Identify a sequence of transformation that maps triangle ABC onto A"B"C" in the image below.
A. Clockwise 270 degrees rotation; reflection over the X-axis
B. Counterclockwise 90 degrees rotation; reduction
C. Counterclockwise 270 degrees rotation; reflection over the Y-axis
D. Enlargement; clockwise 90 degrees rotation

Answer:

The length of Side RT of the polygon is [tex]7\ units[/tex]

Step-by-step explanation:

we know that

the formula to calculate the distance between two points is equal to

[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]

we have

[tex]R(-6,2)\\T(1,2)[/tex]  

substitute the values

[tex]d=\sqrt{(2-2)^{2}+(1+6)^{2}}[/tex]

[tex]d=\sqrt{(0)^{2}+(7)^{2}}[/tex]

[tex]dRT=7\ units[/tex]

Answer:

The answer is:  B,C,D

Step-by-step explanation:

16 square yards

16 yards2

16 sq. yards

Answer:

C

Step-by-step explanation:

The total number of different variable names possible is approximately 2,096,883,896,418.

To calculate the number of possible variable names, we need to consider the constraints on the variable names:

1. The first character must be one of the 26 letters.

2. Each subsequent character can be either one of the 26 letters or one of the 10 digits, totaling 36 possible characters (26 letters + 10 digits).

We need to consider variable names of lengths from 1 to 8 characters. We'll calculate the number of possible variable names for each length and then sum them.

1. For a 1-character name:

  - There are 26 possible names (one for each letter).

2. For a 2-character name:

  - The first character has 26 options.

  - The second character has 36 options.

  - Total for 2 characters: [tex]\(26 \times 36\)[/tex].

3. For a 3-character name:

  - The first character has 26 options.

  - Each of the second and third characters has 36 options.

  - Total for 3 characters: [tex]\(26 \times 36 \times 36\)[/tex].

4. For a 4-character name:

  - The first character has 26 options.

  - Each of the second, third, and fourth characters has 36 options.

  - Total for 4 characters: [tex]\(26 \times 36 \times 36 \times 36\)[/tex].

5. For a 5-character name:

  - The first character has 26 options.

  - Each of the second, third, fourth, and fifth characters has 36 options.

  - Total for 5 characters: [tex]\(26 \times 36 \times 36 \times 36 \times 36\)[/tex].

6. For a 6-character name:

  - The first character has 26 options.

  - Each of the second, third, fourth, fifth, and sixth characters has 36 options.

  - Total for 6 characters: [tex]\(26 \times 36 \times 36 \times 36 \times 36 \times 36\)[/tex].

7. For a 7-character name:

  - The first character has 26 options.

  - Each of the second, third, fourth, fifth, sixth, and seventh characters has 36 options.

  - Total for 7 characters: [tex]\(26 \times 36 \times 36 \times 36 \times 36 \times 36 \times 36\)[/tex].

8. For an 8-character name:

  - The first character has 26 options.

  - Each of the second, third, fourth, fifth, sixth, seventh, and eighth characters has 36 options.

  - Total for 8 characters: [tex]\(26 \times 36 \times 36 \times 36 \times 36 \times 36 \times 36 \times 36\)[/tex].

Now we sum these values to get the total number of possible variable names:

[tex]\[\begin{aligned} \text{Total} = & \ 26 + 26 \times 36 + 26 \times 36^2 + 26 \times 36^3 \\ & + 26 \times 36^4 + 26 \times 36^5 + 26 \times 36^6 + 26 \times 36^7\end{aligned}\][/tex]

Calculating each term separately and summing them:

[tex]\[\begin{aligned} & 26 = 26 \\ & 26 \times 36 = 936 \\ & 26 \times 36^2 = 33,696 \\ & 26 \times 36^3 = 1,213,056 \\ & 26 \times 36^4 = 43,669,056 \\ & 26 \times 36^5 = 1,572,085,056 \\ & 26 \times 36^6 = 56,595,062,016 \\ & 26 \times 36^7 = 2,038,722,232,576\end{aligned}\][/tex]

Summing these:

[tex]\[\begin{aligned} \text{Total} = & 26 + 936 + 33,696 + 1,213,056 + 43,669,056 \\ & + 1,572,085,056 + 56,595,062,016 + 2,038,722,232,576 \\ \approx & 2,096,883,896,418\end{aligned}\][/tex]

The value of the variables u, v, w, y, and z will be 6.2 yards, 7.9 yards, 52°, 38°, and 10 yards, respectively.

The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.

The ratio of the matching sides will remain constant if two triangles are comparable to one another.

The two triangle-shaped gardens are congruent. Then the corresponding side will be equal. Then we have

u = 6.2 yards

v = 7.9 yards

y = 38°

w + y = 90°

w + 38° = 90°

w = 52°

z = 10 yards

The value of the variables u, v, w, y, and z will be 6.2 yards, 7.9 yards, 52°, 38°, and 10 yards, respectively.

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Answer: B

Step-by-step explanation:

The solution is Option B.

The volume of the triangular prism is given by the equation V = 432 feet³

A three-dimensional solid object called a prism has two identical ends. It consists of equal cross-sections, flat faces, and identical bases. Without bases, the prism's faces are parallelograms or rectangles.

The volume of a prism is the product of its base area and height

Volume of Prism = B x h

where B = base area of prism

h = height of prism

Given data ,

Let the volume of the prism be represented as V

Now , the equation will be

Let the base area of the prism be B

Let the height of the prism be h = 2 feet

Now , the length of the prism L = 18 feet

The width of the prism W = 12 feet

So , the base area B = L x W

Substituting the values in the equation , we get

The base area of the prism B = 216 feet²

So , Volume of Prism = B x h

Substituting the values in the equation , we get

Volume of Prism V = 216 x 2 feet³

Volume of Prism V = 432 feet³

Hence , the volume of prism is 432 feet³

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The Probability of that 'j' will not be selected by Amanda in  Fraction is [tex]\frac{7}{8}[/tex]

The Probability of that 'j' will not be selected by Amanda in  Decimal is 0.875

The Probability of that 'j' will not be selected by Amanda in  Percentage is 87.5%

What is Probability ?

Probability is a "Possibility, that deals with a Occurrence of Random event".

According to the question,

Sample Space n(s) = 8

Number of Favourable Events (Amanda will not be Select 'j' letter) = 7.

Formula to find Probability of an event = [tex]\frac{Number of Favourable Events }{Total number of events}[/tex]

=[tex]\frac{7}{8}[/tex]

The  Probability of Amanda will not be Select 'j' letter = [tex]\frac{7}{8}[/tex]

Hence,

In Fraction, the Probability of Amanda will not be Select 'j' letter =[tex]\frac{7}{8}[/tex]

In Decimal, the Probability of Amanda will not be Select 'j' letter = 0.875

In Percentage, the cof Amanda will not be Select 'j' letter

= [tex]\frac{7}{8}[/tex] × 100 = 87.5%.

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It takes, 2, minutes to prepare one bag. If Ashley works alone, it will take her 900 bags× 2 minutes each =1800 minutes to prepare the bags.

Since there are 60 minutes in an hour, that's the same as 1800/60 which equals to 30 hours. If there are 6 people sharing Ashley's work Ashley + 5 friends the work will be finished 6 times as fast.

A team of 6 people can finish the job 30/6 which equals 5