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3 years ago

Choose the following rule that CORRECTLY describes a dilation :

Mathematics

1 answer:

kkurt [141]3 years ago

4 0

I believe that answer choice D is correct, I know it is not C, A or D unless your teacher made a mistake presenting answer C. Hope this helps.

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Jacob the dog eats dry food that contains 324kcal/cup. Jacob eats 3.5 cups a day. The food contains 3.6 g of fat in 100 kcals of

PtichkaEL [24]

Answer:

His daily fat intake is 40.824g.

His daily Vitamin D intake is 290.304 IU.

Step-by-step explanation:

The first step to solve this problem is finding the daily kcal intake of the dogs.

Each cup has 324 kcal, and he eats 3.5cups a day. So:

1 cup - 324 kcals

3.5 cups - x kcals

$x = 324*3.5$

$x = 1134$ kcals.

His daily intake is of 1134 kcals.

The food contains 3.6 g of fat in 100 kcals of energy. what is his daily fat intake?

There are 3.6g of fat in 100 kcals of energy. How many g of fat are there in 1134 kcals?

3.6g - 100 kcals

xg - 1134 kcal

$100x = 1134*3.6$

$x = \frac{1134*3.6}{100}$

$x = 11.34*3.6$

$x = 40.824$ g

His daily fat intake is 40.824g.

The food contains 25.6 IU of Vitamin D3 in 100 kcals of energy. what is his daily Vitamin D inake?

Similar logic as above.

25.6IU - 100 kcals

x IU - 1134 kcal

$100x = 1134*25.6$

$x = \frac{1134*25.6}{100}$

$x = 11.34*25.6$

$x = 290.304$ IU

His daily Vitamin D intake is 290.304 IU.

7 0

3 years ago

For any real number r, which of the following must be greater than r?

adelina 88 [10]

C) r^2 + 1 because any number squared (positive or negative) will be positive

6 0

4 years ago

How does an individual affect the society

finlep [7]

Answer:

When a individual tries and modifies their bodies away from the knowledge of the society, it makes no difference. However, when individual tries to modify the society by habits and behavior, it creates a social impact.

Step-by-step explanation:

Hope it helps :)

3 0

3 years ago

Read 2 more answers

Determine the value of e.

Softa [21]

9514 1404 393

Answer:

A) 16

Step-by-step explanation:

The ratio of long-side to short-side is the same for all of these similar triangles, so we have ...

e/8 = 8/4

e = 8(8/4) = 8(2) = 16

The value of e is 16.

7 0

3 years ago

Let an = –3an-1 + 10an-2 with initial conditions a1 = 29 and a2 = –47. a) Write the first 5 terms of the recurrence relation. b)

zlopas [31]

We can express the recurrence,

$\begin{cases}a_1=29\\a_2=-47\\a_n=-3a_{n-1}+10a_{n-2}7\text{for }n\ge3\end{cases}$

in matrix form as

$\begin{bmatrix}a_n\\a_{n-1}\end{bmatrix}=\begin{bmatrix}-3&10\\1&0\end{bmatrix}\begin{bmatrix}a_{n-1}\\a_{n-2}\end{bmatrix}$

By substitution,

$\begin{bmatrix}a_{n-1}\\a_{n-2}\end{bmatrix}=\begin{bmatrix}-3&10\\1&0\end{bmatrix}\begin{bmatrix}a_{n-2}\\a_{n-3}\end{bmatrix}\implies\begin{bmatrix}a_n\\a_{n-1}\end{bmatrix}=\begin{bmatrix}-3&10\\1&0\end{bmatrix}^2\begin{bmatrix}a_{n-2}\\a_{n-3}\end{bmatrix}$

and continuing in this way we would find that

$\begin{bmatrix}a_n\\a_{n-1}\end{bmatrix}=\begin{bmatrix}-3&10\\1&0\end{bmatrix}^{n-2}\begin{bmatrix}a_2\\a_1\end{bmatrix}$

Diagonalizing the coefficient matrix gives us

$\begin{bmatrix}-3&10\\1&0\end{bmatrix}=\begin{bmatrix}-5&2\\1&1\end{bmatrix}\begin{bmatrix}-5&0\\0&2\end{bmatrix}\begin{bmatrix}-5&2\\1&1\end{bmatrix}^{-1}$

which makes taking the $(n-2)$ -th power trivial:

$\begin{bmatrix}-3&10\\1&0\end{bmatrix}^{n-2}=\begin{bmatrix}-5&2\\1&1\end{bmatrix}\begin{bmatrix}-5&0\\0&2\end{bmatrix}^{n-2}\begin{bmatrix}-5&2\\1&1\end{bmatrix}^{-1}$

$\begin{bmatrix}-3&10\\1&0\end{bmatrix}^{n-2}=\begin{bmatrix}-5&2\\1&1\end{bmatrix}\begin{bmatrix}(-5)^{n-2}&0\\0&2^{n-2}\end{bmatrix}\begin{bmatrix}-5&2\\1&1\end{bmatrix}^{-1}$

So we have

$\begin{bmatrix}a_n\\a_{n-1}\end{bmatrix}=\begin{bmatrix}-5&2\\1&1\end{bmatrix}\begin{bmatrix}(-5)^{n-2}&0\\0&2^{n-2}\end{bmatrix}\begin{bmatrix}-5&2\\1&1\end{bmatrix}^{-1}\begin{bmatrix}a_2\\a_1\end{bmatrix}$

and in particular,

$a_n=\dfrac{29\left(2(-5)^{n-1}+5\cdot2^{n-1}\right)-47\left(-(-5)^{n-1}+2^{n-1}\right)}7$

$a_n=\dfrac{105(-5)^{n-1}+98\cdot2^{n-1}}7$

$a_n=15(-5)^{n-1}+14\cdot2^{n-1}$

$\boxed{a_n=-3(-5)^n+7\cdot2^n}$

6 0

3 years ago