Answer:
1
Step-by-step explanation:
tan 45 = cos 45 / sin 45.
Since sin(x)=cos(90-x), cos 45 = sin 45, so tan 45 = 1
we have that

using a graph tool
see the attached figure
statements
case a) The domain is {x|x ≤ –2}-------> Is False
the domain is all real numbers---------> the interval (-∞,∞)
case b) The range is {y|y ≤ 6}.------> Is True
The range is the interval (-∞,6]
case c) The function is increasing over the interval (–∞ , –2).-----> Is True
See the attached figure
case d)The function is decreasing over the interval (−4, ∞).-----> Is False
In the interval (-4,-2) the function is increasing and in the interval (-2,∞) the function is decreasing (See the attached figure)
case e)The function has a positive y-intercept.------> Is True
The value of y-intercept is 
Title:
<h2>The worker's highest wage is $400.</h2>
Step-by-step explanation:
Due to the joining of the 11th worker, the firm's output increases 10 units.
The price of each unit is $40.
The price of 10 units are
.
The worker's wage will be highest if he will be paid all the amount which is the resultant of the output's increase, that is (90 - 80) = 10 units.
<u>Given</u>:
The given expression is 
We need to determine the equivalent number.
<u>Equivalent expression:</u>
To determine the equivalent number, let us solve the expression 
Thus, let us apply the exponent rule
, we get;

Also, the term 10³ can be written as 
Thus, we get;

Dividing, we get;
0.001
Hence, the equivalent number is 0.001
Hence, Option c is the correct answer.
The statements that are rue for <span>all invertible n×n matrices A and B are:
</span><span>(A+B)(A−B)=A^2−B^2
</span>and
<span>(ABA^−1)^4=AB^4A^−1
</span>From the above results we can conclude that the correct options among all the options that are given in the question are option "B" and option "E". I hope the answer helps you.