All Answers 358087 Answers

2x = -4y

5x - 4y = 0

divide the first equation by 2

x = 2y       substitute 2y into the second equation for x

5(2y) - 4y  = 0    simplify

10y  - 4y = 0     

6y =  0    divide both sides by 6

y = 0

And x = 2y = 2(0)  = 0

So....the solution  is (x, y)  = (0, 0)

Here's a graph of the solution: https://www.desmos.com/calculator/ctjdqulg47

Note that the lines only intersect at the origin, i.e.,  (0,0)

what sq footage  of my 1200 sq ft house is 92X123 inches

 Well just multiply 92 X 123=11,316 square inches, but 1 sq. foot=12 x12=144 sq.inches,

So, 11,316 / 144=78.5833 sq. feet, which is probably you Master Bathroom!!!!!!!!!!!.

6(5-8v)+12=-54    simplify

30  - 48v  + 12   =  -54      combine like terms

42  - 48v =  -54        subtract 42 from both sides

-48v  =  -96       divide both sides by -48

v = 2

Hi,

You do NOT need to take the log.

You take the log ONLY when you are trying to determine the exponent!    (power)

The inverse of cubing is cube rooting!

cube root of 243 = 7

Just divide total money raised by the price of 1 jacket=Total number of jackets that you can buy.

Or, $740.00/$46.25=16.

Disregard the first answer.....this statement isn't quite correct... "The first matrix is the identity of your matrix"

The second answer is better......!!!!  ......"The first matrix is your matrix transformed to an identity matrix"

Your answer is:

v=2

2   9   -4        1    0    0

3   5    1         0   1    0

2   3   -2        0    0    1        multiply the 1st row by 1/2

1  9/2   -2       1/2  0   0

3   5      1        0   1   0

2   3     -2        0    0   1      multiply the 1st row by -3   add this to the 2nd row

1     9/2   - 2        1/2  0   0

0  -17/2    7        -3/2  1   0 

2     3      -2          0    0   1      multiply the the 1st row by -2 add this to the 3rd row

1     9/2    -2          1/2   0   0

0   -17/2   7           -3/2  1   0

0    -6       2           -1     0   1    multiply the first two rows by 2

2    9      -4             1   0   0

0   -17    14           -3   2   0

0   -6       2            -1  0    1        multiply the 2nd row by 9/17  add to the 1sr row 

2   0    58/17         -10/17   18/17   0

0  -17    14            -3            2        0

0  -6       2             -1            0        1      multiply the 2nd row by -6/17 add to the 3rd row

2   0    58/17         -10/17   18/17    0

0   -17   14             -3             2       0

0    0   -50/17        1/17      -12/17   1   multply the 1st and 3rd rows by 17

34   0   58             -10     18      0

0  -17  14                -3      2       0

0   0   -50                1    -12     17      multiply the 3rd row by 58/50  add to the 1st row

34   0   0            -221/25   102/25   493/25

0   -17  14              -3           2           0

0    0   -50               1          -12        17       multiply the 3rd row by 14/50  add to the 2nd row

34   0   0          -221/25    102/25    493/25

0   -17  0            - 68/25     -34/25    119/25

0   0    -50             1           -12          17        

divide the 1st row by 34, the 2nd by -17,  and the 3rd by   -50

1  0  0            -13/50    3/25    29/50

0  1  0               4/25    2/25    -7/25

0  0  1              -1/50    6/25     -17/50 

The first matrix is your matrix transformed to an identity matrix.......the second matrix is the inverse of your matrix.....

