kitty<3

Oh, it's fine:) Thanks!

Ok, so the function form is y = a * b^x.

Substitute in the values:

750 = a * b⁵

and

48 = a * b²

Then divide the two equations:

750/ 48 = (a * b⁵) / (a * b²)

So: 

15.625 = b³

Take the cube root of both sides:

2.5 = b

Now, substitue b into one of the equations (the one with 48 has smaller numbers and is easier to work with.)

48 = a * 2.5²

Simplify.

48 = a * 6.25

Divide both sides by 6.25

7.68 = a

Now substitute in a and b to write the exponential function: 

y = 7.68 * 2.5^x

2x² = x² - 1

First, subtract x² from both sides.

x²= -1

Then take the square root of both sides.

so $${\mathtt{x}} = {\sqrt{-{\mathtt{1}}}}$$ and $${\mathtt{x}} = {\mathtt{\,-\,}}{\sqrt{-{\mathtt{1}}}}$$

But in real numbers, you cannot have the square root of a negative number. So instead, there is this number, $${i}$$ , the imaginary number.

$${i}$$ by definition is the square root of -1

So x = i or x = -i

And as CPhill said earlier, too

It would certainly help if you gave an example along with your question, but no worries:)

There are quite a few ways to solve for a side in a right triangle, and one of the most common is the Pythagorean Theorem: 

 $${{\mathtt{a}}}^{{\mathtt{2}}}{\mathtt{\,\small\textbf+\,}}{{\mathtt{b}}}^{{\mathtt{2}}} = {{\mathtt{c}}}^{{\mathtt{2}}}$$

a and b are legs of the triangle (the two shorter sides) and c is the hypotenuse (longer, diagonal side)

If you have the measure of an angle, you can use trigonometry to solve for an unknown side (using sine, cosine, tangent)

It really depends on what info you have about the triangle. . .

5+3(x-4)

First, expand the expression by distributing the 3 into (x-4)

5 + (3*x) - (3*4)

5 + 3x - 12

Then add the 5 and -12

The simplified expression would then be

3x - 7

I'm assuming you mean the sin of ((-8/17) + (-3/5)) since you seemed to have a partial set of parentheses. . .

So the sine of the whole thing, inputted into this site's calculator, would be $$\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{sin}}{\left({\mathtt{\,-\,}}\left({\frac{{\mathtt{8}}}{{\mathtt{17}}}}\right){\mathtt{\,-\,}}\left({\frac{{\mathtt{3}}}{{\mathtt{5}}}}\right)\right)} = -{\mathtt{0.018\: \!684\: \!202\: \!361}}$$

On the other hand, if you didn't mean the extra parentheses and meant sin(-8/17) added onto (-3/5) instead, it would be

$$\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{sin}}{\left({\mathtt{\,-\,}}{\frac{{\mathtt{8}}}{{\mathtt{17}}}}\right)}{\mathtt{\,-\,}}\left({\frac{{\mathtt{3}}}{{\mathtt{5}}}}\right) = -{\mathtt{0.608\: \!213\: \!221\: \!784}}$$

Well, first of all I don't see "the following" solutions, but no worries!

You can graph the two equations in a graphing calculator by writing them in the y = mx + b form, where m is slope and b is the y-intercept.

For the first equation 2x + y = 1 you would move the 2x to the right and rewrite it as:

y = -2x + 1

The second equation stays the way it is: 

y = -12x + 1

Now graph both of them on the same axes, and look at the point where they intersect.

They intersect at (0, 1)

There are 5 diagonals, no repeats. For example, AD and DA are the same diagonal, so it should be a combination.

To get inverse of trigonometric functions (sin, cos, tan. .  .) click on "2nd" and they will pop up in place of the regular trig functions. There is also an inverse for numbers, the "1/x" button at the top, fourth from the left.