In △abc, m∠cab = 60° and point d ∈ bc so that ad = 10 in, and the distance from d to ab is 5in. prove that ad is the angle bisector of ∠a.

Given:

In △ABC, m∠CAB = 60° and point D ∈ BC so that AD = 10 in, and the distance from D to AB is 5 in.

The distance from D to AB is 5 in.

Construction:

Take point E on AB and join ED such that ED⊥AB

Proof:

Let E be the point on AB which is 5 in from point D.

DE would be perpendicular to AB because distance is always measure in perpendicular form.

Therefore, ΔAED is a right angle triangle.

where, ∠AED=90° , AD=10 and ED=5

In ΔAED, ∠AED=90°

Using trigonometry identities

Therefore, ∠EAD=30°

But ∠CAB=60°

∠BAD=∠CAB-∠EAD=60-30 = 30°

Therefore, ∠BAD=∠EAD=30°

We can say line AD is angle bisector of ∠A. Because it divided ∠A into two equal part.

Hence Proved

3.4 pizzas

step-by-step explanation:

given is a scatter plot showing number of pizzas sold during weeks for different issues of coupon

y represents number of pizzas sold and x number of coupons issued

y is marked verticaly and x horizontally

the trend line is given as

y =3.4x+43

this says that even when no coupon is issued pizzas sold will be 43

and rate of change of pizza sold for 1 unit of coupon = slope = 3.4

i.e. when x increases by 1 unit y increases by 3.4 units

hence for each additional coupon issued 3.4 pizzas more will be sold

(-5,-28)

i graphed to on desmos.