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djverab [1.8K]
2 years ago
9

Figure 1 and figure 2 are two congruent parallelograms drawn on a coordinate grid as shown below:

Mathematics
1 answer:
LenKa [72]2 years ago
7 0

Answer:

  (a)  Reflection across the y-axis, followed by translation 10 units down

Step-by-step explanation:

Figure 2 is not a reflection across the origin of Figure 1, so neither of the double reflections will map one to the other.

Reflection across the y-axis will put the bottom point at (5, 3). The bottom point on Figure 2 is at (5, -7), so has been translated down by 3-(-7) = 10 units.

Figure 1 is mapped to Figure 2 by reflection over the y-axis and translation down 10 units.

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Write an equation for the nth term of the arithmetic sequence. Then find a40.
Olegator [25]

Answer:

The nth term is: a_n = \frac{1}{4} + \frac{1}{4}(n-1)

a40 = 10

Step-by-step explanation:

Arithmetic sequence:

In an arithmetic sequence, the difference between consecutive terms is always the same, and this difference is called common difference.

The nth term of a sequence is given by:

a_n = a_1 + (n-1)d

In which a_1 is the first term and d is the common difference.

1/4,1/2

This means that:

d = \frac{1}{2} - \frac{1}{4} = \frac{2}{4} - \frac{1}{4} = \frac{1}{4}

1/4

This means that a_1 = \frac{1}{4}

The nth term is:

a_n = a_1 + (n-1)d

a_n = \frac{1}{4} + \frac{1}{4}(n-1)

Then find a40.

a_{40} = \frac{1}{4} + \frac{1}{4}(40-1) = \frac{1}{4} + \frac{39}{4} = \frac{40}{4} = 10

So

a40 = 10

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Step-by-step explanation:

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