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Neg.

ElectricPavlov is right. She/he is awesome. Sorry. I don't know if you are a girl or boy.

x + y + 2z  = 1        (1)

-2x + 4y + 2z = 1     (2)

y + z  = 1                 (3)

Multiply (3)  by 2  and rearrange  → 2z = 2 - 2y     (4)

Sub (4)  into  (1)    and simplify

x + y + [2 - 2 y]  = 1

x - y  = -1     (5)

Multiply (2) by -1   and add to (1)

3x - 3y   = 0     divide both sides by 3

x - y  = 0      (6)

But.....we have a contradiction  between  (5)  and (6)......x - y  cannot take on two values.....thus.....this system has no solution

Let  √[4x - 3]  =  q^2

So we have

q^2  +  10/q^2   = 7      multiply both sides by q^2

q^4 + 10  = 7q^2

q^4 - 7q^2 + 10   = 0    factor

(q^2 - 5) ( q^2 - 2)  = 0

So either

q^2  = 5     or    q^2   =  2    .....so....

√[4x - 3]  = 5        square both sides

4x - 3   = 25     add 3 to both sides

4x = 28

x = 7

Or

√[4x - 3]  = 2     square both sides

4x - 3  = 4      add 3 to both sides

4x = 7

x = 7/4

Check  x = 7

√[4x - 3] +  10 / √[4x - 3] = 7  ??

√[4*7 - 3] + 10 / √[4*7 - 3]  = 7  ??

5 + 10/5  = 7      is true

Check  x  = 7/4

√[4(7/4) - 3] +  10 / √[4(7/4) - 3] = 7   ??

√[7-3] +  10 / √[7 - 3]] = 7  ??

2 + 10/2   = 7   is also true

So  x   =  7    or   x  = 7/4

thank you!

First find the VOLUME of the lead sphere     Vs = 4/3 pi r^3     (use the RADIUS not the DIAMETER given)   this result will be in  in^3       Multiply this result by the density given to get the weight of the sphere.......in pounds

I will assume you mean

\(\sqrt[3]{162}\) /\( \sqrt[3]{2}\)

cubrt(162) / cubrt(2)  =  cubrt(27 * 6)  /  cubrt (2) =  3 cubrt(6) / cubrt (2)  = 3 cubrt(2)cubrt(3) / cubrt(2) = 3 cubrt (3)

You have the correct answer in METERS.....  Convert to Kilometers and the answer is 'A'

5x + 3z  = 1       (1)

-x + y + z  = 0     (2)

3y + 2z= 5        (3)

Uising (1)  z = [ 1 - 5x] /3      (4)

Using (3)   z =  [5 - 3y] / 2     (5)

Equating (4)   and (5)  we have

[1 - 5x]/ 3  = [ 5-3y ] / 2     cross-multiply

2[ 1 - 5x] = 3 [ 5 - 3y]    simplify

2 - 10x  = 15 - 9y

9y  = 13 + 10x

y = [13 + 10x]/ 9     (6)

Subbing (4) and (6)  into (2), we have

-x +  [13 + 10x]/9  + [1 -5x]/3  = 0

-9x + 13 + 10x + 3  - 15x  = 0

-14x = -16

x = 8/7

And

y = [13 + 10(8/7)]/ 9  = 19/7

And

z = [ 1 - 5(8/7)] /3    =  - 11/7

So   {x, y, z}    =  { 8/7, 19/7, -11/7}

I donno. you tell me

5a - 7b + 3c  =  19                                          --->       5a - 7b + 3c  =     19

2a - 4b +   c  =  77      --->     multiply by -2     --->     -4a + 8b - 2c  =  -154 

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

Add down the columns:                                                 a  +  b  +  c  =  -135                                 

It won't!

A negative plus a negative is a negative.

Solve     sqrt(4x - 3) + 10 / sqrt(4x - 3)  =  7

First note that the expression 4x - 3 is under the square root sign.

