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3 years ago

Which statements are true about reflections? Check all that apply.

Mathematics

1 answer:

maria [59]3 years ago

7 0

Answer:

A, B, C, D, F

Step-by-step explanation:

A. An image created by a reflection will always be congruent to its pre-image.

Congruent means identical or similar. The orientation, size, and shape of the pre-image are not changed after a reflection- therefore, the pre-image and image are congruent.

B. An image and its pre-image are always the same distance from the line of reflection.

When a pre-image is flipped across the line of reflection, both figures are perfectly symmetrical. Nothing has changed aside from orientation and location on the graph. The number of units between the figures and the line of reflection should remain unchanged.

C. If a point on the pre-image lies on the line of reflection, the image of that point is the same as the pre-image.

When you reflect a pre-image with a point that lies on the line of reflection, that point will stay on the line of the reflection as the rest of the figure is flipped.

I will explain these two answers together since they have similar explanations.

D. The line of reflection is perpendicular to the line segments connecting corresponding vertices.

F. The line segments connecting corresponding vertices are all parallel to each other.

In a reflection, the horizontal or vertical (depending on the line of reflection, y-axis or x-axis) coordinates are altered. However, if one were to draw an imaginary line connecting the corresponding vertices, both the image and pre-image are parallel and perpendicular.

I hope this helped, good luck on your work/test!

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The current population of a town is 10,000 and its growth in years can be represented by P(t) = 10,000(0.2)^t, where t is the ti

DiKsa [7]

Answer:

1) 20%

2) Choice a.

Step-by-step explanation:

$P(t)=10000(0.2)^t$

1) $P(0)$ is the population initially.

$P(1)$ is the population after a year.

$\frac{P(1)}{P(0)}$ represents the population increase factor.

So let's evaluate that fraction:

$\frac{P(1)}{P(0)}$

$\frac{10000(0.2)^1}{10000(0.2)^0}$

$\frac{0.2^1}{0.2^0}=\frac{0.2}{1}=0.2$

0.2=20%

2) Let's figure out the population growth in terms of months instead of years.

$P(t)=10000(0.2)^{t}$

We want t to represent months.

A full year is 12 months, in a full year we have that $P(1)=10000(0.2)^1=10000(0.2)=2000$

So we want a new P such that $P(12)=2000$ since 12 months equals a year.

Let's look at the functions given to see which gives us this:

a) $P(12)=10000(0.87449)^{12}=2000 \text{approximately}$

b) $P(12)=10000(0.87449)^{12(12)}=0 \text{ approximately}$

c) $P(12)=10000(0.87449)^{\frac{1}{12}}=9889 \text{approximately}$

d) $P(12)=10000(0.87449)^{12+12}=400 \text{approximately}$

So a is the function we want.

Also another way to look at this:

$P(t)=10000(.2)^t$ where $t$ is in years.

$P(t)=10000(.2^\frac{1}{12})^t$ where $t$ is in months.

And $.2^\frac{1}{12}=0.874485 \text{approximately}$

8 0

3 years ago

What’s 7(c+2) if c=9

ddd [48]

Answer:

Step-by-step explanation:

3 0

3 years ago

Read 2 more answers

Name the points which satisfy the conditions. The ordinate is zero.

sveticcg [70]

9514 1404 393

Answer:

Step-by-step explanation:

The one point with a y-value of 0 is the one on the x-axis: G.

4 0

3 years ago

The mathematics department of a college has 6 male professors, 9 female professors, 5 male teaching assistants, and 6 female tea

Hitman42 [59]

Given:

6 male professores

9 female professores

5 male teaching assistants

6 female teaching assistants

Sol:.

$N(A\text{ or B)=N(A)+N(B)-N(A and B)}$

N (professors)

$\begin{gathered} =6+9 \\ =15 \end{gathered}$

N(Male)

$\begin{gathered} =6+5 \\ =11 \end{gathered}$

N(professors and male)

$=6$

N(professors OR male) = N(professors) + N(males) -N(professor OR male)

$\begin{gathered} N(\text{ Professors OR male)=15+11-6} \\ =20 \end{gathered}$

N(People to choose from)

$\begin{gathered} =6+9+5+6 \\ =26 \end{gathered}$

Then probablitiy is:

$\begin{gathered} =\frac{20}{26} \\ =\frac{10}{13} \end{gathered}$

Then the probability is 10/13

6 0

1 year ago

Compare the exponential functions f, g, and h which are shown below.

Nostrana [21]

Hello,
Please, see the detailed answer in the attached files.
Thanks.

5 0

3 years ago