geno3141

Use the extended distributive property FOIL (First, Outside, Inside, Last):

(4x+ 3)(2x - 5)  =  (4x)(2x) + (4x)(-5) + (3)(2x) + (3)(-5)  =  8x² - 20x + 6x - 15  =  8x² - 14x - 15

x² + 11x + 18  factors into (x + a)(x + b)

To find the values of a and b, find two values so that they add up to 11 and multiply to 18,

then fill them into (x +   )(x +   ).

7/21  =  1/3

You can round this answer; if you do, it becomes 0.

If you must have a non-zero answer, the closest whole number greater than 0 is 1.

Add down the columns, giving:  3x = 3

Divide by 3   --->   x = 1

Substitute this value into either the top equation or the bottom equation:  1 + 3y  =  7   

     --->     3y  =  6     --->   y  = 2

[7x³] / [21xy]

Cancel the 7 in the numerator into the 21 in the denominator, giving 1/3.

Cancel one of the x's in the numberator with the x in the denominator, leaving x² in the numerator.

--->     x² / [3y]

First, find the slope:  m  =  [y₂ - y₁] / [x₂ - x₁]  =  [-5 - -1] / [-3 - 5]  =  [-5 + 1] / [-8]  =  [-4] / [-8]  =  1/2

Now, use the point-slope form for a line:  y - y₁  =  m[x - x₁]     --->     y - -1  =  (1/2)[x - 5]

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

2x² + 8x

Since each term contains both a '2' and an 'x', factor out 2x:  2x(x + 4)

You can put the first ball in any of 3 boxes, the second ball in any of 3 boxes, etc.

There are 3 choices for each ball, so there are 3x3x3x3x3 = 3⁵ choices = 243 choices.

Depends ...

If you mean:  √(3)/2 x 1/√(3), then:  [√(3) x 1 ] / [2 x √(3) ] = 1/2 (the √(3)s cancel).

If you mean:  √(3/2) x 1/√(3), then:  √(3/2) x √(1/3)  =  √(3/6) = √(1/2)  =  √(2)/2.

If each try is independent from every other try and the probability of success is 1/683 and there are 683 tries, then the probability of failure is (682/683)⁶⁸³ because the probability of failure each time is 682/683 and you have to fail each of the 683 times.

So, the probability of success is 1 - (682/683)⁶⁸³ since the probability of success + the probability of failure is exactly 1 --- which means that the probability of success is 1 - probability of failure.