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Galina-37 [17]
3 years ago
7

Segment Y prime Z prime has endpoints located at Y'(0, 3) and Z'(−6, 3). segment YZ was dilated at a scale factor of 3 from the

origin. Which statement describes the pre-image?
A. segment YZ is located at Y (0, 9) and Z (−18, 9) and is three times the size of segment Y prime Z prime.
B. segment YZ is located at Y (0, 3) and Z (−6, 3) and is the same size as segment Y prime Z prime.
C. segment YZ is located at Y (0, 1.5) and Z (−3, 1.5) and is the one-half the size of segment Y prime Z prime.
D. segment YZ is located at Y (0, 1) and Z (−2, 1) and is one-third the size of segment Y prime Z prime.

Mathematics
1 answer:
Klio2033 [76]3 years ago
5 0

Answer:

D. Segment YZ is located at Y(0,1) and Z(−2,1) and is one-third the size of segment Y'Z'

Step-by-step explanation:

When you dilate a point by a factor of x from the origin, you multiply its coordinates by the same factor.

Thus, if the coordinates of the original point are (1,2) and the scale factor is 3, those of its image are (3,6).

If Y'Z' has endpoints at Y'(0,3) and Z'(-6,3) and was dilated by a factor of 3, the coordinates of the endpoints of the pre-image were ⅓ those of the image.

The figure below shows the segments YZ and Y'Z'.

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Let $f$ be a function such that $f(x+y) = x + f(y)$ for any two real numbers $x$ and $y$. if $f(0) = 2$, then what is $f(2012)?$
marusya05 [52]

<span>Given:

f(0) = 2</span>

So first of all, we let x = 2012, y = 0: 

<span>
Then, F(2012) = 2012 + f(0)

Since f(0) = 2, then f(2012) = 2012 + 2 = 2014.

To add, </span>the process that relates an input to an output is called a function.

 

 

<span>There are always three main parts of a function, namely:

</span>Input

The Relationship

The Output

 

The classic way of writing a function is "f(x) = ... ".

 

What goes into the function is put inside parentheses () after the name of the function: So, f(x) shows us the function is called "f", and "x" goes in.

 

 

What a function does with the input can be usually seen as:

 

<span>f(x) = x2</span><span> reveals to us that function "f" takes "x<span>" and squares it.</span></span>

3 0
3 years ago
The object below was made by placing a cone on top of a cylinder. The base of the cone is congruent to the base of the cylinder.
Ber [7]

Answer:

Part 1) The volume of the object is 32\pi\ cm^{3}  or 100.48\ cm^{3}

Part 2) see the procedure

Step-by-step explanation:

<u><em>The picture of the question in the attached figure</em></u>

Part 1)  What is the volume, in cubic centimeters, of the object?

we know that

The volume of the object is equal to the volume of the cylinder plus the volume of the cone

Find the volume of the cone

The volume of the cone is equal to

V=\frac{1}{3}\pi r^{2} h

we have

r=4/2=2\ cm -----> the radius is half the diameter

h=3\ cm

substitute the values

V=\frac{1}{3}\pi (2^{2})(3)=4\pi\ cm^{3}

Find the volume of the cylinder

The volume of the cylinder is equal to

V=\pi r^{2} h

we have

r=4/2=2\ cm -----> the radius is half the diameter

h=(10-3)=7\ cm

substitute the values

V=\pi (2^{2})(7)=28\pi\ cm^{3}

Part 2) Then explain how you found the volume of the total shape

The volume of the total shape is equal to the volume of the cylinder plus the volume of the cone

4\pi\ cm^{3}+28\pi\ cm^{3}=32\pi\ cm^{3} ------> exact value

Find the approximate value of the volume

assume

\pi=3.14

32(3.14)=100.48\ cm^{3}

7 0
3 years ago
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Katena32 [7]

Answer:

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8 0
2 years ago
5 + 1.3 • 8.7? whats the answer?
Elan Coil [88]

Answer:

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Step-by-step explanation:

8 0
2 years ago
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A different species of cockroach has weights that are approximately Normally distributed with a mean of 50 grams. After measurin
Ratling [72]

Answer:

The standard deviation of weight for this species of cockroaches is 4.62.

Step-by-step explanation:

Given : A different species of cockroach has weights that are approximately Normally distributed with a mean of 50 grams. After measuring the weights of many of these cockroaches, a lab assistant reports that 14% of the cockroaches weigh more than 55 grams.

To find : What is the approximate standard deviation of weight for this species of cockroaches?

Solution :

We have given,

Mean \mu=50

The sample mean x=55

A lab assistant reports that 14% of the cockroaches weigh more than 55 grams.

i.e. P(X>55)=14%=0.14

The total probability needs to sum up to 1,

P(X\leq 55)=1-P(X>55)

P(X\leq 55)=1-0.14

P(X\leq 55)=0.86

The z-score value of 0.86 using z-score table is z=1.08.

Applying z-score formula,

z=\frac{x-\mu}{\sigma}

Where, \sigma is standard deviation

Substitute the values,

z=\frac{x-\mu}{\sigma}

1.08=\frac{55-50}{\sigma}

1.08=\frac{5}{\sigma}

\sigma=\frac{5}{1.08}

\sigma=4.62

The standard deviation of weight for this species of cockroaches is 4.62.

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3 years ago
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