geno3141

If you multiply ½ x 2, the answer is 1

if you muliply 1 x 2, the answer is 2

if you multiply 2 x 2, the answer is 4

so, it seems that the next term in this sequaence is found by multiplying the preceding term by 2.

Knowing this, what is the next term?

If the problem is:  [x² + 4x + 4] / [x² + 6x + 8]

factor both the nmerator and the denominator:

[ (x + 2)(x + 2) ] / [ (x + 4)(x + 2) ]

Cancel the (x + 2) factor in the numerator with the (x + 2) factor in the denominator:

=  (x + 2) / (x + 4)

If you can only use real numbers, the answer is "no"

because real numbers only include 0, positive numbers and negative numbers

and, a positive times a positive is positive and a negtative times a negative is also a positive, so there is no way to get a negative for an answer.

However, if you use complex numbers the answer is "yes".

With complex numbers the  √(-1)  is usually written as just the letter 'i'. 

First, find the slope:  m  =  (y2 - y1) / (x2 - x1)

x1 = 1/4  y1 = -1/2  x2 = 3/4  y2 = 2     ---> 

m  =  (2 - -1/2) / (3/4 - 1/4)   =   (5/2) / (1/2)   =  5

Use the point-slope form for the equation of the line:    y - y1  =  m(x - x1)

y - -1/2  =  5(x - 1/4)     --->     y + 1/2  =  5x - 5/4     --->     y  =  5x -7/4

Distance  =  rate x time

Your rate is 55 mph and you are to represent the time traveled by the letter 'x':

Distance = 55 · x

y  =  55 · x

Now, find the y-values when x = 0, x = 5, and x = 10.

Since the cost for the gas is $4.98 times the number of gallons, the equation will be:  y  =  4.98x.

e^[2·ln(x)]

Since a multiplier times a log goes inside the log as an exponent:

= e^[ln(x²)]     

Sinc e^ln(z)  =  z,

= x²

If you are refering to a quadratic function (a parabloola), there are various ways:

1) graph the equation and read the values from the graph

2) complete the square and get the equation into the form:  y  = a(x - h)² + k; the vertex will be (h, k)

3) use the formulas:  x = -b/(2a)    y = (b² -4ac)/(4a) to find the x- and y-values of the vertex

Compound interest formula:      A  =  P(1 + r/n)^(n·t)

A = final amount              P = beginning amount = $5000.00               r = rate (as a decimal) = 0.03

n = number of times compounded each year = 1                                 t = number of years = 2

 A  =  P(1 + r/n)^(n·t)     --->      A  =  5000(1 + 0.03/1)^(1·2)      --->     $5304.50

Use floor().