Four points are drawn on the coordinate plane and connected with straight lines to form a rectangle. Three vertices of the rectangle are located at (2,1), (2,4), and (-4,4) a. What are the coordinates of the fourth vertex of the rectangle?

B. What are the dimensions of the rectangle?

C. What is the area of the rectangle?

(a) (-4,1)

(b) 3 units by 6 units

(c)18 square units

Step-by-step explanation:

Let the rectangle be ABCD labeled from the top left clockwise.

(a)Considering the y coordinates of BC,

The distance between BC =|4-1|=3 Units

Since BC and AD are congruent

Distance between A(-4,4) and D(-4,y) is also 3 Units

Therefore:

|4-y|=3

y=4-3=1

The coordinates of the fourth vertex of the rectangle at D is (-4,1)

(b)

Height, BC =3 Units

Now, A(-4,4) and B(2,4)

Therefore: Width, AB = |2-(-4)|=2+4=

Width, AB=6 Units

The dimensions of the rectangle are 3 units by 6 units.

(c)

Area of the Rectangle =Width X Height

= 3 X 6

=18 Square units

step-by-step explanation:

i found the life tables for the year 2012. 

life table of males at age 30. probability of dying between ages x and x+1

total population:  

29–30 . . . . . . . . . . . . 0.001030

30–31 . . . . . . . . . . . . 0.001061

males:  

29–30 . . . . . . . . . . . . 0.001420

30–31 . . . . . . . . . . . . 0.001448

white population

29–30 . . . . . . . . . . . . 0.001005

30–31 . . . . . . . . . . . . 0.001037

white males

29–30 . . . . . . . . . . . . 0.001372

30–31 . . . . . . . . . . . . 0.001399

non hispanic white population

29–30 . . . . . . . . . . . . 0.001083

30–31 . . . . . . . . . . . . 0.001116

non hispanic white males

29–30 . . . . . . . . . . . . 0.001477

30–31 . . . . . . . . . . . . 0.001503

jacob, non hispanic white male. 30 years old.

probability that jacob lives to be 30 years old. 

since the given probabilities are probabilities of dying, i think we simply subtract it from 1 to get the probability of living. we will use the probability of non hispanic white male.

                                          probability of living to be 30 y.o.

29 - 30 : 1 - 0.001477 = 0.998523

30 - 31 : 1 - 0.001503 = 0.998497

its 60

4 x 12 = 48

3 x 4 = 12

48 + 12 = 60

yeeeet