Use the diagram to answer the following questions

  a. line AR, line AV

  b. plane TSR, plane QTZ, plane RSZ

  c. A, R, V

  d. Q, R, S, T

  e. QR

  f. RQ, RS

Step-by-step explanation:

a. In addition to a name given to a line ("line p"), a line can be named by any two points on that line. Here, possible names are ...

  line AR, line RA, line AV, line VA, line RV, line VR

any two of these names will appropriately answer this part of the question.

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b. In addition to a name given to a plane ("plane W"), a plane can be named by any three points in that plane. Here, there are 5 named points in the plane (3 of which are collinear), so there are 54 possible different names for the plane. Some of them are ...

  plane RST, plane TSR, plane QTZ, plane RSZ

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c. In this diagram, each of the lines shown has three named points on it. Possible answers to this part of the question are ...

  {Q, R, S} or {A, R, V}

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d. Any four of the 5 named points shown in plane W will serve to answer this question. Possible answers are ...

  {R, S, T, Z} or  {Q, S, T, Z} or  {Q, R, T, Z} or  {Q, R, S, Z} or  {Q, R, S, T}

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e. Any pair of collinear points will name a line segment. Here, there are 12 possible names for line segments, including ...

  QR, RQ, QS, SQ, RS, SR, AR, RA, ...

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f. Opposite rays can be named by choosing the end point as the middle of three collinear points. Here, the only such middle point is R. We can name pairs of opposite rays on either line. The endpoint of the ray is named first.

  {RA, RV}  or  {RQ, RS}

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