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N is a four-digit positive integer. Dividing N by 9, the remainder is 5. Dividing N by 7, the remainder is 3. Dividing N by 5, the remainder is 1. What is the smallest possible value of N?

The smallest 4-digit n =1256

1256 mod 9 =5

1256 mod 7 =3

1256 mod 5 =1

7 . (14 - 2 · 4) : (4 + 15 : 5) - 24 : 8

Hello Guest!

\(\frac{7\cdot (14-2\cdot 4)}{4+\frac{15}{5}}-\frac{24}{8}\\ =\frac{7\cdot 6}{7}-3\\ =6-3\)

\(\frac{7\cdot (41-2\cdot 4)}{4+\frac{15}{5}}-\frac{24}{8}=3\)

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You and a friend go to Taco Bell for Lunch. You order three soft tacos and three burritos and your bill totals out to 11.25  Your friend's bill is 10.00 for four soft tacos and two burritos. How much do soft tacos cost? How much do burritos cost? 

Hello Guest!

\(3T+3B=11.25\\ 4T+2B=10\\ 6T+6B=22.5\\ \underline{12T+6B=30}\)

6T=7.5

\(T=1.25\)

\(4T+2B=10\\ 5+2B=10\\ 2B=5\)

\(B=2.50\)

soft tacos do cost 1.25

burritos    do cost 2.50

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Fill in the blank, so that that the resulting expression is the square of a binomial:
x^2 + 6/5*x +__

Hello Guest!

\(x^2+\frac{6}{5}x+\)__

\(a^2+2ab+b^2\\ a=x\\ 2ab=\frac{5}{6}x\)

\(2xb=\frac{6}{5}x\\ b=\frac{6\cdot x}{5\cdot 2\cdot x}\\ b=\frac{3}{5}\)

\(x^2+\frac{6}{5}x+(\frac{3}{5})^2=(x+\frac{3}{5})^2\)

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The dot product is 18.

When 482, 992, and 1094 are divided by a positive integer D, the remainders are all 74. What is D?

D =102

482 mod 102=74,  992 mod 102=74  and 1094 mod 102=74

Favorable/Possible

Possible=6C2=15

Favorable= 8:

1,2

1,3

1,5

1,6

4,2

4,3

4,5

4,6

8/15

The vaue of D is 131.

ok

6x-8=-48

12x-4=-48

12+-4=8

(6x+12)(x-4)

x=-2

x=4

explain

The sum of all the different possible areas of cool rectangles is 37.

When N is divided by 12, the remainder is 7.

The side length of the small square is 2 - sqrt(3).

Yes but we have assumed that individuals do not matter.

Our answers assume only gender matters.

If individuals also matter then

I think

4C2*3  *  2  =  4*3*2 = 24 is the answer.

Arrange in y = mx+ b form    m is the slope     parallel slopes are =

2y-9x = 11

y =  9/2 x + 11/2

-5y + kx = 4            ( I assume you mis typed this one)

5y = kx - 4 

y = k/5 x - 4/5              k/5   has to equal   9/2    

k/5 = 9/2     now you can solve for 'k'

Thanks!

Odd multiples of 6       and odd multiples of 6     + 1   wind up in row f

2011/6 = 335   R 1   

row f

Perfect squares would be 1 or 4

for ONE die

1         2 3 5 6

4          2 3 5 6

The same for the other die  

  so out of 36 possible rolls there are 16 rolls where ONE die has a square   16/36 = 4/9

In a triangle the 3 angles have to sum to 180   so add them up and equate them to 180:

x+2y     +   6x-5y     +     8x+3y     = 180       when yo add them the y's will be gone....solve for x

Since you only have 5 letters, then the number of 5-letter "words" is simply 5! = 120 "words". This is on the condition that 5 letters cannot be repeated. But, since you have a bowl of 5 letters repeated over and over, then the number of 5-letter "words" will be: 5^5 =3,125 possible "words".

Angle B is 34 degrees.

If you look at it carefully, you will see that from 6 and up every  FOURTH and FIFTH numbers are odd. So:

6 + 4=10 and 6 + 5 =11  and 10 + 4=14  and 10 + 5=15  and 14 +4=18 and 14 + 5 =19.....and so on.

Bowl shaped parabola.....minimum point  is the vertex....to find the x value of the vertex

-b/2a  = x of the vertex

16/6        sub in this for 'x'  to find k which makes the equation = to 1

3 (16/6)^2  - 16 (16/6)  + k = 1      k = 22 1/3