Answer:





Step-by-step explanation:
Part 1) Find the measure of angle 1
we know that
-----> by supplementary angles

Part 2) Find the measure of angle 2
we know that
-----> by alternate exterior angles
Part 3) Find the measure of angle 3
we know that
-----> by vertical angles
Part 4) Find the measure of angle 4
we know that
------> by corresponding angles
Part 5) Find the measure of angle 5
we know that
-----> by vertical angles
so

Part 6) Find the measure of angle 6
we know that
-----> by supplementary angles
we have

substitute


Answer:
(f • g)(x) = log (-x + 1)
Step-by-step explanation:
Here is a composite function
What we simply have to do here is to make a substitution
the substitution we are going to make is that we will substitute the value of x in f(x) with the entirety of g(x)
This simply mean that we replace every x we find in f(x) with the entire equation of g(x)
we have this as;
f(g(x)) = log (-x + 1)
Tim has 56 more postcards than Paul.
Step-by-step explanation:
Total postcards boys have = 280
Let,
x = Paul's postcards
y = Shawn's postcards
z = Tim's postcards
According to given statement;
x + y + z = 280 Eqn 1
Eqn 2
Eqn 3
Putting value of y from Eqn 3 in Eqn 2
Eqn 4
Putting value of x and y from Eqn 4 and Eqn 3 in Eqn 1

Multiplying both sides by 

Putting z=120 in Eqn 3

Putting y=96 in Eqn 2

Difference of Tim and Paul = 120-64 = 56
Tim has 56 more postcards than Paul.
Keywords: linear equation, substitution method
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Answer:
108 hours and 15 minutes
Step-by-step explanation:
Answer:
<h2>
11</h2>
Step-by-step explanation:
n, n + 1, n + 2 - three consecutive integers
The equation:
n(n + 1) = 8(n + 2) + 2 <em>ust the distributive property</em>
n² + n = 8n + 16 + 2
n² + n = 8n + 18 <em>subtract 8n from both sides</em>
n² - 7n = 18 <em>subtract 18 from both sides</em>
n² - 7n - 18 = 0
n² - 9n + 2n - 18 = 0
n(n - 9) + 2(n - 9) = 0
(n - 9)(n + 2) = 0 ⇔ n - 9 = 0 or n + 2 =0
n - 9 = 0 <em>add 9 to both sides</em>
n = 9
n + 2 = 0 <em>subtract 2 from both sides</em>
n = -2 < 0
n + 2 = 9 + 2 = 11