Hi there!
j is 7 times greater than 6.
When j is 7 times greater than a number, we get the following equation:
j / 7 = 6
Multiply both sides by 7.
j = 42
Add both numbers together then subtract 180 from the sum of the two numbers
You can choose to expand the equation to find the coefficient of x7 but that would take a lot of time. Here is a useful tactic that can help;
11C(something)(1)(x)⁷ ----> This gives the coefficient of x⁷
11C7(1)⁴(x)⁷ ----> You know that pascal's triangle is equal on both sides
11C7×1⁴ = coefficient of x⁷ (just ignore x⁷)
330x1⁴=330
This means that the coefficient of x⁷ is 330. You can double check by expanding the equation. If you do not understand what I did there, you can ask me how I got to the solution.
Hope I helped :)
Answer:
See explanation
Step-by-step explanation:
Let 
be the coordinates of the point which has to be dilated with the scale factor of 
with the center of dilation at point 
(the origin).
The dilation with the scale factor and the center of dilation at the origin has the rule
So, you have simply to multiply each coordinate of the point by to get the image's coordinates.
Step-by-step explanation:
you know, a single side cannot be longer than the other 2 sides combined.
otherwise, the triangle cannot "close".
so, it starts with 12 cannot be longer than 5 + n.
therefore, n must be at least 7.
and n cannot be longer than 5+12 = 17
7 and 17 I would normally rule out a well, because in these cases the triangle would just be a flat line, when the 3rd side is as long as the other 2 combined.
so, in reality for a real, visible triangle, the range of valid values is 8 .. 16.
that is 9 positive integer values.
