1/9 of the aquarium was filled with 1/7 liter
1 whole fraction of the aquarium will be filled = 1/7 ÷ 1/9
= 1/7 * 9/1 = 9/7
9/7 liters or 1 2/7 liters will be needed.
The answer is 45°
By determining the angles of triangle ACB (A=30°, B=45°, C=105° (total of 180°)) and knowing that angle 1 correlates to angle 4 ((1)°=(4)°), we can find angle 1, which is 45°, equal to angle 4.
Answer:
=x^3 y^3-3x^3y^2+4x^2y^3+3
Step-by-step explanation:
Answer:
180
Step-by-step explanation:
1. Write a proportion.
=
2. Cross multiply.
6x60=360
360/2=180
x=180
OR
1. Write a proportion.
=
If you look at the bottom, since 2 times 30 is 60, 6 times 30 is 180, making the fractions equal.
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.
