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if a is 4 percent of b and b is 25 percent of c, what percent of a is c?

Hello weredumbmaster!

\(a=\dfrac{4}{100}\cdot b\ |\ \cdot \frac{100}{4}\\ b=25a\\ b=\dfrac{25}{100}\cdot c\\ \ b\ equate\)

\(\dfrac{25}{100}\cdot c=25a\ |\ \cdot \frac{100}{25}\\\)

\(c=\dfrac{25\cdot 100}{25}\cdot a\\ \color{blue}c=100\cdot a\)

\(c\ is 100\cdot 100\%=\color{blue}10\ 000\%\ of\ a.\)

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Oh thank you!! What a cool surprise

And thank you Melody! That is a super cute picture ☺️☺️☺️

Use the slope formula to find the slope m

m=1

What variable are you trying to solve for?

you plug it into the slope formula(https://www.cuemath.com/slope-formula/) and get 1 as your slope.

0.02843 x 100 = 2.843  

were you asked to multiply it by 100?   No you were not.

Leave the decimal point right where it is

So you need the 0.02  but if the next number is 5 or bigger than 5 then the last digit, the 2 will go up one to 3

Here the 3rd digit after the point is 8, which is a big number (bigger or equal to 5) so the 2 goes up to 3

\(0.0 2| \boxed{8}=0.03\qquad \text{To 2 decimal places}\)

AC = sqrt(41 - 25) + sqrt(34 - 25) 

AC = 7

CX = 1/4(AX)

BX / AX = CX / BX

By Pythagoras, AC = 9.

Question: A lecture hall contains 20 chairs, all lined in a row.  What is the number of ways that five chairs can be chosen, so that no two chairs are adjacent?

Answer: By stars and bars, the number of ways is C(18,6) = 18564.

.02843 is rounded to .03. The 8 after the 2 rounds up and the 2 becomes a 3. 

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Kai folded x + 21 starts

Dinny folded x + 39 starts

(x + 21)/(x + 39) = (3/7)/(4/7)

x = 33

Kai folded 54 starts

Spencer paid = 2x/9

Nigel paid      = 5/8(2x/9)

2x/9 + 5/8(2x/9) = 793

x = 2196

Hence, Greta paid $1403

55x7

12/3 ==4 - this is the common ratio.

Your sequence looks like this:

3 , 12 , 48 , 192 , 768 , 3072 , 12288 , 49152 , >>Number of terms = 8>>Total Sum == 65535

The algebra was vile and I likely made a careless error but I got

\(\displaystyle \frac{d^2y}{dx^2}=\frac{0.5-6y^{0.5}+24y-32y^{1.5}}{(1-16y)^3}\)

You don't need y' in your answer because you already know its value from the first part of the question.

Find all points that are 13 units away from the point (-2,7) and that lie on the line x - 2y = 10.

Hello Guest!

\(y=-\sqrt{13^2-(x+2)^2}+7\\ x - 2y = 10 \\-2y=10-x\\ y=\dfrac{x}{2}-5\)

\(\color{blue}-\sqrt{13^2-(x+2)^2}+7=\dfrac{x}{2}-5\\ -\sqrt{13^2-(x+2)^2}=\dfrac{x}{2}-12\\ +\sqrt{13^2-(x+2)^2}=12-\dfrac{x}{2}\\ 169-(x+2)^2=144-12x+\dfrac{x^2}{4}\\ 169-x^2-4x-4=144-12x+\dfrac{x^2}{4}\)

\(1.25x^2-8x-21=0\)

\(x = {8 \pm \sqrt{64+4\cdot 1.25\cdot 21} \over 2\cdot 1.25}\)

\(x=\dfrac{8\pm 13}{2.5}\\ y=\dfrac{x}{2}-5\)

\(\mathbb L=\{(-2,-6);(8.4,-0.8)\}\)

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Try looking at this unit of work.  This is the first video of a set.

Khan acadamy is a great free resource. 

Firstly you do not need to be given  y(5)=-26     You can work that out for yourself.

Like this, sub in x=5 and solve for y

\(5*5^2+5*5+5y=20\\ \text{divide through by 5}\\ 25+5+y=4\\ y=-26\)

So giving you that was probably a bit of a red herring.

\(5x^2+5x+xy=20\\ \text{differentiate both sides}\\ 10x+5+x\frac{dy}{dx}+1y=0\\ \text{Sub in x=5}\\ 50+5+5\frac{dy}{dx}+y=0\\ 5\frac{dy}{dx}=-55-y\\ \text{but we already know that when x=5, y=-26 so sub that in too}\\ 5\frac{dy}{dx}=-55+26\\ 5\frac{dy}{dx}=-29\\ \frac{dy}{dx}=-5.8\\ \)

y'(5) = -5.8

LaTex:

5x^2+5x+xy=20\\
\text{differentiate both sides}\\
10x+5+x\frac{dy}{dx}+1y=0\\
\text{Sub in x=5}\\
50+5+5\frac{dy}{dx}+y=0\\
5\frac{dy}{dx}=-55-y\\
\text{but we already know that when x=5, y=-26 so sub that in too}\\
5\frac{dy}{dx}=-55+26\\
5\frac{dy}{dx}=-29\\
\frac{dy}{dx}=-5.8\\

Thanks Bliss,

And welcome to web2.0calc forum.

I know already that I am going to like you.

Your answer is right but you forgot the brackets.  Without the brackets your answer really is not right.

x+1/8-3x = x+3x-1/8 = 4x - 0.125

this is not what you intended.

Maybe you already know this but the inverse of a function is the reflection of the graph across the line y=x

So you can always check your answer by graphing it.

Desmos is a very nice online graphing calculator.

thanks Bliss, that is a nice straight forward way to approach the problem.

Here is a different way

This is a GP  (Geometric progression)

the first term is -8

the common ratio r= 16/-8 = -2

\(S_n=\frac{a(r^n-1)}{r-1}\\~\\ S_7=\frac{-8((-2)^7-1)}{-2-1}\\~\\ S_7=\frac{-8(-128-1)}{-3}\\~\\ S_7=\frac{-8(-129)}{-3}\\~\\ S_7=\frac{-8(43)}{1}\\~\\ S_7=-344\\~\\\)

I agree my answer is not correct but there is not enough information on that linked page for your answer to be reached.

You should not be dividing by 4 you should be dividing by 10. (to get the arithemtic mean)

the numbers are  w,x,x,y,y,y,z,z,z,z,    There are 10 numbers.

Perhaps you would like to provide more working or another link address that you used.

\(x\ge 0\qquad(1)\\ 2-\sqrt x \ge 0\\-\sqrt x \ge-2\\ \sqrt x \le 2\\ x\le 4\qquad (2)\\ domain\;\;\;[0,4] \)

Solve the 2 equations simultaneously and you get (3,4)  and  (-3,-4)

You have   \(x^2+y^2=\frac{25}{12}xy\qquad and \qquad x^2=7-y^2\)

The algebra is messy and the numbers are big but it is very doable.

Here is the graphical soln.