Aconstruction worker is building a wall. the wall is
20
yd
long. he needs to place a stud every
16
in
. the first stud has already been placed at one end of the wall. how many additional studs are needed, if the last stud will be placed at the other end of the wall? first fill in the blanks on the left side using the ratios shown.

Step-by-step explanation:

First, convert 20 yds to 60 ft. and then from 60 ft to 720 in.

Use the formula for the nth term of an arithmetic sequence:

l = a + (n-1)d:

Here l = 720 ft, and a = 0.  The common difference, d, is 16 in.  Our task is to determine how many studs are needed.

Substituting the knowns, we get 720 = 0 + (n - 1)(16), which simplifies to:

720 = (n-1)(16).

Divide both sides by 16 to isolate (n-1):  45 = n - 1.

Adding 1 to both sides results in 46 = n.

46 studs total are needed; if the worker has already placed the first stud, then 45 additional studs are needed.

the length of o'p' is .

step-by-step explanation:

it is given that the quadrilateral m'n'o'p' is the image of quadrilateral mnop after dilation.

the center of dilation is origin and the scale factor is 1.5.

in dilation the image and preimge are similar figures. it means the sides of image and preimage are proportional.

the scale factor is defined as

the scale factor is 1.5.

multiply both sides by op.

note: if the value of op is given, then multiply the value of op with 1.5 to get the length of side o'p'.

therefore length of o'p' is .