List the coefficients in the row of Pascal's triangle corresponding to n = 7.

9514 1404 393

  1 7 21 35 35 21 7 1

Step-by-step explanation:

Numbering from k=0 to k=7, the k-th coefficient in the row is ...

  C(7, k) = 7!/(k!(7-k)!)

You know the first two in row 7 are 1 and 7. There are 8 in the row, and the row is the same forward and backward. This means you only need to find C(7, 2) and C(7, 3). These are ...

  C(7, 2) = 7!/(2!(5!)) = 7·6/(2·1) = 21

  C(7, 3) = 7!/(3!(4!)) = 7·6·5/(3·2·1) = 35

So, row 7 is ...

  1, 7, 21, 35, 35, 21, 7, 1

answer: they are supplementary angles

step-by-step explanation: 161+19=180. supplementary angles equal 180 degrees

the area of a triangle is determined by the formula: base x height * 1/2

you'll need to assign a base to the triangle. based on the vertices given, the simplest base would be the line segment from (-2,1) to (2,1). the distance between any two numbers is found by just subtracting them. here, you should subtract the x values to find the distance of this side.

2 - (-2) = 4.

so the distance (aka the length of the base) is 4. the height of the triangle is the distance between the base and the highest point on the triangle which is (3,4). we should subtract the y values this time to find the height/distance.

4 - 1 = 3

so the height is 3.

base = 4

height = 3

hope this if needed hmu