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Thank you very much.

I'm actually not that confident working with slopes and lines sometimes because I'm more familiar with equations than graphs.

Still, thanks!

Hi Guest!

I'm sorry to tell that if you are trying to get a specific value for k, you can not since there are three variables and two equations!

However, if you are trying to express k in terms of X, that's great!

k = 3p, so 18p is 6k. Sub that into the first equation to get 10k = 1/4X, and from that you can complete the rest.

Set all of the tickets the three people sold as X.

Joyce: 1/10X

Ken: 1/10X+6

Brandon: 82

we get 4/5X= 88, thus 1/X = 22, thus X = 110

Brandon sold 82(he really sold A LOT),

Joyce sold 11,

and Ken sold 17!

You can plug the answers back and check if you want!

You there?

Find for k

What do you want to find?

The stuff under square root needs to be bigger than 0.

-6x^2+12x+18>= 0

We factor to get: -6(x^2-2x-3)>= 0, thus -6(x-3)(x+1) >= 0.

We can get rid of -6, but we need to change the sign. (x-3)(x+1) <= 0.

Two pairs of possibilities: x-3>= 0, x+1 <=0

and x-3 <= 0, x+1 >=0.

Simplify to get x>=3, x<=-1(which is impossible so we abandon it)

and x<=3, x>=-1(which makes sense)

Finally, the domain is [-1, 3]

The ratio of the number of chocolate cakes to the total number of cakes sold in a shop was 3:8. 1/2 of the remaining cakes in the shop were cheesecakes and the rest were lemon cakes and vanilla cakes in the ratio of 2:1. There were 120 more cheesecakes than vanilla cakes in the shop.

(a)  How many chocolate cakes were there?

(b)  All the chocolate cakes were sold at 2 for $5. How much money was collected from selling all the chocolate cakes?

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Something's wrong with this question. 

The only connection between chocolate cakes and the rest of the cakes is this:

The ratio of the number of chocolate cakes to the total number of cakes sold in a shop was 3:8. 

The ellipsis (the ...) usually indicates continuation forever.  If the sequence is finite then perhaps the number of levels should be specified.

但可靠咳咳咳认可可是看看思考思考

You do not know what the slop is but you do know that the slope between any two points will be the same as between any other 2 points.

\(\frac{3--5}{-a+2-3}=\frac{2--5}{2a+3-3}\\ \frac{8}{-a-1}=\frac{7}{2a}\\~\\ 16a=-7a-7\\ 23a=-7\\ a=\frac{-7}{23} \)

check

\((3,-5),\quad (2\frac{7}{23},3),\quad (2\frac{9}{23},2)\)

LaTex:

\frac{3--5}{-a+2-3}=\frac{2--5}{2a+3-3}\\
\frac{8}{-a-1}=\frac{7}{2a}\\~\\
16a=-7a-7\\
23a=-7\\
a=\frac{-7}{23}

Multiply 0.455555...(we set as x) by 10 to get 4.5555555...(10x)

then, use 4.555555 to subtract 0.455555 to get 4.1 because later repeat digits cancel

4.1 is equal to 9x, and x is 41/90

Oh, Thank you! but I think the sequence is finite, so we can't just say what you did with y(x). 

Let \(a,~b,~c\) be the roots of \(x^3 - x + 4 = 0\).
Compute \((a^2 - 1)(b^2 - 1)(c^2 - 1)\).

Let \(a,~b,~c\) be the roots of \(x^3 - x + 4 = 0\).
Compute \((a^2 - 1)(b^2 - 1)(c^2 - 1)\).

By Vieta:

\(\begin{array}{|rccc|} \hline x^3 &\underbrace{+0*x^2}_{0=-(a+b+c)} &\underbrace{-1*x}_{-1=ab+ac+bc} & \underbrace{+4}_{4=-abc} \\\\ \hline \end{array} \begin{array}{|rcll|} \hline abc &=& -4 \\ ab+ac+bc&=& -1 \\ a+b+c &=& 0 \\ \hline \end{array}\)

\(\begin{array}{|rcll|} \hline a+b+c &=& 0 \\ (a+b+c)^2 &=& 0^2 \\ a^2+b^2+c^2+2*(ab+ac+bc) &=& 0 \\ a^2+b^2+c^2+2*(-1) &=& 0 \\ \mathbf{a^2+b^2+c^2} &=& \mathbf{2} \\ \hline \end{array} \\ \begin{array}{|rcll|} \hline ab+ac+bc &=& -1 \\ (ab+ac+bc)^2 &=& (-1)^2 \\ a^2b^2+a^2c^2+b^2c^2+2*(a^2bc+ab^2c+abc^2) &=& 1 \\ a^2b^2+a^2c^2+b^2c^2+2*abc*(a+b+c) &=& 1 \\ a^2b^2+a^2c^2+b^2c^2+2*abc*(0) &=& 1 \\ \mathbf{a^2b^2+a^2c^2+b^2c^2} &=& \mathbf{1} \\ \hline \end{array}\)

\(\begin{array}{|rcll|} \hline && \mathbf{(a^2 - 1)(b^2 - 1)(c^2 - 1)} \\\\ &=& a^2b^2c^2-(a^2b^2+a^2c^2+b^2c^2)+a^2+b^2+c^2-1 \\ &=& (-4)^2-(1)+2-1 \\ &=& 16-2+2 \\ &=& \mathbf{16} \\ \hline \end{array}\)

\((a^2 - 1)(b^2 - 1)(c^2 - 1) = \mathbf{16}\)

Area = 234 cm² 

A wooden block has rectangular faces and sides of lengths L, W, and H. The faces have areas of 18.7 cm², 38.5 cm², and 23.8 cm² as shown. Find the lengths of the sides. 

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

W * L = 38.5

W * H = 18.7

L * H = 23.8

------------------

W = 18.7 / H

L = 23.8 / H

------------------

W * L = 38.5

(18.7 / H)(23.8 / H) = 38.5

H = 3.4 cm

W = 18.7 / H = 5.5 cm

L = 38.5 / W = 7 cm

Beast, what does that have to do with anything? 

Well I am glad you are entertaining yourself Ginger :)

I have not done this question but this is how I would start.

Let the cost of a pin be p cents

Let the cost of a keychain by k cents

Let the entire amount of her money be  M cents

Now start setting up true equations.

See if you can do something with that.

i tried number one and it was wrong

The range of j(x) is [9,15].