Taryn is making a quilt using fabric in the shape of parallelograms that have side lengths of 12 cm and 4.5 cm as shown. She sews two right triangles to either end of the parallelogram to make a rectangle. The length of OP is 2.5 cm.

What is the length of MN?

O A V2.5 cm

OB. 14 cm

OC 4.5 cm

OD 26.5 cm

OE 7 cm

Step-by-step explanation:

Given

Required

Find MN

First, we calculate QP using Pythagoras theorem

Collect like terms

Take square roots

To solve MN, we have:

So:

the temperature will be -18 just do 62 + (-40) + (-40)

step-by-step explanation:

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for