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Thank you tastybanana 

The system of equations is:

p - 2q = 3 q - 2r = -2 p + r = 9

We can solve this system using Gaussian Elimination.

First, we can add the first and second equations to get:

p - 2q + q - 2r = 1

This simplifies to:

-q - 2r = 1

Now, we can subtract the third equation from this equation to get:

-q - 2r - (p + r) = 1 - 9

This simplifies to:

-2q = -8

Therefore, q = 4.

Now, we can substitute this value into the second equation to get:

4 - 2r = -2

This simplifies to:

2r = 6

Therefore, r = 3.

Finally, we can substitute these values into the first equation to get:

p - 2(4) = 3

This simplifies to:

p = 5

Therefore, the ordered triple that satisfies the system of equations is (5, 4, 3).

a=1;i=0; c=a % 11; if(c==6, goto4, goto6);i=i+1;printa; a++;if(a<1000, goto2, 0);print i

There are 91 such positive integers as follows:

6 , 17 , 28 , 39 , 50 , 61 , 72 , 83 , 94 , 105 , 116 , 127 , 138 , 149 , 160 , 171 , 182 , 193 , 204 , 215 , 226 , 237 , 248 , 259 , 270 , 281 , 292 , 303 , 314 , 325 , 336 , 347 , 358 , 369 , 380 , 391 , 402 , 413 , 424 , 435 , 446 , 457 , 468 , 479 , 490 , 501 , 512 , 523 , 534 , 545 , 556 , 567 , 578 , 589 , 600 , 611 , 622 , 633 , 644 , 655 , 666 , 677 , 688 , 699 , 710 , 721 , 732 , 743 , 754 , 765 , 776 , 787 , 798 , 809 , 820 , 831 , 842 , 853 , 864 , 875 , 886 , 897 , 908 , 919 , 930 , 941 , 952 , 963 , 974 , 985 , 996>> Total = 91 such integers

 p - 2q = 3,   

q - 2r = -2, 

p + r = 9, solve for p, q, r

Use substitutions to get:

p==7,  q==2,  r==2

can you write the answer as (p,q,r) because it says its wrong.

We can solve this system of equations using the substitution method.

Equation 1: p - 2q = 3

Equation 2: q - 2r = -2

Equation 3: p + r = 9

First, we can solve Equation 1 for p:

p - 2q = 3 p = 3 + 2q

Now, we can substitute this expression for p in Equation 3:

(3 + 2q) + r = 9 2q + r = 6

Next, we can solve Equation 2 for q:

q - 2r = -2 q = 2r - 2

Now, we can substitute this expression for q in Equation 2:

(2r - 2) - 2r = 6 -4r = 8 r = -2

Now that we know the value of r, we can substitute it into Equation 2 to find q:

q - 2(-2) = -2 q = -2

Finally, we can substitute the values of q and r into Equation 1 to find p:

p - 2(-2) = 3 p = 3

Therefore, the ordered triple that satisfies the system of equations is (3, -2, -2).

To check our answer, we can substitute these values into each equation and see that they all hold true.

p - 2q = 3 3 - 2(-2) = 3 3 = 3 q - 2r = -2 -2 - 2(-2) = -2 -2 = -2 p + r = 9 3 + (-2) = 9 9 = 9

As you can see, the ordered triple (3, -2, -2) satisfies all three equations. Therefore, it is the solution to the system.

Using CRT + MMI

26m  +  4, where m=0,1,2,3,.......etc.

[26 * 38] + 4 =988 maximum number of people in the marching band.

Check: 988 mod 26 =4 - the remainder.

toast = t

bagels = b

muffins = m

Use systems of equations. I'll help on the first part. Try finishing the rest yourself!

    t+2b+3m = 8.15

-  2t+b = 3.15

        b + m  = 3.50

---------------------------

   -t    +    2m = 1.50

Assume:

the # of yellow marbles is x

the # of green marbles is 2x

the # of blue marbles is 3x

the # of white marbles is 4x

x+2x+3x+4x=180

10x = 180 

x = 18

the # of blue marbles = 3x = 3(18) = 54 marbles

Credit to https://web2.0calc.com/questions/help-pls_10673 for inspiring my solution. :)

Let 3x be the number of juniors and 2x be the number of seniors.

Six more juniors join the class: the number of girls is now  3x + 6

One senior drop the class: rhe number of boys is now  2x - 1

The ratio of juniors to seniors is now 2:3  --->   (3x + 6) : (2x - 1)  =  2 : 3

(3x + 6)/(2x - 1) = 2/3

3(3x+6) = 2(2x-1)

9x+18 = 4x-2

5x  = -20

x = -4

I don't understand it now; the answer is negative??

Can someone help? Thanks!

We can apply the binomial formula here; it would be row 5 of the pascal's triangle. 

I would write the expansion, and I did, but I deleted it accidently. :(

You would get 1920 as your answer.

Hi TastyB, It is nice to see you active here. Welcome to this site  

But..

What makes you think that this is a spam question TastyB ?

It may be repeated because a whole class of  students probably got the same question but that doen't make it a spam question.

Note:  As for it being unsolvable I have not looked at the question at all so I would not know.

The sum of the roots of the quadratic 2x2 - 8x + 7 = 0 is given by -(-8)/2 = 4. The product of the roots is given by 7/2.

We can compute a3 + b3 as follows:

a3 + b3 = a3 + ab2 + b2a + b3 = (a + b)(a2 - ab + b2) = (4)(a2 - ab + 7/2)

We know that a2 - ab + b2 = (a + b)2 - 2ab = 16 - 8 = 8. Therefore, a3 + b3 = (4)(8) = 32.

Therefore, the answer is 32.

The roots of the quadratic 2x2 - 8x + 7 = 0 are given by the quadratic formula:

x = (8 ± √(8^2 - 4 * 2 * 7)) / (2 * 2) = (8 ± √(64 - 56)) / 4 = (8 ± 2√2) / 4 = 2 ± √2

a3 + b3 = (2 + √2)^3 + (2 - √2)^3 = 8 + 12√2 + 2 + 8 - 12√2 + 2 = 35

Therefore, a^3 + b^3 = 35.

4x -3 = 2x + 3 

Add three to both sides and divide 2 by both sides which should give 2x = 6 which gives x = 3

Yeah, HumenBeing cheats on a o p s hw and defends other cheaters

HumenBeing is cheating again.

You had the right idea, but remember you are tossing 6-sided die 6 times. So you can't have numbers > 6.

 135566 ( 180 ) , 233556 ( 180 ) , 333455 ( 60 ) , >>Total combinations = 3

>>Totals in parentheses = 420 permutations (or different sequences of rolls)

That is incorrect, sorry!

Can anyone else help?

Thanks, that's right!