Math III midterm

End behavior A is positive

upward sloping right side

A is negative

downward sloping right side

n is even

same

n is odd

opposite

Writing an absolute value inequality

|x-Midpoint| (inequality sign) distance

Midpoint

(#+#)/2

Distance

(big-small)/2

Circumcenter

Perpendicular bisectors;Midpoint of the side of the triangle and is perpendicular to that side

Equidistant from the vertices to the triangle

incenter

Angle bisectors; A ray that bisects an angle of a triangle

Equidistant to the sides of the triangles

Centroid

A segment that connects a vertex to the midpoint of the opposite side

2/3 distance from a vertex in a triangle

Centroid to the vertex

2/3

centroid to the side

1/3

Altitudes

A segment that connects a vertex to the opposite side and is perpendicular to that side

Orthocenter

Tthe altitudes of a triangle

parallelogram side properties

Opposite sides are parallel

Opposite sides are congruent

Parallelogram angle properties

Opposite angles are congruent

consecutive angles are supplementary

Parallelogram diagonals properties

diagonals bisect each other

Rhombus

All sides are congruent

Area of a parallelogram

A=BH

Area of a triangle

A=1/2BH

Trapezoid

A=1/2h(b1+b2)

Regular polygon

A=1/2p(a)

Apothem

a=(1/2side)/Tan1/2(angle)

Angle

Angle=360/number of sides

Circle

pi(r²)

Volume of a prism

V=BH

Volume of a cylinder

V=pi(r²)h

Volume of a pyramid

V=(1/3)bh

Volume of a cone

V=1/3pi(r²)h

Sphere

v=4/3pi(r³)

Hemisphere

2/3pi(r³)

Density

Density=Mass/volume(area)

Center angles

m<=arc

On the line

m<=1/2(arc)

Inside (but not center)

m<=1/2(sum of arcs)

Outside

M<=1/2(big arc-small arc)

Segments intersected within a circle

part(part)=part(part)

Segments that intersect outside the circle

Out(whole)=out(whole)

Area of a sector of a cirlce

theta/360(pi)(r²)

Compound interest

p(1+r/n)^nt

Exponential Growth

A=P(1+r)^t

Exponential Decay

A=p(1-r)^t