Can anyone help me with this geometry two column proof

Step-by-step explanation:

∠1 + ∠2 = 180                      Linear pair

∠4 + ∠5 +∠ 3 = 180             form straight line

∠1 + ∠2 = ∠4 + ∠5 + ∠3        from statement 1 and 2

∠3 +∠2 = ∠4 + ∠5 + ∠3          ∠1 and ∠3 are vertically opposite angles.

∠2 = ∠4 + ∠5                           Proved

y-y1=4(x-x1)

step-by-step explanation:

this is point-slope form since you only have 4 as the slope it goes in place of m

hope this : )

1 number

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.