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2 years ago

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Dalia is performing transformations on the preimage of a triangle in the coordinate plane. She shifts and the spins the triangle

. Which names the transformations she performed, in order?
rotation, reflection
translation, reflection
translation, rotation
reflection, rotation

1 answer:

Zielflug [23.3K]2 years ago

6 0

Answer:

translation, rotation

Step-by-step explanation:

A translation is sliding around or moving around/shifting so the first one is translation. A rotation is spinning it around to a different angle so the second is a rotation. Hope this helps!!

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The first, third and thirteenth terms of an arithmetic sequence are the first 3 terms of a geometric sequence. If the first term

Salsk061 [2.6K]

Answer:

The first three terms of the geometry sequence would be $1$ , $5$ , and $25$ .

The sum of the first seven terms of the geometric sequence would be $127$ .

Step-by-step explanation:

<h3>1.</h3>

Let $d$ denote the common difference of the arithmetic sequence.

Let $a_1$ denote the first term of the arithmetic sequence. The expression for the $n$ th term of this sequence (where $n\!$ is a positive whole number) would be $(a_1 + (n - 1)\, d)$ .

The question states that the first term of this arithmetic sequence is $a_1 = 1$ . Hence:

The third term of this arithmetic sequence would be $a_1 + (3 - 1)\, d = 1 + 2\, d$ .
The thirteenth term of would be $a_1 + (13 - 1)\, d = 1 + 12\, d$ .

The common ratio of a geometric sequence is ratio between consecutive terms of that sequence. Let $r$ denote the ratio of the geometric sequence in this question.

Ratio between the second term and the first term of the geometric sequence:

$\displaystyle r = \frac{1 + 2\, d}{1} = 1 + 2\, d$ .

Ratio between the third term and the second term of the geometric sequence:

$\displaystyle r = \frac{1 + 12\, d}{1 + 2\, d}$ .

Both $(1 + 2\, d)$ and $\left(\displaystyle \frac{1 + 12\, d}{1 + 2\, d}\right)$ are expressions for $r$ , the common ratio of this geometric sequence. Hence, equate these two expressions and solve for $d$ , the common difference of this arithmetic sequence.

$\displaystyle 1 + 2\, d = \frac{1 + 12\, d}{1 + 2\, d}$ .

$(1 + 2\, d)^{2} = 1 + 12\, d$ .

$d = 2$ .

Hence, the first term, the third term, and the thirteenth term of the arithmetic sequence would be $1$ , $(1 + (3 - 1) \times 2) = 5$ , and $(1 + (13 - 1) \times 2) = 25$ , respectively.

These three terms ( $1$ , $5$ , and $25$ , respectively) would correspond to the first three terms of the geometric sequence. Hence, the common ratio of this geometric sequence would be $r = 25 /5 = 5$ .

<h3>2.</h3>

Let $a_1$ and $r$ denote the first term and the common ratio of a geometric sequence. The sum of the first $n$ terms would be:

$\displaystyle \frac{a_1 \, \left(1 - r^{n}\right)}{1 - r}$ .

For the geometric sequence in this question, $a_1 = 1$ and $r = 25 / 5 = 5$ .

Hence, the sum of the first $n = 7$ terms of this geometric sequence would be:

$\begin{aligned} & \frac{a_1 \, \left(1 - r^{n}\right)}{1 - r}\\ &= \frac{1 \times \left(1 - 2^{7}\right)}{1 - 2} \\ &= \frac{(1 - 128)}{(-1)} = 127 \end{aligned}$ .

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2 years ago

Whats is 51,487 rounded to the nearest thousands?

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50,000 is the answer to the question

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The two dot plots below show the heights of some sixth graders and some seventh graders:

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2.0 because if you divide 1.2 by 0.6 it equals 2.0

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Plz I need help with geometry homework FIND THE ANGLES

Talja [164]

Answer:

a = 36°
b = 36°
c = 72°
d = 72°
e = 108°
f = 16°
g = 74°
h = 70°

Step-by-step explanation:

You are expected to know and make use of the following relations:

vertical angles are congruent
angles of a linear pair are supplementary
angles of a triangle sum to 180°
alternate interior angles are congruent (at parallel lines)
corresponding angles are congruent (at parallel lines)
acute angles of a right triangle are complementary
base angles of an isosceles triangle are congruent

__

For this problem, it isn't always easiest to work the questions in order. It is best to start with the angles easiest to find from those given.

b and 144° are a linear pair, so b = 180° -144° = 36°

a and b are alternate interior angles, so a = b = 36°

2d and 144° are corresponding angles, so d = 144°/2 = 72°

e is the apex angle of an isosceles triangle with base angles 36°, so is 180° -2(36°) = 108° = e

f and 164° are a linear pair, so f = 180° -164° = 16°

g and f are complementary, so g = 90° -16° = 74°

g+h is a vertical angle with 144°, so is congruent to that. h = 144° -74° = 70°

c is the base angle of an isosceles triangle with b as the vertex angle. That means c = (180° -36°)/2 = 72°

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The answer is 90.
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