geno3141

Factor:  2x² - x - 6

                               =  (2x + 3)(x - 2)

Solve:    2x² / sqrt( x⁴ )  +  2   =   5 / sqrt( 3^x )

Since  sqrt( x⁴ )  =  x²     --->    2x² / sqrt( x⁴ )     --->     2x² / x²     --->     2

Therefore:    2x² / sqrt( x⁴ )  +  2   =  2 + 2  =  4

The problem reduces to:     4  =  5 / sqrt( 3^x )

Multiply both sides by  sqrt( 3^x )  to get  4·sqrt( 3^x )  =   5

Square both sides:        16 · 3^x  =  25

--->                                       3^x  =  25 / 16

Find the log of both sides:      log( 3^x )  =  log( 25 / 16)

--->                                       x · log( 3)  =  log( 25 / 16 )

--->                                                    x  =  log( 25 / 16) / log( 3 )

--->                                                    x  =  0,406228   (approximately)

What numbers multiply to  -210  but add to  -1?

Since the product is a negative, one number must be positive and the other must be negative.

Since the sum is -1, the two numbers (in absolute value) must be consecutive numbers.

Find the square root of  210   --->  it is 14.49...

So the two numbers (in absolute value) should be 14 and 15.  

Since their sum is a negative, the numbers are  14  and  -15.

I believe that you entered 48 146 134( 1 + 0,089 ) ^ 1  (etc.)

I believe that you thought that you entered  1 + 0 .0089  but you actually entered  1 + 0.089  for each of the problems.

Is the equation  g(x)  =  6x² + 3  odd, even, or neither?

g(x)  =  6x² + 3  can be written as  g(x)  =  6x² + 3x⁰  

Since each term has an even power (zero is an even number) of its variable, it is an even function.

A line passes through the point  (-3, -1) with a slope of -3/2.

What is the equation of the line perpendicular to that line that passes through that point?

Lines that are perpendicular have slopes that are negative reciprocals.

So, if the first line has a slope of  -3/2  the line perpendicular to it will have a slope of  2/3.

Using the point slope form of a line for the line that passes through the point (-3, -1) with a slope of  2/3:

y - y₁  =  m(x - x₁)     --->     y - -1  =  (2/3)(x - -3)     --->     y + 1  =  (2/3)(x + 3)

You can simplify that equation:     y + 1  =  (2/3)x + (2/3)(3)

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

                                                           y  =  (2/3)x + 1

The usual formula for the area of a cirlce is:  A  =  pi·r²

Since the clock face has a diameter of 20 centimeters, it will have a radius of 10 centimeters.

--->     The area of the clock face will be:  A  =  pi·10²     --->     A  =  100pi

Since there are 12 cngruent sectors on the clock face, the area of each sector is:  100pi / 12  =  25pi / 3

Solve for z:  x  =  y / z

Multiply both sides by z:  x · z  =  y

Divide both sides by x:         z  =  y / x

Solve:  log₄(x - 3) + log₄(x + 3)  =  2

--->          log₄ [ (x - 3)(x + 3) ]  =  2

--->                      (x - 3)(x + 3)  =  4²

--->                                 x² - 9  =  16

--->                                      x²  =  25

--->                                       x  =  5          (The possible solution -5 doesn't check.)

Solve for b:  h  =  -b / (2a)

Multiply both sides by 2a:     h·2a  =  -b

                                 --->       2ah  =  -b

Multiply both sides by -1:      -2ah  =  b