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:
160 cm³
Step-by-step explanation:
→ Write down the formula for the volume
Length × Width × Height
→ Find each value
Length = 4, Width = 4 and Height = 10
→ Substitute into formula
4 × 4 × 10 = 160 cm³
Step-by-step explanation:
Rational numbers are numbers that terminate or are a repeating decimal.
4 rational numbers between -1/3 and -1/2 are
-5/12,
-0.583333333333333333333333333...,
-0.54166666666666..., and
-0.5208333333...
Answer:
x=-2
Step-by-step explanation:
divide both sides by 3
you get x=-2
go to -2 on the x axis and draw a line straight down, x=-2 will intercept the x axis at the point -2
same thing for y=-5 (example)
go down five on the y axis and draw a horizontal line to the y axis intercepting at point (0,-5)
A. discrete
b. categorical
c. continuous
d. continuous
e. discrete (but possibly categorical)
f. continuous
g. categorical
