1,260 possible arrangements of "balloon" using 7!/[2!*2}
Answer:
y = -1/6x +2
Step-by-step explanation:
The black vertical line in the middle of the graph is the y-axis. The blue line crosses it a the point marked 2. This is known as the y-intercept.
The slope of the line is the ratio of "rise" (vertical change) to "run" (horizontal change).
There is a marked point on the line at the y-intercept, where x=0 and y=2. There is another marked point to the right of that, where x=6 and y=1.
The vertical change between those two points is 1 -2 = -1.
The horizontal change between those two points is 6 -0 = 6
The slope is then -1/6.
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The slope-intercept form of the equation of a line is often written as ...
y = mx + b
where "m" is the slope (-1/6), and "b" is the y-intercept.
Using the values we found above, the equation of the line is ...
y = -1/6x +2
Factor by grouping.
0 = (x^3 +4x^2) +(9x +36) = x^2(x+4) +9(x+4) = (x^2+9)(x+4)
The first factor is the difference of squares (in complex numbers), so the form for factoring that can be used:
a^2 - b^2 = (a -b)(a +b)
Here, a=x, b=3i.
Then the factorization in complex numbers is
0 = (x -3i)(x +3i)(x +4)
Solutions are the values of x that make these factors be zero.
x = -4, -3i, 3i
Answer:
1 3/5
Step-by-step explanation:
First, convert the mixed number into an inproper fraction. 1 4/7 becomes 28/7 (7 times 1, plus 4)
Then just multiply across. 28 times two is 56, 7 times 5 is 35. Now you have 56/35.
Simplify that/divide, the answer is 1.6.
To convert to a fraction, it would become 1 6/10, which becomes 1 3/5 (6 divided by 2 is 3, 10 divided by 2 is 5, 3/5).
Answer is 1 3/5. Good luck!
