For all real numbers x and y, if x # y = x(x-y), then x # (x # y) =My question is, how does x # (x # y) = 8 and how does it also equal to x(squared) - x(cubed) + x(squared) y?

Is there a rule of the function that I have forgotten?

Thanks

Answers

Answer 1

Answer: $x\#y=x(x-y)\n\nx\#(x\#y)\n\nx\#y=x(x-y)=x^2-xy\n\nx\#(x\#y)=x\#(x^2-xy)=x[x-(x^2-xy)]=x(x-x^2+xy)\n\n=x^2-x^3+x^2y$

$x^2-x^3+x^2y=8\n\nx^2(1-x+y)=8\n\nx^2(1-x+y)=2^2\cdot4\iff x^2=2^2\ and\ 1-x+y=4\n\nx=2\ and\ y=4-1+x\n\nx=2\ and\ y=3+2\n\nx=2\ and\ y=5$

Answer 2

Answer: if x # y = x(x-y) => x # (x # y) = x # [x(x-y)] =x[ x - x(x-y)] = x( x - x^2 +x*y ) = x^2 - x^3 + ( x^2 ) * y;

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There are a total of 30 white and black marbles in a box. There are 14 more white marbles than black marbles. How many black marbles are in the box?

Answers

Answer:

Step-by-step explanation:

30-14=16

Final answer:

The box contains 8 black marbles.

Explanation:

The question is asking about a box containing a total of 30 marbles, with the white marbles numbering 14 more than the black ones. So, we can first create an equation which equates the total number of marbles (30) to the sum of the black marbles and the white marbles. Let's denote the number of black marbles as B. The number of white marbles can then be expressed as B + 14.

Therefore, the equation would be: B + (B + 14) = 30, simplifies to 2B + 14 = 30.

To solve for B, subtract 14 from both sides of the equation so you have 2B = 16. Now, divide each side by 2 to solve for B, which gives us B=8.

Therefore, there are 8 black marbles in the box.

Learn more about Basic algebra here:

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A store buys an item for $50 and marks it up 100%. What is the price?

Answers

Answer

= $100

Explanation

Profit = selling price - buying price

percentage profit = profit/buying price × 100%

100% = profit /$50

Profit = 100% × $50

= 100/100 × $50

= 1 × $50

= $50

Selling price = buying price + profit

= $50 + $50

= $100

$100

100% would be doubling it.

Estimate then find the sum or difference 8.5+1.8

Answers

Estimating usually means rounding to the nearest whole number to make it so that you can do the math in your head.
So, 8.5 becomes 9, and 1.8 becomes 2.
The sum would then be 11
And the difference is 7

Which two numbers add up to ___ and multiply to ___?1. multiply to -18 add to -17
2. multiply to 36 add to -13
3. multiply to -24 add to -5
4. multiply to -18 add to 7
5. multiply to -36 add to 9
6. multiply to 24 add to 10
7. multiply to 18 add to -9
8. multiply to -36 add to -16

I need help ASAP!

Answers

Ok so let's start :)

Ok so first one, numbers need to add to $-17$ AND multiply to $-18$
First of all you need to check the signs which stands near to those numbers. As you see there is $(-)$ next to both of them, it means that ONLY one number needs to be with $(-)$ sign. Why? There is short "instruction" which you need to remember:

$(-)*(-)=(+)$
$(-)*(+)=(-)$

If there are to signs next to each other, you can "change" them using "rules" below ;P

$(-)+(-)=(+)$
$(-)+(+)=(-)$

So it is possible to add two numbers with $(-)$ sign next to them which would be equal to $-17$ (for example $-5+(-12)$ but it is impossible to find two numbers which have $(-)$ sign next to them which will give you also negative number after multiplication :)

Ok it's enough theory for now, it should be much easier now :D

1. So you can multiply $1*-18$ which is $-18$
Also $-18+1$ which is $-17$

Rules above should help you to understand what I did below :) In case of any questions you can help me anytime :)

It's quite simple :)

1. $\ \boxed{-18\ AND\ 1}\ because\ -18+1=-17\ AND\ (-18)*1=-18$

2. $\ \boxed{-9\ AND\ -4}\ because\ -9+(-4)=-13\ AND\ (-9)*(-4)=36$

3. $\ \boxed{-8\ AND\ 3}\ because\ -8+3=-5\ AND\ (-8)*3=-24$

4. $\ \boxed{9\ AND\ -2}\ because\ 9+(-2)=7\ AND\ 9*(-2)=-18$

5. $\ \boxed{12\ AND\ -3}\ because\ 12+(-3)=9\ AND\ 12*(-3)=-36$

6. $\ \boxed{6\ AND\ 4}\ because\ 6+4=-10\ AND\ 6*4=24$

7. $\ \boxed{-6\ AND\ -3}\ because\ -6+(-3)=18\ AND\ (-6)*(-3)=18$

8. $\ \boxed{-18\ AND\ 2}\ because\ -18+2=-16\ AND\ -18*2=-36$

It's quite simple :)
1. $-18\ \&\ 1$ because $-18+1=-17$ AND $(-18)*1=-18$
2. $-9\ \&\ -4$ because $-9+(-4)=-13$ AND $(-9)*(-4)=36$
3. $-8\ \&\ 3$ because $-8+3=-5$ AND $(-8)*3=-24$
4. $9\ \&\ -2$ because $9+(-2)=7$ AND $9*(-2)=-18$
5. $12\ \&\ -3$ because $12+(-3)=9$ AND $12*(-3)=-36$
6. $6\ \&\ 4$ because $6+4=-10$ AND $6*4=24$
7. $-6\ \&\ -3$ because $-6+(-3)=18$ AND $(-6)*(-3)=18$
8. $-18\ \&\ 2$ because $-18+2=-16$ AND $-18*2=-36$