Annie is creating a stencil for her artwork using a coordinate plane. The beginning of the left edge of the stencil falls at (1, −1). She wants to align an important detail on the left edge of her stencil at (3, 0). She knows this is 1:3 of the way to where she wants the end of the stencil. Where is the end of the stencil located?

Step-by-step explanation:

The given line is divided in the ratio 1:3 and the coordinate of the point P at which the line is divided is (3,0).

The best approach is to use the section formula which relates to the internal division of a line.

Given a line from which is divided in the ratio m:n, the coordinates of the point P of division is derived using the formula:

In our given case,

P(x,y)=(3,0)

m:n=1:3

Our goal is to determine the end of the stencil

Thus:

Therefore, the end of the stencil is located at,

see explanation

step-by-step explanation:

since the sequence is geometric there is a common ratio r between consecutive terms, that is

r = 4 ÷ - 2 = - 2

r = - 8 ÷ 4 = - 2

r = 16 ÷ 8 = - 2

the next term - 13 must be incorrect as it should be - 32 for the sequence to be geometric.

the first 4 terms are therefore geometric with common ratio r = - 2

answer: it's d

step-by-step explanation: