(a) To find: The coordinate of the image for ( 7 , 14 ) under the translation ( x , y ) → ( x + 3 , y − 4 )

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Answer 1

Question

Chapter 14.1B, Problem 3A

To determine

(a)

To find:

The coordinate of the image for (7,14) under the translation

(x,y)→(x+3, y−4)

To determine

(b)

To find:

The coordinate of the image for (−3,−5) under the translation (x,y)→(x+3, y−4)

To determine

(c)

To find:

The coordinate of the image for (h,k) under the translation (x,y)→(x+3, y−4)

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By considering appropriate series expansions, e². e²²/2. e²³/3. .... = = 1 + x + x² + · ... when |x| < 1. By expanding each individual exponential term on the left-hand side the coefficient of x- 19 has the form and multiplying out, 1/19!1/19+r/s, where 19 does not divide s. Deduce that 18! 1 (mod 19).

Proof: LN⎯⎯⎯⎯⎯LN¯ divides quadrilateral KLMN into two triangles. The sum of the angle measures in each triangle is ˚, so the sum of the angle measures for both triangles is ˚. So, m∠K+m∠L+m∠M+m∠N=m∠K+m∠L+m∠M+m∠N=˚. Because ∠K≅∠M∠K≅∠M and ∠N≅∠L, m∠K=m∠M∠N≅∠L, m∠K=m∠M and m∠N=m∠Lm∠N=m∠L by the definition of congruence. By the Substitution Property of Equality, m∠K+m∠L+m∠K+m∠L=m∠K+m∠L+m∠K+m∠L=°,°, so (m∠K)+ m∠K+ (m∠L)= m∠L= ˚. Dividing each side by gives m∠K+m∠L=m∠K+m∠L= °.°. The consecutive angles are supplementary, so KN⎯⎯⎯⎯⎯⎯∥LM⎯⎯⎯⎯⎯⎯KN¯∥LM¯ by the Converse of the Consecutive Interior Angles Theorem. Likewise, (m∠K)+m∠K+ (m∠N)=m∠N= ˚, or m∠K+m∠N=m∠K+m∠N= ˚. So these consecutive angles are supplementary and KL⎯⎯⎯⎯⎯∥NM⎯⎯⎯⎯⎯⎯KL¯∥NM¯ by the Converse of the Consecutive Interior Angles Theorem. Opposite sides are parallel, so quadrilateral KLMN is a parallelogram.

By considering appropriate series expansions, ex · ex²/2 . ¸²³/³ . . .. = = 1 + x + x² +…… when |x| < 1. By expanding each individual exponential term on the left-hand side and multiplying out, show that the coefficient of x 19 has the form 1/19!+1/19+r/s, where 19 does not divide s.

Answer 2

Question

Chapter 14.1B, Problem 3A

To determine

(a)

To find:

The coordinate of the image for (7,14) under the translation

(x,y)→(x+3, y−4)

To determine

(b)

To find:

The coordinate of the image for (−3,−5) under the translation (x,y)→(x+3, y−4)

To determine

(c)

To find:

The coordinate of the image for (h,k) under the translation (x,y)→(x+3, y−4)

Expert Solution & Answer

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Check out a sample textbook solution

See solution

Answer 3

Question

Chapter 14.1B, Problem 3A

To determine

(a)

To find:

The coordinate of the image for (7,14) under the translation

(x,y)→(x+3, y−4)

To determine

(b)

To find:

The coordinate of the image for (−3,−5) under the translation (x,y)→(x+3, y−4)

To determine

(c)

To find:

The coordinate of the image for (h,k) under the translation (x,y)→(x+3, y−4)

Expert Solution & Answer

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Check out a sample textbook solution

See solution

Answer 4

Question

Chapter 14.1B, Problem 3A

To determine

(a)

To find:

The coordinate of the image for (7,14) under the translation

(x,y)→(x+3, y−4)

To determine

(b)

To find:

The coordinate of the image for (−3,−5) under the translation (x,y)→(x+3, y−4)

To determine

(c)

To find:

The coordinate of the image for (h,k) under the translation (x,y)→(x+3, y−4)

Expert Solution & Answer

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Check out a sample textbook solution

See solution

Answer 5

Chapter 14.1B, Problem 3A

To determine

(a)

To find:

The coordinate of the image for (7,14) under the translation

(x,y)→(x+3, y−4)

To determine

(b)

To find:

The coordinate of the image for (−3,−5) under the translation (x,y)→(x+3, y−4)

To determine

(c)

To find:

The coordinate of the image for (h,k) under the translation (x,y)→(x+3, y−4)

Answer 6

Chapter 14.1B, Problem 3A

To determine

(a)

To find:

The coordinate of the image for (7,14) under the translation

(x,y)→(x+3, y−4)

Answer 7

Chapter 14.1B, Problem 3A

To determine

(a)

To find:

The coordinate of the image for (7,14) under the translation

(x,y)→(x+3, y−4)

Answer 8

To determine

(b)

To find:

The coordinate of the image for (−3,−5) under the translation (x,y)→(x+3, y−4)

Answer 9

To determine

(b)

To find:

The coordinate of the image for (−3,−5) under the translation (x,y)→(x+3, y−4)

Answer 10

To determine

(c)

To find:

The coordinate of the image for (h,k) under the translation (x,y)→(x+3, y−4)

Answer 11

To determine

(c)

To find:

The coordinate of the image for (h,k) under the translation (x,y)→(x+3, y−4)

Answer 12

Expert Solution & Answer

Answer 13

Expert Solution & Answer

Answer 14

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Answer 15

Ch. 14.1 - Prob. 1MC Ch. 14.1 - Prob. 3MC Ch. 14.1 - Prob. 5MC Ch. 14.1 - Prob. 6MC Ch. 14.1 - Prob. 7MC Ch. 14.1 - A drawing of a cube, shown in the following...Ch. 14.1 - Wall stenciling has been used to obtain an effect...Ch. 14.1 - Prob. 10MC Ch. 14.1 - The following figure is a partial tessellation of...Ch. 14.1 - Prob. 12MC

(a) To find: The coordinate of the image for ( 7 , 14 ) under the translation ( x , y ) → ( x + 3 , y − 4 )

Solution Summary: The author explains that the coordinate of the image for (7,14) under the given translation is

Concept explainers

Videos

(a)

To find:

The coordinate of the image for (7,14) under the translation

(x,y)→(x+3, y−4)

(b)

To find:

The coordinate of the image for (−3,−5) under the translation (x,y)→(x+3, y−4)

(c)

To find:

The coordinate of the image for (h,k) under the translation (x,y)→(x+3, y−4)

Want to see the full answer?

Chapter 14 Solutions

(a) To find: The coordinate of the image for ( 7 , 14 ) under the translation ( x , y ) → ( x + 3 , y − 4 )

Solution Summary: The author explains that the coordinate of the image for (7,14) under the given translation is

Concept explainers

Videos

(a) To find: The coordinate of the image for (7,14) under the translation (x,y)→(x+3, y−4)

(b) To find: The coordinate of the image for (−3,−5) under the translation (x,y)→(x+3, y−4)

(c) To find: The coordinate of the image for (h,k) under the translation (x,y)→(x+3, y−4)

Want to see the full answer?

Chapter 14 Solutions

(a)

To find:

The coordinate of the image for (7,14) under the translation

(x,y)→(x+3, y−4)

(b)

To find:

The coordinate of the image for (−3,−5) under the translation (x,y)→(x+3, y−4)

(c)

To find:

The coordinate of the image for (h,k) under the translation (x,y)→(x+3, y−4)