Which of the following similarity statements about the triangles in the figure are true?

ΔPQS ≈ ΔPQR ≈ ΔPQS    

Step-by-step explanation:

In the given picture we have a right triangle PQR inw hich SQ is perpendicular  to PR.

Then ΔPQS and ΔQRS are also right triangle.

Now, in ΔPQS and ΔPQR

∠PSQ=∠PQR [right angle]

∠P=∠P [common]

∴ΔPQS ≈ ΔPQR        [BY AA similarity ]                          → (1)

In ΔPQR and ΔPQR

∠RSQ=∠PQR [right angle]

∠R=∠R [common]

∴ΔPQR ≈ ΔPQR      [BY AA similarity ]                          → (2)

From (1) and (2), we have

    ΔPQS ≈ ΔPQR ≈ ΔPQS    

Because if two triangles is similar to one triangle then all three triangles are similar to each other  [BY AA similarity ]          .

x = -3

y = -18

step-by-step explanation:

to solve by substitution, substitute one variable and solve for the other. then substitute again to find the remaining variable.

x-1/3(3x-9) = -3 since y=3x-9 substittute y.

x-1/3(3x-9)=-3

x + x +3 = -3

2x+3=-3

2x+3-3= -3-3

2x=-6

x=-3

substitute again into y=3x-9

y=3(-3)-9

y=-9-9

y=-18

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.