Ows Challenge The members of the city cultural center have decided to put on a
play once a night for a week. Their auditorium holds 500 people. By selling
tickets, the members would like to raise $2,850 every night to cover all
expenses. Let d represent the number of adult tickets sold at $7.50. Lets
represent the number of student tickets sold at $4.50 each. If all 500 seats are
filled for a performance, how many of each type of ticket must have been sold
for the members to raise exactly $2,850? At one performance there were three
times as many student tickets sold as adult tickets. If there were 480 tickets sales sold at that performance, how much below the goal of 2,850 did ticket sales fail

pentagon

step-by-step explanation:

the coordinates   a(5, -2), b(3,-1),c(-4,-4) d(-3,8) and e(-1,4) forms the vertices of the polygon when they are connected in order.

in order to classify that which polygon is it with the given coordinates, first count the number of vertices and then count the number of sides it can make with these vertices.

since, the given coordinates have five vertices, therefore, it will make five sides. moreover, pentagon is regular in nature therefore it will be convex.

now, a polygon with five sides is known as pentagon, therefore, the given polygon is the pentagon.

central angle of a triangle has the same measure as its intercepted arc.

step-by-step explanation:

< xcy ≅ < xby

step-by-step explanation:

in δcax and δbax,

so, δcax ≅ δbax (side-angle-side or sas)

since δcax ≅ δbax, we can conclude < acx ≅ < abx

in δacy and δaby,

so, δacy ≅ δaby (side-angle-side or sas)

since δacy ≅ δaby, we can conclude < acy ≅ < aby

now,

< acy ≅ < aby

=> < acx + < xcy ≅ < abx + < xby

=> < acx + < xcy ≅ < acx + < xby   (since < acx ≅ < abx already proved above)

subtracting < acx from both sides, we get

< acx + < xcy -< acx ≅ < acx + < xby -< acx

cancelling out < acx and -< acx from both sides, we get

< xcy ≅ < xby (proved)