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3 years ago

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What is the volume of the rectangular prism? A prism has a length of 5 centimeters, height of 8 and one-half centimeters, and wi

dth of 3 and three-fourths centimeters. 17 and one-fourth cm3 18 and three-fourths cm3 27 and one-fourth cm3 159 and StartFraction 3 Over 8 EndFraction cm3

2 answers:

Luden [163]3 years ago

8 0

Answer:

d

Step-by-step explanation:

nlexa [21]3 years ago

3 0

Answer:

<em>Option D: 159 3/8 cm^3 </em>

Step-by-step explanation:

1. Let us rewrite the dimensions, and the options to make this a little more clear ~ (dimensions) 5 cm, 8 1/2 cm, 3 3/4 cm ⇒ (options) 17 1/4 cm^3, 18 3/4 cm^3, 27 1/4 cm^3, and 159 3/8 cm^3

2. To find the volume of most 3-dimensional figures, you would have to multiply the Base * height, so for a rectagular prism ⇒ <em>Base * height = length * width * height</em>

3. Substitute and compute the volume through algebra:

5 cm * 8 1/2 cm * 3 3/4 cm =

5 cm * 17/2 cm * 15/4 cm =

85/2 cm^2 * 15/4 cm =

1275/8 cm^3 =

<em>159 3/8 cm^3</em>

4. This means that the<em> Volume of the Rectangular Prism = 159 3/8 cm^3 (Option D)</em>

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The solution to 4.2x = 19.32 is x = ___. 0.28 0.45 4.6 15.12

AVprozaik [17]

The solution to this equation is x=4.6 because 19.32/4.2=4.6

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3 years ago

Find the midpoint of the line segment whose endpoints are (2.6,5.1) and (3,4.7).

svp [43]

Answer:

Mid point is: (2.8;4.9)

Step-by-step explanation:

To find midpoint of a line segment we can use the general equation:

$Mid=\frac{x_1+x_2}{2} ;\frac{y_1+y_2}{2}$

Where the point of the line are: (x₁;y₁) and (x₂;y₂).

In the problem, x₁ = 2.6, y₁ = 5.1 and x₂ = 3 and y₂ = 4.7. Replacing in the equation:

$Mid=\frac{2.6+3}{2} ;\frac{5.1+4.7}{2}$

<h3>Mid point is: (2.8;4.9)</h3>

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3 years ago

1) After a dilation, (-60, 15) is the image of (-12, 3). What are the coordinates of the image of (-2,-7) after the same dilatio

BARSIC [14]

Answer:

a) k = 5; (-10, -35)

Step-by-step explanation:

Given:

Co-ordinates:

Pre-Image = (-12,3)

After dilation

Image = (-60,15)

The dilation about the origin can be given as :

Pre-Image $(x,y)\rightarrow Image(kx,ky)$

where $k$ represents the scalar factor.

We can find value of $k$ for the given co-ordinates by finding the ratio of $x$ or $y$ co-ordinates of the image and pre-image.

$k=\frac{Image}{Pre-Image}$

For the given co-ordinates.

Pre-Image = (-12,3)

Image = (-60,15)

The value of $k=\frac{-60}{-12}=5$

or $k=\frac{15}{3}=5$

As we get $k=5$ for both ratios i.e of $x$ and $y$ co-ordinates, so we can say the image has been dilated by a factor of 5 about the origin.

To find the image of (-2,-7), after same dilation, we will multiply the co-ordinates with the scalar factor.

Pre-Image $(-2,-7)\rightarrow$ Image $((-2\times5),(-7\times 5))$

Pre-Image $(-2,-7)\rightarrow$ Image $(-10,-35)$ (Answer)

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3 years ago

You are given the following sequence:

borishaifa [10]

<h2> Question No 1</h2>

Answer:

7.5 is the 4th term of the sequence $60, 30, 15, 7.5, ...$ .

In other words: $\boxed{a_4=7.5}$

Step-by-step explanation:

Considering the sequence

$60, 30, 15, 7.5, ...$

As we know that a sequence is said to be a list of numbers or objects in a special order.

so

$60, 30, 15, 7.5, ...$

is a sequence starting at 60 and decreasing by half each time. Here, 60 is the first term, 30 is the second term, 15 is the 3rd term and 7.5 is the fourth term.

In other words,

$a_1=60$ ,

$\:a_2=30$ ,

$a_3=15$ , and

$a_4=7.5$

Therefore, 7.5 is the 4th term of the sequence $60, 30, 15, 7.5, ...$ .

In other words: $\boxed{a_4=7.5}$

<h2> Question # 2</h2>

Answer:

The value of a subscript 5 is 16.

i.e. When n = 5, then h(5) = 16

Step-by-step explanation:

To determine:

What is the value of a subscript 5?

