geno3141

Since the coefficients are rational numbers, if one answer is a complex number, the other answer will be its conjugate.

The conjugate of  4 + 3i  is  4 - 3i.

Therefore, the problem, when factored will become:  [ x - (4 + 3i)  ][ x - (4 - 3i) ]  =  0

Multiplied out, it becomes:  x² - 8x + 25  =  0, which means that  k = 8.

If she had subtracted 2 from 20, she would have gotten 18.

Since she subtracted a little more than 2, her answer should be a little less than 18, which it is.

Let  x  represent one number.

The other number is  2x.

The sum of their reciprocals is 1/4:  1/x  +  1/(2x)  =  1/4.

The lowest common denominator is 4x; multiply both sides of the equation by 4x:

      4(1/x)  +  4(1/(2x))  =  4(1/4)

          4      +       2       =    x

Thus, x =  6  and 2x  =  12.

The two numbers are  6  and  12

To multiply numbers with the same base, add the exponents:

5³ x 5⁴  =  5^{3 + 4}  =  5⁷

Slope-intercept form is the equation solved for y:

     5x + 10y  =  60

Subtracting 5x from both sides:

            10y  =  -5x + 60

Dividing by 10:

                y  =  (-1/2)x + 6

The slope is the coefficient of x:  slope = -1/2.

The y-intercept is the number added to the x-term:  y-intercept = 6

I'm assuming that you want to factor this:

x³ + 5x² - 4x - 20  =  x²(x + 5) - 4(x + 5)  =  (x + 5)(x² - 4)  =  (x + 5)(x + 2)(x - 2)

Marti's statement won't be correct if the fractions don't add up to 1.000  (100%).

Using the common denominator of 60:

           2/5  +  1/6  +  1/3  +  1/4  =  24/60  +  10/60  +  20/60  +  15/60  =  69/60  

For the statement to be correct, the sum must be 60/60; so the statement isn't correct.

99 + 9/9  = 199

If you use the usual rules of operations, multiplications and divisions and calculated, in order, from left to right.

3 / 3 x 2  =  (3 / 3) x 2  =  1 x 2  = 2

3 x 2 / 2  =  (3 x 2) / 2  =  6 / 2  =  3

Since roosters don't lay eggs (hens do!), I wouldn't worry about it. ...