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Let Tim's age today  = x

Five years ago his mom's age was 3x

So....her age now is  3x+ 5

So

3x+ 5 + x  = 45

4x + 5 = 45

4x = 40

x = 10

And her age now is   3(10)+ 5  =  35

Ah.....just a slight typo....I have mixed up sin and cos in the original denominator....see my corrected answer!!!

Certainly (4,3) is a solutions . Thanks guest

I have found 5 other solutions as well.

There are probably others   

Here is the graph.

I think when you multiply by 6/6 in your solution, you should wind up with

30x + 30 in the numerator.

As EP said, substitute \(x=3\) and \(x=-3\) into your equations, and solve from there.

You are very welcome!

:P

Thanks man!

Multiply by \(\frac{x+1}{x+1}\) and get \(\frac{5(x+1)}{\frac{x+1}{6}+1}\), then multiply by \(\frac{6}{6}\) and get \(\frac{30x+6}{x+7}\) .

You are very welcome!

:P

r = √ [ x^2 + r^2]         

cos θ   = x / r = x /  √ [ x^2 + r^2]  

sin θ =  y / r =    y /  √ [ x^2 + r^2] 

So we have

√ [ x^2 + r^2]  =      -5

                          ___________________

                          ( 2x + y )  / √ [ x^2 + r^2]

√ [ x^2 + r^2]  =  -5 √ [ x^2 + r^2] 

                          ______________

                             2x +  y

1  =    - 5

         ______

          2x + y

2x + y  =  - 5

y = -2x + -5

The y intercept is  -5

CORRECTED !!!!

\(f(-2)=(-2)^3-2(-2)=-8+4=-4\)

You are very welcome!

:P

Simplify the following:
5/(1/6 + 1 + 1/x)

5/(1/6 + (x+1)/x)

5/(x + 6x + 6) /6x

5/(7x + 6)/6x      cross multiply

30x / (7x + 6)

x = 4     and      y = 3

x = 7  and  y = 2

Here is a picture:

3.

I had to do this one graphically to figure out how to deduce this.....

Since the circle is on the origin too, it is of the form

x^2 +y^2 = r^2

      now for a square to be on this circle (centered on the origin, along with the ellipse), the x's and the y's absolute value in all of the quadrants must be equal (think about it)

          so the point that the line uintersects the ellipse will be   x,y    but x=y    so  x,x 

This point has to be on the ellipse, so let's substitute this in to the ellipse equation and solve for x (and also y)

x^2/16 + x^2/9 = 1

9x^2/144 + 16x^2/144 = 1

9x^2 + 16x^2 = 144

25 x^2 = 144

x^2 = 144/25     x = 12/5 = y = 2.4

Now since we have the x and y coordinates of a point on the circle we can calculate r^2 = 2.4^2 + 2.4^2 = 2(2.4^2) = 11.52

Then the circle becomes    x^2 + y^2 = 11.52

So side of square is 2 x 2.4 = 4.8    area = 4.8 x 4.8 = 23.04 sq units

(there probably is a better way!)

2.

x^2/a^2  + y^2/b^2 = 1       a = 1/2 of 13 = 6.5       b = 1/2 of 12 = 6

x^2/(6.5^2)  + y/6^2 =1

1.

Basic fromula for an ellipse     x^2/b^2  + y^2/a^2 =1        b = minor axis (given as 4 because ellipse is centered at origin and point 4,0 is on it  ...s o b = 4 &   b^2 = 16))

a is 3 times b (given)   then a = 12    (a^2 =144)

so    x^2/16 + y^2/144 =1         

You sure it isn't   1.00333^48    because .003333^48 is essentially ZERO it is sooooo small

1.00333^48 =1.1730