Describe the pattern. Then find the next two numbers in the pattern. 2,8,32,128

1 answer:

8 0

<span>2, 8, 32,128

8/2 = 4
32/8 = 4
128/32 = 4

Each number is being multiplied by 4.
128*4 = 512
512*4 = 2048

512 and 2048 are the next two numbers.</span>

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Write 800 as the product of its prime factors.

Alex_Xolod [135]

800|2
800|2
400|2
200|2
100|2
50|2
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5|5
1

$800=2^5\cdot5^2$

8 0

3 years ago

The vertices of a square CDEF are C(1,1), D(3,1), E(3,-1) and F(1,-1). What formulas prove that the diagonals are congruent perp

Oxana [17]

To prove that the diagonals are congruent, you need to formula to compute the distance between two points:

$d(A,B) = \sqrt{(A_x-B_x)^2 + (A_y-B_y)^2}$

Using that formula, you may prove that $d(C,E) = d(D,F)$ , which means that the two diagonals have the same length.

To prove that they are perpendicular, you need the formula to compute the slope of a segment. The slope, knowing the enpoints, is given by

$m = \cfrac{\Delta y}{\Delta x} = \cfrac{A_y-B_y}{A_x-B_x}$

You can use this formula to prove that

$m_{CE} = -\cfrac{1}{m_{DF}}$

In fact, if one slope is the opposite of the reciprocal of the other, the two segments are perpendicular.

Finally, to prove that they bisect each other, you first need to find the point where they meet. First of all, you need to find the line the segments lie on: the formula is

$y-y_0 = m(x-x_0)$

where $(x_0,y_0)$ is one of the points belonging to the line, and you already know how to find the slope. Then, you find the point of intersection, say A, by solving the system involving the two lines: