All Answers 358203 Answers

Of course it isn't 40.  Or if it is, one or more of the other values is incorrect.  

That's why I said that there was something wrong in the problem as stated. 

Let us see if I understand your question:

Let "n" be a positive integer. I will choose "n" to be = 4. So, 2^n = 2^4 =16, and 16 mod 13 =3. And let "k" be the number of positive integers LESS than 2^4 or 16. In other words, "k" will range from 1 to 15. So, the question is: what is the remainder when"k" is divided by 13? Well, if "k" is from 1 to 15, then you have the following:

1 mod 13 = 1 - the remainder

2 mod 13 = 2 - the remainder

3 mod 13 = 3 - the remainder.

4 mod 13 = 4 - the remainder.

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.

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13 mod 13 = 0

14 mod 13 = 1 - the remainder

15 mod 13 = 2 -the remainder. And so on. And this pattern will continue for any "n" you choose.

And that is the way I read it! 

Rhombus ABCD has a perimeter of 148, and one of its diagonals has a length of 72. What is the area of ABCD?

Area = 615.168 units squared. 

Find a linear inequality with the following solution set. Each grid line represents one unit.

Mary has 6 identical basil plants, and three different window sills she can put them on. How many ways are there for Mary to put the plants on the window sills, if no window sill can have all six plants?

Put  one plant on each window sill then use stars and bars to work out the number of possible outcomes.  3 plants left

three stars and 2 bars

       P P | P | 

5C2= 10 ways

That is assuming that the plants are all identical.

Have you tried setting up some equations?    Show us what you have been able to do?

The names have been chosen to be easy.  A,B,C,D

Triangles BCF and EDF are similar so  y/20 = 9/10

You can take it from here.

It is really nice to see that you have learned from me.   It is a pity that you are a guest and not a member but not to worry.

Your answer is almost correct.

Note that it could be   ua  or    au   so you will need to multiply your answer by 2.  

Let

y=| x - 1 | + | x - 1.5 | + | x - 3 |

The roots of this will be x=1, x=1.5 and x=3

Work out what the y funtion expression will be for each of these regions  (it will be a line segment each time)

x<1

1<=x<1.5

1.5<=x<3

x>3

Graph each of the line segments that you get and see where the lowest value of the function is.

If you have questions then ask.

Please no one answer over me.

Given that x < 5, rewrite x - | x - 5 | without using absolute value signs.

Hello Guest!

\(if\ x<5\ then\ is\\ x-|x-5|=\color{blue}2x-5 \)

  !

Here is a long video that looks like it could be quite good...

That is if you want some insight.

Find all complex numbers z such that z^4=-4

It is a power of 4 so there are 4 answers.

first solution   

\(z^4=-4\\ z^4=4cis180\\ z=(4cis180)^{1/4}\\ z=\sqrt2(cis(180*\frac{1}{4}))\\ z=\sqrt2(cis(45))\\ z=\sqrt2(1+i)\\ \text{The other solutions will be }\\ z=\sqrt2(-1+i),\quad z=\sqrt2(-1-i)\quad z=\sqrt2(1-i) \)\(\)

EG ≠ 40  

We have a triangle ABC and a point K on BC such that AK is an altitude to triangle ABC. If AC = 10, BK = 7, and BC = 12, then what is the area of triangle ABC?

AK = sqrt (AC² - CK²)

Area = 1/2 (AK * BC)

I'll let you play with the numbers.

Simplify sqrt{28x} * sqrt{15x} * sqrt{20x}. Express your answer in simplest radical form in terms of x.

Hello Guest!

\( \sqrt{28x}\cdot \sqrt{15x} \cdot \sqrt{20x}=\sqrt{x^3\cdot 2^2\cdot 7\cdot 3\cdot 5\cdot 2^2\cdot 5}\) = \(2^2\cdot 5\cdot x\cdot \sqrt{3\cdot 7\cdot x}\)

\(=20x\cdot \sqrt{21x}\)

  !

(a,b) = (-5,4).

Welcome to the forum Eunice.

u sure?

It was not censored.

I wanted to display the code not the output but it refused to display that way.

So I whited  (literally) it out.