Calculus

(x-3)(x+6) = 0

x = 3 or x = -6

x = 6.6

1.95 + x = 0.408

1.95 - 0.408 + x = 0.408 - 0.408

1.542 + x = 0

1.542 + x - x = 0 - x

1.542 = -x

-1.542 = x

So:

1.95 - 1.542 = 0.408

It's value.

x = -3

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13 over 8 plus 12 over 3, I'm assuming?

Well first, you need to find a common denominator... multiply 8 x 3. This gets 24. This is your denominator for both sides.

Multiply the numerator of one of these by the denominator of the other. So 13(3) = 39 and 12(8) = 96. Add these together: 39 + 96 = 135. Put this over your common denominator, 24. 135/24. Simplify. 5 5/8.

This has 3 real valued solutions: approx x = -92.877, x = 21.590, x = 81.287

I plotted it to get the approximate solutions.

No. They can have none, one, finitely many or infinitely many.

4

x3 - 3x2 - 9x - 5 = 0

(x + 1)(x2 - 4x - 5) = 0

(x + 1)(x - 5)(x + 1) = 0

x ∈ {-1, 1, 5}

The solution comprises every point on a parabola which is symmetric about the y axis and has its apex at (0,1).

One option is "cannot exist".

The equation is linear and linear equations do not have vertices.

It is the average of -2 and +6, that is, x = 2

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First you have to convert the fractions to the same denominator (bottom number):

3/16 + 1/4 = 3/16 + 4/16

Then add the numerators (top numbers):

3/16 + 4/16 = 7/16

I suppose the expression would be 1/x - 1/ sin x.

The conditions for de l'Hopital's rule doesn't apply here, since neither of the fractions is of type 0/0. However, you can find a common denominator - this results in the fraction (sin x - x) / (x sin x). Here, you do have a fraction of type 0/0 - thus, the conditions for de l'Hopital's rule do apply.

If you take the derivative, you again get a fraction of type 0/0. You need to take the derivate a second time to get a result that can be evaluated.

7.3684

which is also equal to 7.37

The first derivative is m and the second is 0 so the third is also 0.

93.79765... about 93.8

12

It's spelled square root... and it doesn't have one.

Subtract x from each side: 5 = x - 3 so x = 8

If x = 8 satisfies the equation 19 - x = 12, then it is a solution of the equation.

19 - x = 12

19 - 8 = ? 12

11 ≠ 12

Since x = 8 does not satisfy the equation, x = 8 it is not a solution.