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This is just to give an explanation for I's answer:

If the two equal digits are both 0, they must be found in the last two positions, while there are nine

possibilities for the first digit:  100, 200, 300, 400, 500, 600, 700, 800, 900.

If the two equal digits are both 1, they must be found in the first two position, while there are five

possibilities for the last digit:  110, 112, 114, 116, 118.

(The same is true if the two equal digits are both 3, 5, 7, and 9; for a total of twenty five.)

If the two equal digits are both 2:

-- if they are in the last two positions, there are 8 possibilities for the first position:

          122, 322, 422, 522, 622, 722, 822, and 922.

(The same is true if the two equal digits are both 4, 6, and 8; for a total of thirty two.)

-- if they are in the first and third position, there are 9 possibilities for the second position:

          202, 212, 232, 242, 252, 262, 272, 282, and 292.

(The same is true if the two equal digits are both 4, 6, and 8; for a total of thirty six.)

-- if they are in the first and second position, there are 4 possibilites for the third position:

          220, 224, 226, and 228.

(The same is true if the two eaual digits are both 4, 6, and 8; for a total of sixteen.)

When I total these, I get:  9 + 25 + 32 + 36 + 16  =  118.

If you draw the height of the base, you will create two right triangles, each will have an hypotenuse of 15

and a side of 12.  Using the pythagoren theorem, you get the third side to be:  9.

The area of each trianglular base is:  ½·24·9  =  ...  (remember that there are two bases, so multiply by 2)

One side will be 30x15, another side will be 30x15, and the third side will be 24x 30

Add these area together to get the final answer.

Simplifying  x² / x⁹      --->     divide both the numerator and denominator by x²

                                   --->     1 / x⁷     is the simplified answer.

First equation:  3a + 4b  =  7

Simplifying the second equation:  6a + 4b  =  k - 3a - 8b

                                                    9a + 12b  =  k

To have infinitely many solutions, get the coefficients of a and b to be the same:

    first equation:            3a + 4b  =  7     --->   x3   --->     9a + 12b  =  21

    second equation:                                                          9a + 12 b  =  k  

There will be infinitely many solutions when  k = 21.

(There will be none if  k isn't 21.)

someone can you help her i cant

hey sorry but i need more detail cause there nothining 

763 thousanths is equal to 0.763, or \(\color{brown}\boxed{7.63 \times {10^{-1}}}\)

What is the smallest distance between the origin and a point on the graph?

Hello Guest!

\(\color{blue}f(x)= y=\dfrac{1}{\sqrt{2}} (x^2 - 18)\\ y= \dfrac{x^2}{\sqrt{2}}-9\cdot \sqrt{2}\\ \color{blue}\dfrac{dy}{dx}=y\ '=\sqrt{2}\cdot x\)

\(g(x)=-\frac{1}{y\ '}(x-0)+0\\ g(x)=-\frac{1}{\sqrt{2}\cdot x}(x-0)+0\ |\ point\ direction\ equation\\ \color{blue}g(x)= -\frac{1}{\sqrt{2}}\)  

\(\color{blue}g(x)=f(x)\\-\dfrac{1}{\sqrt{2}}=\dfrac{1}{\sqrt{2}} (x^2 - 18)\\ x^2-18+1=0\\ x= \sqrt{17}\)

\(x=4.1231\)

\( y=\dfrac{1}{\sqrt{2}} (x^2 - 18)\\ y=\dfrac{1}{\sqrt{2}} (17 - 18)=-\dfrac{1}{\sqrt{2}}\\\)

\(y=0.7071\)

\(d=\sqrt{x^2+y^2}=\sqrt{17+\frac{1}{2}}\)

\(d=4.1833\)

 The smallest distance between the origin and a point on the graph is 4.1833 .

  !

Correct

There are a total of 4 choose 2 = 6 pairs that can be chosen. This number is small enough to go through each pair one by one.

(1, 2), (1, 3), (1, 4): one divides into every number, so all of these work

(2, 3): 2 does not divide evenly into 3

(2, 4): 2 divides evenly into 4

(3, 4): 3 does not divide evenly into 4

This gives 4 pairs that work for an overall probability of 4/6 = 2/3.

I answered that here: https://web2.0calc.com/questions/inequality_134

118 numbers.

I know this may come out confusing, but I think they mean that you have two ways to factor that you should try before using ax^2+bx+c.

Linda, Miah, and Noah are all wearing hats with numbers on them. Each person adds the two numbers on the other two hats, and they come up with the totals 11, 17, and 28. What is the largest number that is on a hat?  

I think you can set it up like this: 

Let x stand for the number on one hat  

Let y stand for the number on another hat.  

Let z stand for the number on the final hat. 

so     x + y = 11      –>>    y  = 11 – x  

         x + z = 17      –>>    z  = 17 – x  

         y + z = 28  

so     y + z = 28       –>>  (11 – x) + (17 – x) = 28  

                                          11 – x + 17 – x = 28  

                                           28 – 2x = 28  

                                                – 2x = 0      –>>    x = 0  

sub in original expressions    0 + y = 11     –>>    y = 11  

                                              0 + z = 17    –>>     z = 17  

so the largest number on a hat is 17  

_.

(a_1, a_2) = (-3/5, 4/5).

16 + 9 - 5 = _________

The angle is 5*pi/32.

The non-integer root is 1/3.

It is not but I need the answer to this ASAP please and thank you.

Uh... is it my problem or can i not see the cards

So we start by thinking. Since 44 students take ONLY spanish, 97 - 44 = 53 students take chinese (ONLY and both languages). Since there are 8 more students in chinese than spanish, there are 53 - 8 = 45 students take spanish (ONLY and both languages). 45 - 44 = 1 student not taking ONLY spanish but still takes spanish so there are only 1 student taking both languages. (How lonely...)

(Please upvote!)

Plug  '1'  into the equation to get the height at t = 1

Plug  '3'  into the equation to get the height at t = 3

   this is an interval of two seconds

  then   (height3 - height1 ) / 2  = average velocity  over the interval from 1 to 3 sec

the others are similar ....

The largest possible value of the middle number is 375.

l = 2w      w = 1/2 l

l = h-8     h = l+8

l

2* (   lw  + wh  + lh)  = 100

2 ( l (1/2 l)  + 1/2 l (l+8)  + l ( l+ 8 ) ) = 100        Now expand this and solve for l     then h = l + 8  

                                                                                 ( you will need to use the Quadratic Formula)

225  x  1==225

225 x   2==450

225  x  3 ==675

225 x   4==900 [ All these are multiples of 225.] However, multiples of 900 which must all be "1s" and "0s" implies that we must have at least 9 "ones" + the two "0s" of 900. So, the multiple of 900 must necessarily be: 11,111,111,100 which is mod 900==0, and consequently mod 225 ==0.