Performance Task Review 1
Given the diagram below, find all the values listed in simplified radical form except
for f and g which should be found to the nearest tenth. Show complete work for
obtaining fand g.
a-
=
b=
d-
e
I 8
L
f=
56°
11
5
K
H
d
30°
45°
a

a = 5; b = 5; c = 10; d = 5; e = 5; f = 6.93; g = 13

= 12.5; = 55; = 12.5; = 38.1

Step-by-step explanation:

Value of e:

sin 45 =

e = 5.

e = 5

Value of a:

e² = 5² + a²

a =

a = 5

Value of b:

The figure J is a rectangle, so opposite sides have the same value. Since b is opposite side of the side measuring 5, b = 5.

Value of c:

sin 30 =

c = 5. 2

c = 10

Value of d:

cos 30 =

d = 10.

d = 5

Value of g:

cos 56 =

g =

g = 13

Value of f:

g² = 11² + f²

f =

f = 7

Area of H:

=

= 12.5

Area of J:

= 11.5

= 55

Area of K:

=

= 12.5

Area of L:

=

= 38.5

55.44 inches

step-by-step explanation:

part a. assuming a perfectly linear relationship, we can find the slope from the first two data points.

slope = m = (change in rainfall)/(change in years)

= (61.80 -62.33)/(2005 -2004) = -0.53/1 = -0.53

then the point-slope form of the equation of the line can be written as

y = m(x -h) +k . . . . . m = -0.53, (h, k) = (0, 62.33)

y = -0.53x +62.33 . . . x = years after 2004

part b. in 2017, x = 2017 -2004 = 13. then the predicted rainfall is

y = -0.53·13 +62.33 = 55.44 . . inches

the predicted rainfall in 2017 is 55.44 in.

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