You should have as many students and non-studentsas follows:

Students=327 x $1.75=$572.25

Others    258 x $2.50 =$645.00

2   9   -4        1    0    0

3   5    1         0   1    0

2   3   -2        0    0    1        multiply the 1st row by 1/2

1  9/2   -2       1/2  0   0

3   5      1        0   1   0

2   3     -2        0    0   1      multiply the 1st row by -3   add this to the 2nd row

1     9/2   - 2        1/2  0   0

0  -17/2    7        -3/2  1   0 

2     3      -2          0    0   1      multiply the the 1st row by -2 add this to the 3rd row

1     9/2    -2          1/2   0   0

0   -17/2   7           -3/2  1   0

0    -6       2           -1     0   1    multiply the first two rows by 2

2    9      -4             1   0   0

0   -17    14           -3   2   0

0   -6       2            -1  0    1        multiply the 2nd row by 9/17  add to the 1sr row 

2   0    58/17         -10/17   18/17   0

0  -17    14            -3            2        0

0  -6       2             -1            0        1      multiply the 2nd row by -6/17 add to the 3rd row

2   0    58/17         -10/17   18/17    0

0   -17   14             -3             2       0

0    0   -50/17        1/17      -12/17   1   multply the 1st and 3rd rows by 17

34   0   58             -10     18      0

0  -17  14                -3      2       0

0   0   -50                1    -12     17      multiply the 3rd row by 58/50  add to the 1st row

34   0   0            -221/25   102/25   493/25

0   -17  14              -3           2           0

0    0   -50               1          -12        17       multiply the 3rd row by 14/50  add to the 2nd row

34   0   0          -221/25    102/25    493/25

0   -17  0            - 68/25     -34/25    119/25

0   0    -50             1           -12          17        

divide the 1st row by 34, the 2nd by -17,  and the 3rd by   -50

1  0  0            -13/50    3/25    29/50

0  1  0               4/25    2/25    -7/25

0  0  1              -1/50    6/25     -17/50 

The first matrix is the identity of your matrix.......the second matrix is the inverse of your matrix.....

Silly child, obviosly the answer is "cheeseburga"

I assume you mean x^3=343

We take the log of both sides,

Log(x^3)=Log(343)

3*Log(x)=2.5353=Log(x)=2.5353/3=.8451, But we already know the log(x) to be 3. So we now have to find the antilog of x=10^.84511=7

So, x=7, because 7^3=343.

the answer is 21 -___-

seriously? 

It's 10

x3=343

3      3

x=114 1/3

-5(1-5x)+5(-8x-2)=-4x-8x

-5+25x+(-40x)-10=-4x-8x

-15-15x=-4x

     +15x +15x

-15=11x

11    11

-1 4/11=x

Your problem can be written this way=2^5 (exponent means the power you raise a number to),

So, 2^5=32. Bye the way, it also means that you multiply 2 by itself 5 times, 2 x 2 x 2 x 2 x 2=32

5980000000000000000000000

thank you!!

Your answer is=103

This simplifies to:

-128 x^16

CPhill: Are the 2 results(yours & Guest's) equivalent? If not, then one of them is wrong. The Guest's answer was arrived at by WolframAlpha Computing Engine.

If you take the simple average of the interest rate, then it naturally is 6+7+8=21/3=7%

Therefore, the total investment will be $2,037.00/.07=$29,100. However, the more accurate method would be to compound the interest thus:1.06 x 1.07 x 1.08=1.224936^(1/3)=6.996884644.

Therefore the total investment would be=$2,037.00/.06996884644=$29,112.96.

As you can see, the difference is quite minor, but in the long run it would make significant impact.

I'm assuming that the investment is for one year......remember that:  I = Pr     where I is the interest earned, P is the principal, and r is the interest rate.....so we have.......

.06P + .07P + .08P = 2037    simplify

P(.21)  =  2037      divide both sides by .21

P  = $9700     ......so this is the equal amount invested at the different rates

I assume this is :

(12 b^4c^5)/(18 b^8c^9)   ... remember that....  aⁿ / a^m  =  a ^n-m  ..  and...... a^-b = 1/a^b....so we have

(12/18)  x (b⁴ / b⁸)  x (c⁵ / c⁹)  =

(2/3)  x (b^-4 )  x (  c^-4)   =

(2/3) x (1/b4) x (1/c⁴)   =

(2) / (3b⁴c⁴)