Answer:
A. △P'Q'R' does not equal △P''Q''R''.
B. Reflecting across UT would change the orientation of the figure.
C. The sequence does not include a reflection that exchanges U and S.
D. Rotating about point U is not a rigid motion because it changes the orientation of the figure.
E. Translating point R' to Q' is a non-invertible transformation because it changes the location of P'.
(D) Rotating about U is not a rigid motion because it changes the orientation of the figure. [I think D is an incorrect answer choice.]
Step-by-step explanation:
Proof No.1
Jordan wants to prove △PQR≅△STU using a sequence of rigid motions. This is Jordan's proof. Translate △PQR to get △P'Q'R' with R'=U. Then rotate △P'Q'R' about point U to get △P''Q''R''. Since translation and rotation preserve distance, R''Q''=RQ=UT, and Q''=T. Reflect △P''Q''R'' across UT to get △P'''Q'''R''. Since reflection preserves distance, P'''R'''=PR=US, and P'''=S. A sequence of rigid motions maps △PQR onto △STU, so △PQR≅△STU.
Proof No.2
Jordan wants to prove △PQR≅△STU using a sequence of rigid motions. This is Jordan's proof. Translate △PQR to get △P'Q'R' with R'=U. Then rotate △P'Q'R about point U to get △P''Q''R'' so that R''Q'' and UT coincide. Since translation and rotation preserve distance, R''Q''=RQ=UT, and Q''=T. Reflect △P''Q''R'' across UT to get △P'''Q'''R''. Since reflection preserves distance, P'''R'''=PR=US, and P'''=S. A sequence of rigid motions maps △PQR onto △STU, so △PQR≅△STU.
Answer:
20 times an hour so 20 times 48 is 960 1920-960 is 960 gallons so there is 960 gallons of water left
The area of the floor is (16-ft x 14-ft) = 224 square feet.
IF carpet cost $16 per square foot, THEN enough carpet
to cover that floor would cost
(224) x ($16) = $3,584 ,
and PLUS, you'd need to buy 224 square feet of pad to lay down
under the carpet, and pay more to have the whole thing installed.
That's an awful lot of money for a little dinky 12' x 14' bedroom !
Carpet does NOT cost $16 per square foot.
It's more like $16 per square YARD (plus pad and installation).
9 square feet = 1 square yard.
The area of the bedroom is (224/9) = 24-8/9 square yards
At $16 per each of those, the carpet costs (24-8/9) x ($16) = $398.22 .
Much more reasonable !
268.08
V=4/3(pi)r(cubed)
Plug and chug —> the volume of this sphere is about(squiggly equality sign) 268.08 feet
Answer
Their combined score is 331 points
Explanation
Determine each person's score
Collin score: 139
Brian: 139 + 53 = 192
Add the scores together
139 + 192 = 331
