Which is a possible number of distinct real roots for a cubic function? select all that apply. 0 1 2 3 4

The answer is  1 and 3.

Step-by-step explanation:  We are to select the correct options about the number of real roots of a cubic function.

We know that there are three roots of a cubic function, out of which one must be real because the least number of real roots of an odd degree function is 1.

Also, if the second root is real, then the third one must also be real because the complex roots of a function occur in pairs.

Therefore, there is one real root or three real roots for a cubic function.

Thus, the answer is 1 and 3.

p ÷ r = tan(x)

step-by-step explanation:

given that there is a figure below shows a right triangle: a right triangle is shown with hypotenuse equal to q units and the length of the legs equal to p units and r units.

graph is missing so i will create the graph as per given information.

the angle between the legs having lengths p units and q units is y degrees. the angle between the legs having lengths r units and q units is x degrees.

now we need to find about what is p ÷ r equal to.

so we can use trigonometric ratio tan(x)=[altitude]/[base] to find the value of p ÷ r, because p is the altitude and r is the base.

p ÷ r=tan(x)

hence final answer is p ÷ r=tan(x).