Since this value must be positive:      4x - 3  >=  0     --->     4x  >= 3     --->     x >= 4/3

To remove the denominator from the problem multiply each side by  sqrt(4x - 3):

     sqrt(4x - 3) [ sqrt(4x - 3) + 10 / sqrt(4x - 3) ]    =    sqrt(4x - 3) [ 7 ]

--->     sqrt(4x - 3) · sqrt(4x - 3)  +  sqrt(4x - 3) · 10  sqrt(4x - 3)    =    7· sqrt(4x - 3)

--->                (4x - 3)                  +                  10                            =    7 · sqrt(4x - 3)

--->                                     4x + 7   =   7·sqrt(4x - 3)

Square both sides:             [ 4x + 7 ]²   =   [ 7·sqrt(4x - 3) ]²  

                                   4x² + 56x + 49   =   49(4x - 3)

--->                             4x² + 56x + 49   =   196x - 147

Subtract 196x from both sides, add 147 to both sides:

--->                          4x² - 140x + 196   =   0

Divide both sides by 4:

--->                            x² - 35x + 49   =   0

Factor:                      (4x - 7)(x - 7)  =  0

So, either 4x - 7  =  0   --->    x = 7/4     or     x - 7  =  0     --->   x = 7

Since both answers are > 4/3, these are possible answer.

I'll leave the check for you ...

Solve:

5x       + 3z  =  1

-x +  y +   z  =  0

      3y + 2z  =  5

This is a nasty problem -- if you have a calculator that handles matrices, it would be easy to solve.

If you have to do it by hand:

Combine the first and the second equations:

5x      + 3z  =  1                                  --->       5x        + 3z  =  1

-x + y +   z  =  0     --->  multiply by 5  --->     -5x + 5y + 5z  =  0

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

Add down the columns:                                          5y + 8z  =  1                                   --->        5y + 8z  =     1 

Combine this answer with the third equation:         3y + 2z  =  5     --->  multiply by -4  --->     -12y - 8z  =  -20

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

Add down the columns:                                                                                                                -7y        =  -19

Divide by -7:                                                                                                                                           y  =  19/7

Take this value for y and substitute it into the third equation:

     3y + 2z  =  5     --->        3(19/7) + 2z  =  5     --->     57/7 + 2z  =  5    --->     2z  =  5 - 57/7

                                                                                                                 --->     2z  =  -22/7

Divide by 2:                                                                                                            z  =  -11/7

Take this value for z and substitute it into the first equation:

     5x + 3z  =  1     --->     5x + 3(-11/7)  =  1     --->     5x -33/7  =  1     --->     5x  =  1 + 33/7 

                                                                                                              --->     5x  =  40/7

Divide by 5:                                                                                                         x  =  8/7

Honestly, I don't understand. What grade are you in? You should know what mellie said. I'm not trying to be mean, but really?

Hey, Mellie......it's tough to see the whole problem, but I guess you want the solutions

[ and their product ] for :

6x^2 + 10x  = 4 - 10x - 6x^2   simplify

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

3x^2 + 5x - 1   = 0 

The solutions are  :

[ -5 + √37] / 6     and   [ -5 - √37] / 6

The product of the solutions   =   ( [ -5 + √37] / 6] ) *  ( [ -5 - √37] / 6 )  =  [25 - 37] / 36  =  -12/36  =   -1/3

If this is not what you asked for......sorry  !!!!

10*19=190.

When you multiply anything by ten, you only have to add a 0 at the end of the number. Ten times the amount.

ok Im stuck since I plugged the numbers in and got 24 m/s/.65m/s^2 then (24+0)?2 then I got 443.076999977 what do I do?

Centillion  is either 1 followed by 303 zeroes [US definition]  or 1 followed by 600 zeroes  [ Great Britain]

There are many "large" numbers that are greater.......check out "googleplex", or  "Graham's Number"

OK    use      vf = vo + at     to find   't'   (note 'a' is negative)

Use this value of 't'     x = xo + vo t + 1/2 a t^2     to find the distance in METERS.....  (xo=0 in this instance)

Do you want to know where  f(x)  = g(x) ???

Here's a graph that might help : https://www.desmos.com/calculator/chlxcf4kpw

There are two intersection points :   at about (-2.46673, 0)  and at (2, 0)

x^2 + y^2 = - 8 – 9x    move the -9x term to the left side  [it changes signs]

x^2 + 9x + y^2   = -8        complete the square on x

x^2 + 9x + 81/4 + y^2  = -8 + 81/4      simplify

(x + 9/2) + y^2   =  -32/4 + 81/4

(x + 9/2)^2  + y^2  = 49/4

The right side is the radius squared......so......take the square root to find the radius  = sqrt(49/4)  = 7/2  = 3.5  units

Here's a graph of the original function :  https://www.desmos.com/calculator/2s9iegula0