geno3141

The problem is to find two numbers which, when multiplied together have an answer of 54, and when added have a sum of 29.  The factors contain two negative signs because the last term is positive and the middle term is negative.

27 x 2  =  54  and  27 + 2  =  19

So:  x² - 29x + 54  =  (x - 27)(x - 2)

y = 4x - 2

3x + 2y  =  -4

Substituting the value for y from the top equation into the bottom equation:

3x + 2(4x - 2)  =  -4

Solving:

Distributing the 2:                    3x + 8x - 4  =  -4

Adding the x-terms together:  11x - 4  =  -4

Adding 4 to both sides:           11x  = 0

Dividing by 11:                            x  =  0

Substituting 0 for x into the first equation:

                                                   y  =  4(0) - 2

                                                   y  =  -2

The solution to the set of equations is:  x = 0,  y = -2.

sqrt(288)  =  sqrt(144·2)  =  sqrt(144)·sqrt(2)  =  12·sqrt(2)

sqrt(x³)  =  sqrt(x²)·sqrt(x)  =  x·sqrt(x)

sqrt(y)  =  sqrt(y)

sqrt(z⁵)  =  sqrt(z⁴)·sqrt(z)  =  z²·sqrt(z)

So:  sqrt(288·x³·y·z⁵)  =  12·x·z²·sqrt(2·x·y·z)

Since area = length times width,

to find the width, divide the area by the length.

18*12  =  13*h

   216  =  13*h

  216/13  =  h                           (divide both sides by 13)

h  =  16 8/13 

(3b² - 2b + 1)(2b² -3b - 4)

=  (3b²)(2b²) + (3b²)(-3b) + (3b²)(-4)

                     +  (-2b)(2b²) + (-2b)(-3b) + (-2b)(-4)

                                          +  (1)(2b²) + (1)(-3b) + (1)(-4)

=  6b⁴ - 9b³ - 12b²

          - 4b³ +   6b² + 8b

                   +  2b² - 3b - 4

=  6b⁴ - 13b³ - 4b² + 5b - 4

Their solutions will occur where they intersect.

If the lines are straight lines, their solution will be the one point where they intersect.

Of course, if they don't intersect, there will be no solutions.

I'm going to assume that you mean:  8^{3x + 4}  =  4^{2x - 1}

Since 8 = 2³ and 4 = 2²:                    (2³)^{(3x + 4)}  =  (2²)^{(2x - 1)}

Multiplying exponents:                         2^{9x + 12}  =  2^{4x - 2}

Since the bases are equal, the exponents must be equal:     9x + 12  =  4x - 2

                                                                                               5x + 12  =  -2

                                                                                                       5x  =  -14

                                                                                                         x  =  -14/5

It depends upon how many tests that you have already taken.

If you have taken only one, then one way to solve the problem is this:  (71 + 3x)/4  =  77

--->     71 + 3x  =  308   

--->             3x  =  237

--->               x  =  79

You would have to average 79 on the last three tests.

So, it can be either red (only) or white spots (only) or red with white spots.

The probability of being any of the above three is 0.80.

The probability of being red (either only red or red with white spots) is 0.62.

The probability of having white spots (either only white spots or red with white spots) is 0.35.

If you add these two probabilities together, you get 0.62 + 0.35  =  0.97.

But, the total probability of all three is just 0.80.

Subtracting  0.97 - 0.80 means that there is an overlap of 0.17.

The overlap is the probability of getting one that is red with white spots.  Answer:  red with white spots  =  0.17.

Red only will be 0.62 - 0.17  =  0.45.

White spots only will be 0.37 - 0.17  =  0.18.

Checking by adding the three probabilities:  0.17 + 0.45 + 0.18  =  0.80.