Astudent drew a circle and two secant segment. he concluded that if pq ~= ps, then qr ~= st. do you agree with the student’s conclusion? why or why not?

  Yes

Step-by-step explanation:

You can get there a couple of ways. One makes use of the secant rules that tell you ...

  PQ × PR = PS × PT

Substituting for PR and PT, you have ...

  PQ × (PQ + QR) = PS × (PS + ST)

  PQ² + PQ×QR = PS² + PS×ST

Substituting PQ for PS everywhere, we have ...

  PQ² + PQ×QR = PQ² + PQ×ST

Dividing by PQ gives ...

  PQ + QR = PQ + ST

and subtracting PQ leads us to the conclusion ...

  QR = ST

Another way to look at it is to draw the chord QS. Then ΔQPS is an isosceles triangle, and the perpendicular bisector of QS bisects ∠P and also goes through the circle center. Then the figure is symmetrical about that diameter secant, making QR ≅ ST.

8

step-by-step explanation:

to find the amount of gift bags to use all the supplies, find the gcf or greatest common factor. this is the largest number which multiplies evenly into each term.

48 has factors: 1, 2, 3, 4, 6, 8, 12. 16, 24, 48

80 has factors: 1, 2, 4, 5, 8, 10, 16, 20, 40, 80

64 has factors: 1, 2, 4, 8, 8, 16, 32, 64

the highest number factor they all share in common is 8. this means there will be 8 bags with 6 pencils, 10 markers, and 8 stickers in each bag.