Which statement must be true ?

Segment FG begins at point F(-2, 4) and ends at point G(-2, -3). The segment is translated 3 units left and 2 units up, then ref

Alexus [3.1K]

Answer:

$F'G' = 7$

Step-by-step explanation:

Given

$F = (-2,4)$

$G = (-2,-3)$

Required

Distance of F'G'

The transformation that give rise to F'G' from FG are:

Translation
Reflection

The above transformations are referred to as rigid transformation, and as such the side lengths remain unchanged.

i.e.

$F'G' = FG$

Calculating FG, we have:

$FG = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}$

Where:

$F = (-2,4)$ --- $(x_1,y_1)$

$G = (-2,-3)$ --- $(x_2,y_2)$

$FG = \sqrt{(-2 - -2)^2 + (4 - -3)^2}$

$FG = \sqrt{(0)^2 + (7)^2}$

$FG = \sqrt{0 + 49}$

$FG = \sqrt{49}$

Take positive square root

$FG = 7$

Recall that:

$F'G' = FG$

$F'G' = 7$

6 0

3 years ago

Find the distance between (-8, 4) and (-8, -2).<br>10 units<br>2 units<br>6 units<br>8 units

svp [43]

Answer:

10

Step-by-step explanation:

6 0

4 years ago

2. Check the boxes for the following sets that are closed under the given

son4ous [18]

The properties of the mathematical sequence allow us to find that the recurrence term is 1 and the operation for each sequence is

a) Subtraction

b) Addition

c) AdditionSum

d) in this case we have two possibilities

* If we move to the right the addition

* If we move to the left the subtraction

The sequence is a set of elements arranged one after another related by some mathematical relationship. The elements of the sequence are called terms.

The sequences shown can be defined by recurrence relations.

Let's analyze each sequence shown, the ellipsis indicates where the sequence advances.

a) ... -7, -6, -5, -4, -3

We can observe that each term has a difference of one unit; if we subtract 1 from the term to the right, we obtain the following term

-3 -1 = -4

-4 -1 = -5

-7 -1 = -8

Therefore the mathematical operation is the subtraction.

b) $0. \sqrt{1}. \sqrt{4}, \sqrt{9}, \sqrt{16}, \sqrt{25}$ ...

In this case we can see more clearly the sequence when writing in this way

$0, \sqrt{1^2}. \sqrt{2^2}, \sqrt{3^2 } . \sqrt{4^2} , \sqrt{5^2}$

each term is found by adding 1 to the current term,

$\sqrt{(0+1)^2} = \sqrt{1^2} \\\sqrt{(1+1)^2} = \sqrt{2^2}\\\sqrt{(2+1)^2} = \sqrt{3^2}\\\sqrt{(5+1)^2} = \sqrt{6^2}$

Therefore the mathematical operation is the addition

c) $... \frac{-10}{2}. \frac{-8}{2}, \frac{-6}{2}, \frac{-4}{2}. \frac{-2}{2}. ...$

The recurrence term is unity, with the fact that the sequence extends to the right and to the left the operation is

To move to the right add 1

- $\frac{-10}{2} + 1 = \frac{-10}{2} - \frac{2}{2} = \frac{-8}{2}\\\frac{-8}{2} + \frac{2}{2} = \frac{-6}{2}$

To move left subtract 1

$\frac{-2}{2} - 1 = \frac{-4}{2}\\\frac{-4}{2} - \frac{2}{2} = \frac{-6}{2}$

Using the properties the mathematical sequence we find that the recurrence term is 1 and the operation for each sequence is

a) Subtraction

b) Sum

c) Sum

d) This case we have two possibilities

If we move to the right the sum

If we move to the left we subtract

Learn more here: brainly.com/question/4626313

5 0

3 years ago

Maria walked 3 km west and 4 km south calculate how far she is from her starting point.

Rufina [12.5K]

Answer:

5 km

Step-by-step explanation:

We are given the distances walked by Maria;

3 km west and 4 km south

We are required to determine the displacement from her starting point;

We are going to use Pythagoras's theorem;

a² + b² = c²

Taking, the distances towards south and towards west as the legs of the triangle;

Then, c² = 3² + 4²

= 25

c = √25

= 5 km

Therefore, the displacement from the starting point is 5 km

8 0

3 years ago

2. Consider the following dot plot and answer the following questions : A. Find the measures of central tendency Construct the B

zubka84 [21]

The measures of central tendency for this data set are as follows:

Mean = 3.55.
Median = 3.5.
Mode = 3.

<h3>How to calculate measures of central tendency?</h3>

In Mathematics, there are three (3) main measures of central tendency and these include the following:

Mean

Median

Mode

For the mean, we have:

Mathematically, the mean for this data set would be calculated by using this formula:

Mean = [F(x)]/n

For the total number of data, we have:

F(x) = 0 + 1 + 1 + 1 + 2 + 2 + 3 + 3 + 3 + 3 + 4 + 4 + 4 + 5 + 5 + 5 + 6 + 6 + 6 + 7

F(x) = 71

Substituting the parameters into the formula, we have:

Mean = [F(x)]/n

Mean = 71/20

Mean = 3.55.

For the median, we have:

First of all, we would order the data from lowest to highest and then determine the median as follows:

Data = {0, 1, 1, 1, 2, 2, 3, 3, 3,} 3, 4, {4, 4, 5, 5, 5, 6, 6, 6, 7}

Median = {3 + 4}/2

Median = 7/2

Median = 3.5.

<h3>How to calculate the mode?</h3>

A mode refers to the most frequently occurring number in a data set. Thus, the mode for this data set is equal to 3.

In conclusion, a box plot of the measures of central tendency for this data set is shown in the image attached below.

Read more on mean here: brainly.com/question/9550536

#SPJ1

6 0

2 years ago