What is the reason for step 2 in this proof?

given:

angles a and b are supplementary.
the measure of angle a = 45º.

find the measure of angle b. proof:

1. angles a and b are supplementary and angle a = 45º. (reason: given)

2. measure of angle a + measure of angle b = 180º ( reason: ? ? )

3. 45º + measure of angle b = 180º (reason: substitution)

4. measure of angle b = 135º (reason: subtraction property of equality)

a) substitution property of equality
b) definition of supplementary angles
c) transitive property of equality

Angles A and B are said to be supplementary. This piece of information should be used. Supplementary angles are angles whose sum equals 180˚. This would be later used in the further steps to fin the unknown angle B.

Thus, the answer is B) Definition of Supplementary Angles

the formula of a slope:

from a table we have

substitute:

the slope of f(x) is -1.

the graph of funcfion g(x) is a horizontal line. the slope of a horizontal line is equal 0. therefore the slope of g(x) is 0.

-1 < 0

answer: 204

step-by-step explanation:

we are told that the revenue is

x⋅(4080−10x)=−10x^2+4080x

this is a quadratic function, so to maximize it we should find the x-value of its vertex. recall that the x-value of the vertex of the parabola ax^2+bx+c is given by the formula −b/2a.

so in this case, we have a=−10 and b=4080, so the x-value of the vertex is

−b/2a= −(4080)/2(−10)=204