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Hints :

For question 1 and 2 use this triangle

hint for question 3.

Here is an interactive unit cirlce for trigonometry.  Try and work really understand what it is telling you.

WHEN you fully understand it advanced trig will become easier.

Cos of an angle is given by the x  value on the circumference of the unit circle.  See if you can work out why.

$${\mathtt{9.884}}{\mathtt{\,\times\,}}{{\mathtt{10}}}^{{\mathtt{6}}} = {\mathtt{9\,884\,000}}$$

just move the decimal point over 6 places in the direction to make the number bigger.

(Bigger because the 6 is positive so $${{\mathtt{10}}}^{{\mathtt{6}}}$$   is a big number.)

Or 9.323874524181354e11

932387452418.135401762816

This answer is common sense.

Order of Operations:

1. Solve the paranthesis

2. Multiply (*)   /    Divide (:)

3. Add (+)    /   Subtract    (-)

(2⋅52 - 72)1714 = (104 - 72)1714 =  32*1714 = <Your answer>

If you have a usual French deck consisting of 52 different card, and want to know how many different ways to list all the cards, you can use factorial.

The total # of different ways to list all the 52 cards, such that you have a 1st card, 2nd card and so forth, is 52!

52! = 52*51*50*49* ... *4*3*2*1 ≈ 8,1 *10⁶⁷.

Why is this?

Your 1st card have to be one of the 52 cards: 52 possibilites.

Your 2nd card have to be one of the remaining 51 cards: a total of 52*51 possibilities.

Your 3rd card have to be one of the remaining 50 cards: a total of 52*51*50 possibilities.

Your 4th card have to be one of the remaining 49 cards: a total of 52*51*50*49 possibilities.

And so on until there is a single card left.

Scientific notation is in the form: a * 10^b.

We count the number of digits: 10. We know that the exponent is one less than the # of digits. Therefore it's going to be on the form: a * 10⁹. 

We get rid of all the trailing zeros, and put a period after the first digit: 1.205

So the # in scientific form is: 1.205 * 10⁹.

An equation written in slope-intercept form would have the form $${\mathtt{y}} = {\mathtt{mx}}{\mathtt{\,\small\textbf+\,}}{\mathtt{b}}$$ where y and x are variables and m and b are numbers.

An equation in standard form would be: $${\mathtt{ax}}{\mathtt{\,\small\textbf+\,}}{\mathtt{by}} = {\mathtt{c}}$$ where y and x are still variables, and a, b, and c are integers.

So now you would need to make the x and y variables on the same side of the equation, with all the constants (numbers without variables) one the other side.

Say for example you have this equation in slope-intercept form:

y = $${\frac{{\mathtt{3}}}{{\mathtt{4}}}}$$x + 2

You can subtract y from both sides to get x and y on the same side of the equation:

3/4x - y + 2 = 0

Now isolate the 2:

3/4x - y = -2

But since a,b, and c, must be integers, you would need to multiply all terms by the least common denominator of the fraction(s) in the equation. In this case, it is 4:

Standard form: 3x - 4y = -8

x^2 - 4x + 16 = 0    this won't factor.....using the on-site solver, we have

$${{\mathtt{x}}}^{{\mathtt{2}}}{\mathtt{\,-\,}}{\mathtt{4}}{\mathtt{\,\times\,}}{\mathtt{x}}{\mathtt{\,\small\textbf+\,}}{\mathtt{16}} = {\mathtt{0}} \Rightarrow \left\{ \begin{array}{l}{\mathtt{x}} = {\mathtt{2}}{\mathtt{\,-\,}}{\mathtt{2}}{\mathtt{\,\times\,}}{\sqrt{{\mathtt{3}}}}{\mathtt{\,\times\,}}{i}\\
{\mathtt{x}} = {\mathtt{2}}{\mathtt{\,\times\,}}{\sqrt{{\mathtt{3}}}}{\mathtt{\,\times\,}}{i}{\mathtt{\,\small\textbf+\,}}{\mathtt{2}}\\
\end{array} \right\} \Rightarrow \left\{ \begin{array}{l}{\mathtt{x}} = {\mathtt{2}}{\mathtt{\,-\,}}{\mathtt{3.464\: \!101\: \!615\: \!137\: \!754\: \!6}}{i}\\
{\mathtt{x}} = {\mathtt{2}}{\mathtt{\,\small\textbf+\,}}{\mathtt{3.464\: \!101\: \!615\: \!137\: \!754\: \!6}}{i}\\
\end{array} \right\}$$

Note that neither solution is "real"......we could have seen this by using the "discriminant" - (b^2 - 4ac) - where b =-4, a = 1 and c = 16

So we have......  (-4)^2 - 4(1)(16)  = 16 - 64  = -48

And since this is < 0, we will have  "non-real"  solutions...

7+9=25-y

16=25-y/-25 

-9=-y

9=y

7+9 =25-y     simplify the left side

16  = 25 - y    add y to both sides and subtract 16 from both sides

y = 25 - 16 

y = 9

And there you are......!!!

plz help!!!!

THANKS SO MUCH!!!

Four notebooks are just 1/3 of the cost of twelve of them.....so just divide $22.68 by 3.....

Just type in  "abs (-9) "    and hit "="

Thanks for that reference, Alan....

The "triangular" numbers are generated by just adding the sum of the first "N" digits

Here's another way of generating the "formula"

Ist, write down all the first N positive intergers.....and below that, write them in reverse order....so we have

1          2            3         4          5   ......  N-2       N-1    N

N        N-1         N-2      N-3      N-4  ....    3           2      1     ...now...just add each column, this gives

N+1     N+1       N+1      N+1     N+1 ....   N+1      N+1  N+1

Now the total sum is just (N+1) added N times  =  (N+1)(N)

But, we've got twice the sum we really need, so just divide this by 2 and we have

(N)(N+1) / 2

And, presto!!!....there's the "formula"

you cant but to find the absolute value for anything it is just the distance away from zero so the anwser would be 16

you can do .16 times 9.75

if u do 9.5% you can move the decimal over so that it is .95 then multiply that by 40

You work out 1% by: 40 / 100 = 0.4

0.4 / 2 = 0.2 = 1/2%

9 1/2 / 1/2 = 19

19 * 0.2 = 3.8cm  You gotta love MATHS! 

I assume you want the miles per gallon....???

Just divide 1525 by 30......that will be your answer....

Holy Moley......!!!!! ......not just CDD, Nauseated.....but a case of "LUNA-cy," as well.........!!!

I have personally commissioned one your academy "grads" to double-check Alan's answer....I think  I also mentioned something to him about keeping an eye out for a certain "Roman Zero"  - (if he happens across it somewhere in deep space...)

Assuming that the whole field will be mowed (including the center)....The whole area of the field is (24 x 32) yds = 768 sq yds.   So (1/2) of this is 384 sq yds......and that is the measure of the unmoved area when she is half way through the job.   Call the uniform width, x...... so we have

(24 - 2x) (32 - 2x)  = 384     or

2(12 - x) * 2 (16 - x) = 384

4 (12-x) (16-x)  = 384   divide through by 4

(12-x)(16-x)  = 96

192 - 28x + x^2   = 96   expand and re-arrange terms

x^2  - 28x + 96 = 0  factor

(x - 24) (x - 4)  = 0

And setting each factor to 0, we have x =24 or x = 4  reject 24

So, the uniform width is 4 ft.   and the area of the unmowed center is (24-2(4)) (32- 2(4))  = (16)(24) = 384 sq yds, just as we expect....