Determine if this function is even, odd or neither. Explain/Show work.
f(x) = 5x + x^3

Odd  

Step-by-step explanation:

To determine if a function is even or odd, substitute -x for every x in the function. Then, simplify. If you receive the same function as before, then the function is even. If you receive a function in which all the terms' signs have been switched, then it is odd. If the function does not qualify as either, then it is neither.

1) Substitute -x for every x in the given function and simplify as shown:

2) Look at the answer. All the signs in the original function have now been switched. The signs were originally positive, but now they are negative. Thus, this function is odd.

greater than one

step-by-step explanation:

hello!

to begin with, we're given that on earth, a rock weighs 20 pounds, and while on jupiter, that same rock weighs 42 pounds. now, we're trying to find the weight of a rock that weighs 10.5 pounds on earth, on jupiter.

to solve this, first, set up a proportion, cross-multiply, and solve it algebraically.

setting up the proportion is the hardest and the most confusing part of the problem, but it's simple.

if on earth, the rock weighs 20 lbs, and on jupiter it weighs 42 lbs, our first part of our proportion is 20/42 lbs. the second part has to be equal to each other. this means that 10.5 has to be on the numerator of the fraction, and x, the value we're trying to find, has to be on the denominator. remember that the rock weighs 10.5 lbs on earth, and we're trying to find the weight of it on jupiter (which is x).

20/42 = 10.5/x

next, you would cross-multiply.

20x = 42(10.5)

20x = 441

now, solve it algebraically by using division.

x = 22.05 lbs

this can be rounded to 22.1 lbs.

therefore, the weight of the rock on jupiter is 22.1 lbs, the fourth choice.