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labwork [276]
3 years ago
6

translate triangle A by vector (-3,1) to give triangle B. Then roste your triangle B 180 degrees around the origin to give trian

gle C. Describe fully the single transformation that maps triangle A onto triangle C

Mathematics
1 answer:
Strike441 [17]3 years ago
8 0

Answer:

<h3>From A to B.</h3>

The first transformation is a reflection across the x-axis, then a shift one unit down. Finally, a reflection acroos the line x = 1.5. These transformations give figure B.

<h3>From B to C.</h3>

To get figure C, we just need to do a 180° rotation across the origin. Or, you can see this transformation as a reflection acroos the origin, it would be the same result.

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Please answer and explain the link below
Leviafan [203]

Answer:

See explanation.

General Formulas and Concepts:

<u>Pre-Algebra</u>

Order of Operations: BPEMDAS

  1. Brackets
  2. Parenthesis
  3. Exponents
  4. Multiplication
  5. Division
  6. Addition
  7. Subtraction
  • Left to Right

<u>Algebra I</u>

  • Functions
  • Function Notation

<u>Calculus</u>

Limits

  • Right-Side Limit:                                                                                             \displaystyle  \lim_{x \to c^+} f(x)
  • Left-Side Limit:                                                                                               \displaystyle  \lim_{x \to c^-} f(x)

Limit Rule [Variable Direct Substitution]:                                                             \displaystyle \lim_{x \to c} x = c

Step-by-step explanation:

<u>Step 1: Define</u>

<em>Identify</em>

\displaystyle f(x) = \left \{ {{\sqrt{x + 1}, \ x < 3} \atop {5 - x, \ x \geq 3}} \right.

<u>Step 2: Find Right Limit</u>

  1. Substitute in variables [Right-Side Limit]:                                                      \displaystyle  \lim_{x \to 3^+} 5 - x
  2. Evaluate limit [Limit Rule - Variable Direct Substitution]:                           \displaystyle  \lim_{x \to 3^+} 5 - x = 5 - 3
  3. Subtract:                                                                                                         \displaystyle  \lim_{x \to 3^+} 5 - x = 2

∴ the right-side limit equals 2.

<u>Step 3: Find Left Limit</u>

  1. Substitute in variables [Left-Side Limit]:                                                       \displaystyle  \lim_{x \to 3^-} \sqrt{x + 1}
  2. Evaluate limit [Limit Rule - Variable Direct Substitution]:                           \displaystyle  \lim_{x \to 3^-} \sqrt{x + 1} = \sqrt{3 + 1}
  3. [√Radical] Add:                                                                                             \displaystyle  \lim_{x \to 3^-} \sqrt{x + 1} = \sqrt{4}
  4. [√Radical] Evaluate:                                                                                       \displaystyle  \lim_{x \to 3^-} \sqrt{x + 1} = 2

∴ the left-side limit equals 2.

<u>Step 4: Find Limit</u>

<em>The right and left-side limits are equal.</em>

∴  \displaystyle  \lim_{x \to 3} f(x) = 2

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Limits

Book: College Calculus 10e

4 0
3 years ago
The height of the doorway is 7 feet less than 5 times its width. if the area is 24 square feet, find the dimensions of the door
blondinia [14]

Answer:

  height: 8 ft

  width: 3 ft

Step-by-step explanation:

You can check your answer against the problem criteria:

  area = (8 ft)(3 ft) = 24 ft^2

  height = -7 +5(3) = -7 +15 = 8 . . . . your height

Your numbers match the requirements.

___

The problem statement asks you to "use polynomials." You have not shown work, so we don't know whether you did. (I like to use a graphing calculator.)

_____

Let x represent the width and y represent the height, both in feet.

  y = -7 +5x . . . . . height is 7 ft less than 5 times width

  xy = 24 . . . . . . . area is 24 square feet

Using the first equation to substitute for y in the second equation, we have ...

  x(-7+5x) = 24

  5x^2 -7x -24 = 0 . . . . . put in standard form (the required polynomial)

  5x^2 -15x +8x -24 = 0 . . . . . facilitate factoring by grouping*

  5x(x -3) +8(x -3) = 0

  (5x +8)(x -3) = 0

The positive solution is x = 3. Then y = 24/3 = 8.

The dimensions are 3 ft wide by 8 ft high.

_____

* To factor this, we look for factors of 5·(-24) = -120 that sum to -7. Those factors are -15 and +8. There are several ways to get to the binomial factors once you have these numbers, but the "factor by grouping" method is the most easily explained.

4 0
4 years ago
The average time before breakdown of a machine is normally distributed and has a mean of 18 weeks and a standard deviation of th
IceJOKER [234]

Answer:

19.24 weeks

Step-by-step explanation:

Given that;

Mean, m = 18

Standard deviation, s = 3

Break down cost = 2000

Preventive maintenance cost = 1400

The optimal preventive maintenance level is Given by :

Mean + service level * standard deviation

Service level = preventive maintenance cost / (breakdown cost + preventive maintenance cost)

Hence,

Service level = 1400/(1400+2000) = 1400 / 3400

Service level = 0.4117647

Optimal preventive maintenance level :

18 + (0.4117647 * 3)

18 + 1.2352941

= 19.235

= 19.24 weeks

8 0
3 years ago
5xy —9cs (-)-3xy + cs simplify
aalyn [17]

Answer:

Step-by-step explanation:

2 • (xy - 4cs)

7 0
4 years ago
What are the missing parts that correctly complete the proof?
kap26 [50]
Point b and point a need to be drawn vertically
5 0
3 years ago
Read 2 more answers
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