The product of a particular number and a second value, which is given by the sum of 8 and the original number, is 65. What is the number?

there are infinite values of sum X + Y = (Y + 65/Y) since there are infinite values of Y.

Step-by-step explanation:

XY = 65. Given that question is asking you find X + Y, it kind of indicates that there could be very limited possible values of X and Y which you can work out. Again it is an indication of such silly questions. It need not be true that you have limited solutions.

One such solution is represented here. I have assumed X and Y are positive integers only.

Factorize 65 = 65 x 1 or 13 x 5

Therefore (X,Y) can be (65,1) or (13,5) .

So X + Y = 66 or 18.

If we include negative integers as well ,

then XY = 65 => Factors are 65 x 1, 13 x 5 or (-13) x (-5) or (-65) x (-1)

So X + Y = -66 or -18 or 18 or 66.

In general,

XY = 65 => X = 65/Y (assuming Y is not 0 else XY would have been 0 too).

Therefore X + Y = Y + 65/Y.

If X, Y belong to real or complex numbers except 0,

there are infinite values of sum X + Y = (Y + 65/Y) since there are infinite values of Y.

fd

step-by-step explanation:

a, b, c, d are correct.

step-by-step explanation:

we have g(x) = 3 and are required to find which option is a translation of g(x).

now, 'translation' is a transformation which means to shift the function in any direction and the general form of translation is g(x) + k, where k is any real number.

so, according to the options we see that all are correct as they satisfy the general form of translation.

also, it can be seen from the graph below that the function g(x) = 3 is shifted from its position in all the four options.