Holly is making a patchwork quilt. she has completed a rectangular section that is 3 patches long and 5 patches wide. each week, she plans to make the quilt 1 patch longer and 3 patches wider. use the drop-down menus below to complete statements using words and symbols to describe the total number of patches after x weeks.

Word: x patch longer after x weeks an 3x patches wider after x weeks

The symbol:   3+ x*1  and 5+ 3x   after x weeks

Step-by-step explanation:

Given that:

For example, we will have a table of values:

WeekLengthWidth  

1             3               5

2           3+1             5+3  

3          3+1+1     5+3 +3  

….                

x           3+ x*1      5+ 3x  

Word: x patch longer after x weeks an 3x patches wider after x weeks

The symbol:   3+ x*1  and 5+ 3x   after x weeks

isocolese triangle

we know that the line connect a and b is the hyptonuse

so first find the hypotonuse length using the distance formula, call the length c

since it is an isocolese triangle, the lengths of the legs are the same

using pythagorean theorem,

in this case, a=b since isocolese triangle so we get

or

we can find c so we can find the distances

we know that if we draw 2 circles, each has center at a and b, and find where they intersect, we can the 2 possible locations for c

if a has center at (xa,ya) and b has center at (xb,yb), then we can solve where

and

intersect to find where they intersect

i'm not going to put an example because i have to go to class. i hope this explanation is enough