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since they have to be different

1x1 = 1

1x2 = 2

1x3 = 3

1x4=4

2x2 = 4

1x5=5

1x6=6

2x3=6

1x7=7

1x8=8

46 tiles

If you mean each numbers must be divisible by 2, 5, and 10 simultaneously, then you have:

Every number ending in zero from 10 to 10000, or 10,000 / 10 = 1,000 such numbers.

Find all the divisors of 126:

126 = 1 | 2 | 3 | 6 | 7 | 9 | 14 | 18 | 21 | 42 | 63 | 

Since 6 the GCD of two numbers in this list, just check one by one:

Since 6 is a divisor of 18 and 42, it therefore follows that they are the 2 numbers sought.

GCD(18, 42) = 6

LCM(18, 42) = 126

Sum =18 + 42 = 60

We can find this by finding how many odd numbers are in one row since each row is numbered 1 to 11 so by couting we find 

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 

That there are exactly 6 odd numbers in one row, So 6 time's how many rows there are will equal our product, which equals our answer. 

 6x^2 + 10x = 4 - 10x - 6x^2     rearrange as

12x^2 + 20x - 4  = 0           divide through by 4

3x^2 + 5x - 1 = 0

Using the quad formula

-5 ±√[ 5^2 - 4(3)(-1) ]                               -5   ±√ [ 37]

______________________  =              ___________

             2 (3)                                                6

P =  -5      Q  = 37      R  =  6

You should be able to evaluate PQR

\(xy = \dfrac32 \)       \(10x + \dfrac{3y}5 \)

y = 3/[2x]

So....let f(x)  =   10x + 3 [ 3]/ [ 5 * 2x]   =  10x + 9/[10x ]  =  10x + (9/10)x^-1

Take the derivative , set to 0 and solve for x

10 -  (9/10)x^-2  =  0

10 = (9/10)x^-2

10x^2  = 9/10

x^2  = 9/100

x = 3/10

And we can prove that  x = 3/10 minimizes f(x)  by evaluating  f " (3/10)

2(9/10)

_______  >  0       so   x = 3/10   minimizes f(x)

(3/10)^3

And  y  = 3 /[2(3/10)]  =  3 / (6/10)  =  30/6  =  5

And   f(x)  =  10(3/10)  +  3(5)/5  =  3 + 3  = 6    = minimum for f(x)

i need help with this prob to

A calculator is broken so that the only keys that still work are the sin, cos, tan, cot, asin, acos, and atan buttons. Assume that the calculator does real number calculations with infinite precision. All functions are in terms of radians.

(a) Find, with proof, a sequence of buttons that will transform x into 1/x.

(b) Find, with proof, a sequence of buttons that will transform sqrt(x) into sqrt(x+1).

(c) The display initially shows 0. Prove that there is a sequence of buttons that will produce 3/sqrt(5).

Provided x can be entered, and
if the calculator uses the reverse polish notation then:

a)  \(​ ​\frac{1}{x}\)         \(x \Rightarrow atan \Rightarrow cot\)       \(\frac{1}{x}=cot(atan (x)) \)      \(x \in \{x|x\in\mathbb {R}\}\) 

Works with DEG and RAD.

I pass.

  !

Delilah writes down the positive factors of  12 on a piece of paper, which she gives to Ezekiel. Next to each factor, Ezekiel writes all of the positive integers that are less than or equal to that number and that share no divisors with the factor other than  other than what? (So, for example, Ezekiel will write 1 next to each of the factors Delilah writes.) How many numbers total does Ezekiel write?

Is some of your question is missing ??

The first just says the current will be the same through two sections in series. The second says the total current through a section comprised of two parallel components will be the sum of the currents through each of the parallel components. The third says the total resistance of two components in series is the sum of the individual resistances. The fourth says to find the total resistance of two components in parallel, add the reciprocal of the component resistances and then take the reciprocal of the result.

Just factor it out:

(3x+2) (x-4) = 0

Hmm I'm not quite sure to be fair. They want me to make a circuit and measure the current intensity in the first two questions, and the resistance in the last two questions. But I can't really do that till I buy a new multimeter or find my old one. If it doesn't bother you, can you maybe add an explanation about your answer, please? I do appreciate the fast reply! 

I guess you are looking for something like the following:

1. I_total = I₁ = I₂ 

2. I_total = I₁ + I₂

3. R_total = R₁ + R₂

4. 1/R_total = 1/R₁ + 1/R₂

See here:  https://www.wolframalpha.com/input/?i=GCF+%5B0,+-5%5D

I'd like to see someone answer this too.

Sorry but your program is not working as intended.

if n=2, the numerator is -5 and the denominator is 0,  These do not have a GCF greater than 1.

maybe you can take a pic of the picture with your phone and uplosd from there?

OR

You need to descibe the picture much better.

You have not even named the pentagon/s !

You are welcome.

The solutions to the equation 6x^2 + 10x = 4 - 10x - 6x^2 can be written in the form x=p+-sqrtQ/R where P and R are relatively prime integers and R>0. What is the product PQR ? 

Just take it all to one side 

then solve it with the quadratic equation.

From there it shouldn't be hard.

I have not done it so if there are problems that i have not noticed then you can let me. or others here, know.

Your questions are being blocked automatically. No moderator is actually doing it.

It is easy for moderarors not to notice questions that are blocked automatically.

Ohhh... I get it now melody. Thank you!

Mmm

x+x+y=23

2x+y=23

y<2x    otherwise the ends cannot join up.

start with tthe middle

8,8,7

9,9,5

10,10,3

11,11,1

7,7,9

6,6,11

And that is it.

So that is 6

And I am so sorry I posted 3 times  in a row... I know this is not a hw web, im not asking for ans, i want very good hints.

I mean yours looks cleaner.

No, they are both the same :)