How do you do this question without looking at the answer choices?

Take a look at the 'proof' below

Step-by-step explanation:

The questions asks us to determine the anti-derivative of the function f(x) = 4x^3 sec^2 x^4. Let's start by converting this function into integral form. That would be the following:

Now all we have to do is solve the integral. Let's substitute 'u = x^4' into the equation 'du/dx = 4x^3.' We will receive dx = 1/4x^3 du. If we simplify a bit further:

Our hint tells us that d/dx tan(x) = sec^2(x). Similarly in this case our integral boils down to tan(u). If we undo the substitution, we will receive the expression tan(x^4). Therefore you are right, the first option is an anti-derivative of the function f(x) = 4x^3 sec^2 x^4.

option 3 . (5x + 1) - (-10x + 6)

step-by-step explanation:

option 1 :

(4x + 3) + (-9x + 4)

or 4x+3 -9x + 4

or -5x + 7

option 2

(x - 2) - (6x - 9)

or x-2-6x + 9

or -5x + 7

option 3

(5x+ + 6)

or 5x + 1 + 10x -6

or 15x -5

option 4

-4x+2x+7-3x

-7x + 2x + 7

-5x + 7

hence only option 3 did   not satisfy the given simplify expression.

answer: 12/52

step-by-step explanation: my reasoning is that there are 12 face cards in a deck and a total of 52 cards in all.