hectictar

(3a * 3a) + (3a² + 3a²) - (4a)²

That is the same thing as:

(3a * 3a) + (3a² + 3a²) - (4a*4a)

Multiply 3a times 3a and 4a times 4a:

(9a²) + (3a² + 3a²) - (16a²)

The parenthesees are not necessary.

9a² + 3a² + 3a² - 16a²

These terms are all alike. They can be combined.

9 apples + 3 apples + 3 apples - 16 apples = -1 apples

9a² + 3a² + 3a² - 16a² = -1a² = -a²

Follow the exact same steps that you needed to do for the other problems. I will try to explain the steps super good so that you can do more problems like this on your own. :)

\(\frac{3x^2+2x+1}{x-1} = 3x + 1\)

Multiply both sides by (x-1):

\((\frac{3x^2+2x+1}{x-1})(x-1) = (3x + 1)(x-1)\)

Multiply out the right side. A lot of teachers teach it with the acroynm FOIL. It just means that you have to multiply each thing in the first set of parenthesees by each thing in the second set of parenthesees and add each product together.

\(3x^2+2x+1 = 3x(x) + 3x(-1) + 1(x) + 1(-1)\)

Multiply:

\(3x^2+2x+1 = 3x^2 - 3x + x - 1\)

Subtract 3x² from both sides:

\(2x+1 = - 3x + x - 1\)

Subtract 2x from both sides:

\(1 = - 3x + x - 1 - 2x\)

Combine like terms:

\(1 = - 4x - 1\)

Add one to both sides:

\(2 = - 4x\)

Divide both sides by -4:

\(-\frac{1}{2} = x\)

If you want an exact answer it is:

\(\frac{26\sqrt{10}}{5}\)

This is how I got it:

\(\sqrt{270.4}=\sqrt{\frac{1352}{5}} \\ = \frac{\sqrt{1352}}{\sqrt{5}} \\ = \frac{26\sqrt{2}}{\sqrt{5}} \\ = \frac{26\sqrt{2}(\sqrt{5})}{\sqrt{5}(\sqrt{5})} \\ = \frac{26\sqrt{10}}{5}\)

\(\frac{5y}{z}-\frac{2y^2}{3z^5} \\ \text{If z is 0 then the problem is undefined. So z ≠ 0.} \\ \frac{5y(3z^4)}{z(3z^4)}-\frac{2y^2}{3z^5} \\ \frac{15yz^4-2y^2}{3z^5}\)

As far as I can tell that is it in the simplest form, and the only restriction is z ≠ 0.

That is what I got but I don't really know what the definition of "simple" is sometimes.

sin x = 0.6691

x = arcsin(0.6691)

x₁ ≈ 41.998º

This is only the angle that makes the sinx  = 0.6691 in the first quadrant.

The other angle that makes sinx = 0.6691 will be in the second quadrant.

The third and fouth quadrants all have negative sin values.

So to find the other angle all you gotta do is subtract  41.998º from 180º

x₂ ≈ 180 - 41.998

x₂ ≈ 138.002°

\(\frac{x^2 +x+1}{x+1}=x+2 \\ x^2 + x + 1 = (x+2)(x+1) \\ x^2 +x+1=x^2+3x+2 \\ 0 = x^2 +3x +2 -(x^2 +x+1) \\ 0 = x^2 +3x +2 -x^2 -x-1 \\ 0 = 2x+1 \\ -1 = 2x \\ -\frac{1}{2}=x\)

If your question was, "What percentage is 2 of 7?"

First, type " 2/7 " into the calculator.

Second, multiply by 100 (or just move the decimal to the right 2 places).

2 is about 28.6% of 7.

Here's another example:

"74 is what percent of 30?"

First, type " 74/30 " into the calculator.

Second, multiply by 100.

74 is about 246.7% of 30

A lot of times I can't remember how to do percents so I just have to go back to what "percent" really means. "Cent" means 100. (A century is 100 years. One cent is one hundredth of a dollar.) Percent literally means per 100.

The question is "2 out of 7 is what out of a hundred?" In other words, if you had 2 out of 7 people with red hair, how many people would have red hair out of 100? How many people would have red hair per 100 people?

This is how to set that up:

\(\frac{2}{7} = \frac{x}{100}\)

Then you solve for x. 200/7 is exactly what we had earlier.

I still go back to thinking of percentages like this just because it is the easiest way for me to think of it.

Lol I realize you probably didn't need a one page essay on this but I just thought I'd share all that.

5/9 = 0.5555555555. . .   (Tbh I just googled what is 0.5 repeating)

5/900 = 0.0055555555. . .

81/100 + 5/900 = 0.815555555. . .

729/900 + 5/900 = 0.815555555. . .

734/900 = 0.815555555. . .

367/450 = 0.81555555. . .

This is a Law of Cosines problem.

Law of Cosines:

\(c^2 = a^2 + b^2 - 2ab\cos C \\ \\ c = TU, a=24, b=12, C=38^{\circ} \\ \text{ (a and b are interchangeable, just pick one and stick with it.)} \\ TU^2 =24^2 +12^2-2(24)(12)\cos38 \\ TU^2 = 576 + 144 - 576\cos38 \\ TU^2 = 720 - 576\cos38 \\ TU = \sqrt{720 - 576\cos38} \\ TU \approx 16.3 \text{ mm}\)

We can use Law of Sines for this.

\(\frac{\sin A}{a} = \frac{\sin B}{b} \\ \frac{\sin A}{9} = \frac{\sin72}{38} \\ \sin A = (9)(\frac{\sin72}{38}) \\ A = \arcsin(\frac{9\sin72}{38}) \\ A \approx 13.018 \text{ degrees}\)

(To the nearest tenth it's 13.0º )