Information fetching and Solution Steps:

Chart with two rows.

The first row is labeled n.

The second row is labeled h of n. i.e. h(n)

The first row contains the numbers three, four, five, and six.

The second row contains the numbers four, nine, sixteen, and twenty-five.

Making the data chart

n 3 4 5 6

h(n) 4 9 16 25

As we can reference a specific term in the sequence by using the subscript. From the table, it is clear that 'n' row represents the input and and 'h(n)' represents the output.

So, when n = 5, the value of subscript 5 corresponds with 16. In other words: When n = 5, then h(5) = 16

Therefore, the value of a subscript 5 is 16.

<h2> Question # 3</h2>

Answer:

We determine that the sequence 33, 31, 28, 24, 19, … is neither arithmetic nor geometric.

Step-by-step explanation:

Considering the sequence

33, 31, 28, 24, 19, …

Lets calculate the common difference 'd' to determine if the sequence is Arithmetic or not.

$\mathrm{Compute\:the\:differences\:of\:all\:the\:adjacent\:terms}:\quad \:d=a_{n+1}-a_n$

$d = 31 - 33 = -2$

$d = 28 - 31 = -3$

$d = 24 - 28 = -4$

$d = 19 - 24 = -5$

As the common difference 'd' is not constant. It means the sequence is not Arithmetic.

Lets now calculate the common ratio 'r' to determine if the sequence is Geometric or not.

$\mathrm{Compute\:the\:ratios\:of\:all\:the\:adjacent\:terms}:\quad \:r=\frac{a_n}{a_{n-1}}$

$\frac{31}{33}=0.93939\dots ,\:\quad \frac{28}{31}=0.90322\dots ,\:\quad \frac{24}{28}=0.85714\dots ,\:\quad \frac{19}{24}=0.79166\dots$

The ratio is not constant. It means the sequence is not Geometric.

From the above analysis, we determine that the sequence 33, 31, 28, 24, 19, … is neither arithmetic nor geometric.

<h2> Question # 4</h2>

Answer:

We determine that the sequence -99, -96, -92, -87, -81... is neither arithmetic nor geometric.

Step-by-step explanation:

From the description statement:

''negative 99 comma negative 96 comma negative 92 comma negative 87 comma negative 81 comma dot dot dot''.

The statement can be translated algebraically as

-99, -96, -92, -87, -81...

Lets calculate the common difference 'd' to determine if the sequence is Arithmetic or not.

$\mathrm{Compute\:the\:differences\:of\:all\:the\:adjacent\:terms}:\quad \:d=a_{n+1}-a_n$

$-96-\left(-99\right)=3,\:\quad \:-92-\left(-96\right)=4,\:\quad \:-87-\left(-92\right)=5,\:\quad \:-81-\left(-87\right)=6$

As the common difference 'd' is not constant. It means the sequence is not Arithmetic.

Lets now calculate the common ratio 'r' to determine if the sequence is Geometric or not.

$\mathrm{Compute\:the\:ratios\:of\:all\:the\:adjacent\:terms}:\quad \:r=\frac{a_n}{a_{n-1}}$

$\frac{-96}{-99}=0.96969\dots ,\:\quad \frac{-92}{-96}=0.95833\dots ,\:\quad \frac{-87}{-92}=0.94565\dots ,\:\quad \frac{-81}{-87}=0.93103\dots$

The ratio is not constant. It means the sequence is not Geometric.

From the above analysis, we determine that the sequence -99, -96, -92, -87, -81... is neither arithmetic nor geometric.

<h2> Question # 5</h2>

Step-by-step explanation:

Considering the sequence

12, 22, 30, 36, 41, …

$\mathrm{Compute\:the\:differences\:of\:all\:the\:adjacent\:terms}:\quad \:d=a_{n+1}-a_n$

$22-12=10,\:\quad \:30-22=8,\:\quad \:36-30=6,\:\quad \:41-36=5$

As the common difference 'd' is not constant. It means the sequence is not Arithmetic.

$\mathrm{Compute\:the\:ratios\:of\:all\:the\:adjacent\:terms}:\quad \:r=\frac{a_n}{a_{n-1}}$

$\frac{22}{12}=1.83333\dots ,\:\quad \frac{30}{22}=1.36363\dots ,\:\quad \frac{36}{30}=1.2,\:\quad \frac{41}{36}=1.13888\dots$

The ratio is not constant. It means the sequence is not Geometric.

From the above analysis, we determine that the sequence 12, 22, 30, 36, 41, … is neither arithmetic nor geometric.

8 0

3 years ago