Complete the reasons for the proof. given: m ∠3 = m ∠4 to prove: ∠1, ∠2 are supplementary

Given: m ∠3 = m ∠4

To Prove: ∠1, ∠2 are supplementary .

Proof : m ∠3 = m ∠4    ( Given)                                              (1)

m<2 + m< 3 = 180 degrees  ( <2 and <3 form a linear pair). (2)

m< 4 = m<1                            (Vertical angles are equal)       (3).

Substituting, m<4 =m<1 in (1), we get

m ∠3 = m ∠1.

Now, substituting m ∠3 = m ∠1 in (2), we get

m<2 + m< 1 = 180 degrees.

Sum of m <1 and m<2 is 180 degrees.

Therefore, ∠1, ∠2 are supplementary by the defination of supplementary angles.

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