Answer:
Z must equal 22° because it will add up to 180° it is an acute scalene triangle
The theorem tells you angles complementary to the same angle are congruent. Both 4 and 1 are complementary to 5, so 4 and 1 are congruent.
The angle congruent to 4 is 1.
You haven't provided the series, therefore, I can only help with the concept.
<u><em>For an infinite geometric series, we have two possibilities for the common ratio (r):</em></u>for r > 1, the terms in the series will keep increasing infinitely and the only possible logic summation of the series would be infinity
for r < 1, the terms will decrease, therefore, we can formulate a rule to get the sum of the infinite series
<u><em>In an infinite series with r < 1, the summation can be found using the following rule:</em></u>sum =

where:
a₁ is the first term in the series
r is the common ratio
<u>Example:</u>
For the series:
2 , 1, 0.5 , 0.25 , ....
we have:
a₁ = 2
r = 0.5
Therefre:
sum =

Hope this helps :)
Answer:
The answer to your question is the height of the lamp is 18.2 ft
Step-by-step explanation:
Data
Street lamp shadow = 31.5 ft
Street sign height = 8 ft
Street sign shadow = 14 ft
Street lamp height = x
Process
1.- To find the height of the lamp use proportions. In this kind of problem, we do not look for the length, but the shadow.
Street lamp height/street lamp shadow = street sign height/street sign
shadow
Substitution
x / 31.5 = 8 / 14
Solve for x
x = (31.5)(8) / 14
Simplification
x = 254.4 / 14
Result
x = 18.2 ft
We know the following relationship:

The
domain of a function are the
inputs of the function, that is, a function

is a relation that assigns to each element

in the
set A exactly one element in the
set B. The set A is the domain (or set of inputs) of the function and the set B contains the range (or set of outputs).Then applying this concept to our function

we can write its domain as follows:
1. D<span>
omain of validity for 
:
</span>
When:

?
when:
where k is an integer either positive or negative. That is:

To match this with the choices above, the answer is:
<span>
"All real numbers except multiples of
"
</span>
2. which identity is not used in the proof of the identity 
:
This identity can proved as follows:

The identity that is not used is as established in the statement above:
<span>
"1 +cos squared theta over sin squared theta= csc2theta"
Written in mathematical language as follows:
</span>

<span>
</span>