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i thought it was fish?

y  = - x  +  3

OK, KJ...let's see

When x  =        Then y  =                           Point

-1                      -(-1) + 3  = 4                    (-1, 4)     so  the first answer isn't correct

1                     -1 + 3    =  2                        (1, 2) 

0                     - 0 + 3  =  3                         (0, 3)    so the second answer isn't correct

0                      0 + 3   =  3                        (0, 3)

4                      -4  + 3  =  - 1                     (4, -1)    Looks like the 3rd answer is correct

Do you see how to do this???

Yep...its 5.

What is this value of k ?

x + y + 3z  = 10    multiply through by -2 ⇒  -2x - 2y - 6z = -20  (1)

-4x + 2y + 5z  = 7   (2)

kx + z  = 3  (3)

Add equations (1) and (2)  and we get that

-6x -z  =  -13   multiply through by -1  ⇒  6x + z = 13   (4)

So  we have equations (3) and (4)

6x + z  = 13

kx + z  = 3

And when k = 6  we have no solutions

its 5 :)

If you have the skills to use a scientific calculator, you should not need a fraction button.

This calculator does have one though. It was added years ago to accommodate morons and imbeciles.

The irony is those who need it are too stupid to find it, and those who do not need it never look.

In addition to that, its best to put parenthesis around it, especially if the fraction isn't the only thing.

See here : https://web2.0calc.com/questions/fractions_114

Hi guest is this for the calculator or the forum questions?

Just plug in the x values and see if we can get the associated y values

So...(1, - 3)  ???    y = (1) - 4  =  - 3      OK

And  (-1, -5) ??? y = (-1) - 4  =  - 5 OK

So....the points  (1, - 3)  and (-1, - 5)  are on the graph

If math did not exist, it would be necessary to invent it.  

QED

That is what the movie "The Matrix" was based on. It was a fabulous movie too!

The possible values of  n  are:

1, 5, 7, 11, 13, 17, 19, 23, 25, 29, 31, 35, 37, 41, 43, 47

And the elements in the set are:

\(\frac{1}{24}, \frac{5}{24}, \frac{7}{24}, \frac{11}{24}, \frac{13}{24}, \frac{17}{24}, \frac{19}{24}, \frac{23}{24}, \frac{25}{24}, \frac{29}{24}, \frac{31}{24}, \frac{35}{24}, \frac{37}{24}, \frac{41}{24}, \frac{43}{24}, \frac{47}{24}\)

So the sum of the elements in the set   =   \(\frac{384}{24}\)   =   16

Draw WY to create △WXY .

△WXY is an isoscelese right triangle so the measure of each base angle is  45°

The length of each leg of  △WXY  is  4  so the length of the hypotenuse is  4√2

m∠XYZ  =  135°

m∠WYZ  =  m∠XYZ - m∠WYX  =  135° - 45º  =  90°

So  △WYZ  is a right triangle, and we know the length of two of the sides.

To find the length of the missing side, we can use the Pythagorean theorem.

a²  +  ( 4√2 )²   =   9²

a²  +  32   =   81

                                Subtract  32  from both sides.

a²   =  49

                                Take the positive sqrt of both sides.

a  =  7

survey

Experiment

observational study

Thanks for your help! :)

y  =  x² + bx + c

The graph of the equation passes through the point  (-1, -11)  so we know....

-11  =  (-1)² + b(-1) + c

-11  =  1 - b + c

                                 Add  b  to both sides.

-11 + b  =  1 + c

                                 Add  11  to both sides.

b  =  12 + c

The graph of the equation passes through the point  (3, 17)  so we know....

17  =  (3)² + b(3) + c

17  =  9 + 3b + c

                                 Subtract  9  from both sides.

8  =  3b + c

                                 And we know  b  =  12 + c  so we can substitute  12 + c  in for  b .

8  =  3(12 + c) + c

                                 Distribute  3  to the terms in parenthesees.

8  =  36 + 3c + c

                                 Subtract  36  from both sides.

8 - 36  =  3c + c

                                 Combine like terms.

-28  =  4c

                                 Divide both sides by  4 .

-7  =  c

Part of this last problem is just like the second problem.......

In the diagram below, we know  \(\tan\theta=\frac34\) . Find the area of the triangle.

Let the base of the triangle be the side with length 60. Draw a height to that base and call it  h .

By the Pythagorean Identity,

Thanks for the great work, but the answer key says that the answer is 16 for some reason. Do you know why?