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17-6x=47+10x

17=47+16x            Add 6x to both sides.

-30=16x                Subtract 47 from both sides.

-1.875=x               Divide by 16.

x=-1.875 is your answer.

It would be tan75=564/x

What you're looking for is the length of the adjacent side.  Given the opposite side is 564, and tan=opp/adj.

Let x=adj

then tan(75)=564/x.     Multiply both sides by x

xTan(75)=564               Divide both sides by tan(75)

x=564/tan(75)

Using the tangent, we have

tan(53°) = x/50   where x is the height of the tree

x = 50tan(53°) = about 66.35 ft. = 66ft.

We have

y = ab^x   ....   and we need to find a and b

So, using (0,5)  we have

5 = ab⁰

5 = a

And using (1, 15), we have

15 = 5b¹

15 = 5b     divide by 5 on both sides

b = 3        So our function is

y = (5)3^x

y=ab^x

let a=5 and b=3

y=5(3^x)  passes through points (0,5) &(1,15)

not sure if this is what you're looking for

This, in science, is water displacement. Have you ever filled a glass of water to the top, then added ice cubes? The water probably spilled over the top of the glass. That situation is very similar to Nancy's situation. Scientifically, the volume of an item placed in water equals the "after" volume minus the "before" volume. In this case, 650-450=200. That means that the volume for 4 golf b***s is 200mL. To find the volume of each golf ball, we divide by 4. The volume of one golf ball is 50mL. I hope this helped!

Since we know an angle and an adjacent side, we can use the cosine function to find the ladder length (the hypoteneuse), and we have......

cos(68°) = 12/x ............ where x is the ladder length

So......

x = 12/ cos(68°) = about 33.03 ft. = 33 ft.

Well...if the water level rose by 200 ml, each of the 4 golf b***s must have contributed to a 50ml rise.......thus, the volume of a single ball must be 50 ml.

This looks like some sort of "decay" function, so I'm going to assume you might mean.........

t(20)=16e^(-0.034x)

So, we're just putting "20" into the function to get an evaluation

So we have

$${\mathtt{16}}{\mathtt{\,\times\,}}{{\mathtt{e}}}^{{\mathtt{\,-\,}}\left({\mathtt{0.034}}{\mathtt{\,\times\,}}{\mathtt{20}}\right)} = {\mathtt{8.105\: \!871\: \!877\: \!849\: \!435\: \!2}}$$

Good job, GL !!!

Your points are a mountin' up !!!

(But, you're still not gonna' catch me !!!....... LOL!!)

(Now...get back to that solo !!!)

Thank you for that, Stu.....I'm sure that will be very helpful for a lot of people on this site...."Thumbs Up" from me !!!

4x-7y=11

-5x+2y=14

OK, I'm going to use something called the "elimination" nethod to solve this. We're going to eliminate a variable (I'll choose "x") which will set up an equation in one variable that will be easy to solve.

Note that if we multiply the top equation by 5 on both sides and the bottom equation by 4 on both sides, we get the following system:

20x - 35y = 55

-20x + 8y = 56    

.......Now, if we just add these together, note how the "x's" "disappear!!"   So we have......

-27y = 111    .... divide by -27 on both sides, and we get

y = 111/-27   =   -37/9

Now using either one of the original equations - I'll use the second one - we can substitute -37/9 for y and find x.  So we have

-5x + 2(-37/9) = 14

-5x - 74/9 = 14       ... multiply through by 9 on both sides

-45x - 74 = 126      .....add 74 to both sides

-45x = 200             .....divide by -45 on both sides

x = 200/-45 = -40/9

So there are our solutions...x = -40/9  and y = -37/9

Not very pretty, is it??   ....but, that's the way it goes sometimes !!!

If you check these in the first original equation, you will see that they "work"  (In fact, they should "work" in all the equations!!!)

$${\frac{\left(\begin{pmatrix}
{\mathtt{1}}
\\
-{\mathtt{2}}
\end{pmatrix}
{\mathtt{\,\small\textbf+\,}}\begin{pmatrix}
{\mathtt{5}}
\\
{\mathtt{9}}
\end{pmatrix}
\right)}{{\mathtt{2}}}} = \begin{pmatrix}
{\mathtt{3}}
\\
{\mathtt{3.5}}
\end{pmatrix}$$

it is very easy to me because 1/4 divided by 2 equals 0.125. I learned that when I was 2 years old 

To divide fractions, invert and multiply.

ie. 1/4 ÷ 2/1 = 1/4 x 1/2  = 1/8

$${\frac{{\mathtt{16.99}}}{{\mathtt{735\,000\,000}}}} = {\frac{{\mathtt{x}}}{{\mathtt{7\,000\,000\,000}}}}$$

$$\mathrm{\ }$$$${\mathtt{735\,000\,000}}{\mathtt{\,\times\,}}{\mathtt{x}} = {\mathtt{7\,000\,000\,000}}$$

$${\frac{{\mathtt{7\,000\,000\,000}}}{{\mathtt{735\,000\,000}}}} = {\frac{{\mathtt{200}}}{{\mathtt{21}}}} = {\mathtt{9.523\: \!809\: \!523\: \!809\: \!523\: \!8}}$$

9.5238095238095238 is the number the 735,000,000 was multiplied by to get 7,000,000,000. Thus, to equal out, you would multiply 16.99 by 9.5238095238095238

$${\mathtt{16.99}}{\mathtt{\,\times\,}}{\mathtt{9.523\: \!809\: \!523\: \!809\: \!523\: \!8}} = {\frac{{\mathtt{3\,398}}}{{\mathtt{21}}}} = {\mathtt{161.809\: \!523\: \!809\: \!523\: \!809\: \!4}}$$

It would cost £161.81

Let me think about this.

Firstly is this what you mean, or is the -1 tacked onto the end?

$$\left(\frac{1}{3}\right)^8=\left(\frac{-1}{3}\right)^{n-1}$$

if (n-1) is even then 

$$\left(\frac{1}{3}\right)^8=\left(\frac{1}{3}\right)^{n-1}$$

n-1=8

n=9

If n-1 is odd it can't work.

okay so n=9 is the only answer in the Real number system.

it is stupid logic

You the expert on STUPID, so you should know!

Thanks, I have emailed the guy who wrote the exam to clarify facts about this matter. Thanks.  In other questions  of indefinate integrals, I believe it was right when calculated in degrees. But have had some problems with this so im not sure. I'l wait for a reply email from the person in question. Thanks for this assistance.

my logic isn't floored. No other number has sqrt that will change, and no other number has a sqrt that increases its size. Your logic is floored, infact it is stupid logic, or stupid as you like to put it. The fact of something does not exist because it is stated. But you're to dim witted to even understand what I'm driving at, that's a given.

The answer was obvious! That you are STUPID!

Sorry!!

I didn't need to ask that. The answer was obvious!