Rotate the parallelogram 180° clockwise about point q.
a.

answer:

12.20.

step-by-step explanation:

variance = ∑( x - m)^2 / n       where m = mean and n = number of readings.

m = 84/12 = 7.

x - m for the first value is 10.4 - 7 = 3.4.

create a table:

x - m   (x - m)^2

3.4       11.56

3.3         10.89

4.7         22.09

4.1         16.81

1             1

-2.6       6.76

-4.4       19.36

-5.2       27.04

-4.5       20.25

-2.6         6.76

0.3         0.09

2.5           6.25

total:

∑(x -m) ^2   =     148.86

so the variance = 148.86 / 12

= 12.20 (answer).

answer:

  (-2, 5), (-2, -19), (5.2, 2.6)

step-by-step explanation:

you can add ±12 to either the x- or the y-coordinate, as was done in the first two answers above.

or, you can figure the side lengths of a triangle with hypotenuse 12 and add those to the coordinates. for example, a 3-4-5 right triangle multiplied by 2.4 will have side lengths of 7.2, 9.6 and a hypotenuse of 12. hence we can find one of your end points to be

  (-2+7.2, -7+9.6) = (5.2, 2.6)

answer:

words:   if hakeem puts $59 from each paycheck into savings and he receives 26 paychecks each year, at the end of one year he will have saved 59 times 26, or $1,534 which is $34 over his goal.

equation:   59 x 26 = a or 1534 = a, where a represents hakeem's total amount saved.

model:  

2     4     6   8   10   12 14   16   18 20 22 24   26 28 30 32 34 36 38 40 42 44   46    

59 59 59 59 59 59 59 59 59 59 59 59 59 59 59 59 59 59 59 59 59 59 59

48   50   52

59   59   59

step-by-step explanation:

this word problem can be solved in multiple ways as the question indicates, asking for words, and equation and a model.   using the key words and phrases from the problem, we can see that hakeem put $59 from each paycheck into saving and he gets paid every two weeks or 26 times.   because of the words 'each' and 'times', i know that i will have to multiply 59 x 26 to get the total amount that hakeem will save for the year: 26 x 59 = $1,534.  

using words, we can write out the steps to solving the problem.

using an equation, we can solve for a variable.

using a model, we can set up the number paychecks received over the course of a year.