let
y=f(x)
Exchange variables x for y and y for x
Isolate the variable y





Let



therefore
f(x) and g(x) is not a pair of inverse functions
Answer:
Step-by-step explanation:
Surface area of objects with flat surfaces like this is simply the area of each surface added together, so let's get to work.
Both have 6 faces, so we will be adding six values together for each.
Container A:
Hopefully you can imagine the six different faces. It's kinda like a cereal box.
The front and back of a cereal box have the same area, as do the two sides and the top and bottom, so that makes it a little easier.
Front and Back: 28 * 36 = 1008
Sides: 36*6 = 216
Top and Bottom: 6*28 = 168
Let me know if you don't understand how I did any of that. Anyway, since there is a matching face for each we add them all together twice.
1008*2 + 216*2 + 168*2 = 2784 in^2
Container B has a similar setup, I won't write out everything like I did unless you want me to work it out with you.
2(16*12+16*22+22*12) = 1616 in^2
So since Container A has a surface area of 2784 and Container B has a surface area of 1616 it's obvious container A has a larger surface area
Answer:
1) 
2) 
Step-by-step explanation:
You can convert he mixed numbers to improper fractions:
1. Multiply the whole number part by the denominator of the fraction.
2. Add the product obtained to the numerator.
3. The denominator does not change.
Then:

Observe that, in each subtraction, the denominators are equal, then you can rewrite the denominator and subtract the numerators:

Divide 15 by 4. The quotient will be 3 and the remainder 3.
Then:
