Given: m
el
=(2x)°, m
lg
=(3x)°
m
gf
=(4x−8)°, m
fe
=(x−12)°
find: m∠lte

m∠LTE = 110°

Step-by-step explanation:

We know that sum of all arcs of a circle is 360°

Therefore

Now we put the values of each arc

10x = 360 + 20

10x = 380

x = 38

Now from the theorem of intersecting chords in a circle

Measure of ∠LTE =

m(arc EL) = 2x = 2×38 = 76°

m(arc GF) = (4x - 8) = (4×38 - 8) = (152 - 8) = 144°

Now we can get the measure of ∠LTE

m∠LTE =

Therefore m∠LTE = 110° is the answer.

question: how many people can she serve?

answer: she can serve 16.66666667 people. so she can only give 16 people a complete serving.

question: does she have enough ice cream for her guests?

answer: no. explanation: she only has enough for 16 people to have a full serving. however, she can give a 17th person a partial serving.

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