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faltersainse [42]
3 years ago
13

The length of a living room is 12 feet and its width is 10.5 feet. The length of the room is being expanded by x feet.

Mathematics
1 answer:
I am Lyosha [343]3 years ago
3 0

Answer:

A) A= 10.5(12 +x)

B) A= 10.5x +126

Step-by-step explanation:

A) Length of living room= 12 ft

Width= 10.5 ft

Since the length expanded by x ft,

New length of living room= (12 +x) ft

Area= length ×width

Let the new area of the living room be A ft².

A= 10.5(12+x)

B) To expand the expression, multiply 10 to each term and constant in the bracket on the right hand side of the equation.

A= 10.5(12 +x)

A= 10.5(12) +10.5x

A= 126 +10.5x

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As this is a relatively complex division, it is worth doing this on the calculator.
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Step-by-step explanation:

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Read 2 more answers
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'
aleksandr82 [10.1K]

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.

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3 years ago
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Answer:

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