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3 years ago

12

Find the volume of a right rectangular prism if the dimensions of the base are 4 centimeters by 9 centimeters and the height is

11 centimeters.

2 answers:

GenaCL600 [577]3 years ago

7 0

Answer:

396 cubic centimeters

Step-by-step explanation:

Given that

The dimension of the base is 4 centimeter by 9 centimeter and the height is 11 centimeter

We need to find out the volume of the right rectangular prism

We need to apply the following formula

As we know that

Volume = lwh

here

l denotes the length

w denotes the width

And, h denotes the height

= (4) (9) (11)

= 396 cubic centimeters

artcher [175]3 years ago

3 0

Answer:

A 396 cm^3 is correct

Step-by-step explanation:

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Jacob solves the system of equations by forming a matrix equation.

Lyrx [107]

Simultaneous equations can be solved using inverse matrix operation.

The complete steps of Jacob's solution are:

$\left[\begin{array}{cc}4&1\\-2&3\end{array}\right]^{-1} \cdot \left[\begin{array}{cc}4&1\\-2&3\end{array}\right]\left[\begin{array}{c}x&y\end{array}\right] = \frac{1}{14}\left[\begin{array}{cc}3&-1\\2&4\end{array}\right] \cdot \left[\begin{array}{c}2&-22\end{array}\right]$

$\left[\begin{array}{c}x&y\end{array}\right] = \left[\begin{array}{cc}4&1\\-2&3\end{array}\right] \cdot \left[\begin{array}{c}2&-22\end{array}\right]$

$\left[\begin{array}{c}x&y\end{array}\right] = \frac{1}{14} \left[\begin{array}{c}28&-84\end{array}\right]$

$\left[\begin{array}{c}x&y\end{array}\right] = \left[\begin{array}{c}2&-6\end{array}\right]$

We have:

$4x + y = 2$

$-2x + 4y = -22$

Calculate the determinant of $\left[\begin{array}{cc}4&1\\-2&3\end{array}\right]$

$|A| = 4 \times 3 -1 \times -2$

$|A| = 12 +2$

$|A| = 14$

So, the inverse matrix becomes

$A = \frac{1}{14}\left[\begin{array}{cc}4&1\\-2&3\end{array}\right]$

Replace the first column with $\left[\begin{array}{c}2&-22\end{array}\right]$ to calculate the value of x

$x = \frac{1}{14}\left[\begin{array}{cc}2&1\\-22&3\end{array}\right]$

So, we have:

$x = \frac{1}{14}(2 \times 3 - 1 \times -22)$

$x = \frac{1}{14}(6 +22)$

$x = \frac{1}{14}(28)$

$x = 2$

Replace the second column with $\left[\begin{array}{c}2&-22\end{array}\right]$ to calculate the value of y

$y = \frac{1}{14}\left[\begin{array}{cc}4&2\\-2&-22\end{array}\right]$

So, we have:

$y = \frac{1}{14}(4 \times -22 - 2 \times -2)$

$y = \frac{1}{14}(-88 +4)$

$y = \frac{1}{14}(-84)$

$y = -6$

Hence, the complete process is:

$\left[\begin{array}{cc}4&1\\-2&3\end{array}\right]^{-1} \cdot \left[\begin{array}{cc}4&1\\-2&3\end{array}\right]\left[\begin{array}{c}x&y\end{array}\right] = \frac{1}{14}\left[\begin{array}{cc}3&-1\\2&4\end{array}\right] \cdot \left[\begin{array}{c}2&-22\end{array}\right]$

$\left[\begin{array}{c}x&y\end{array}\right] = \left[\begin{array}{cc}4&1\\-2&3\end{array}\right] \cdot \left[\begin{array}{c}2&-22\end{array}\right]$

$\left[\begin{array}{c}x&y\end{array}\right] = \frac{1}{14} \left[\begin{array}{c}28&-84\end{array}\right]$

$\left[\begin{array}{c}x&y\end{array}\right] = \left[\begin{array}{c}2&-6\end{array}\right]$

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3 years ago

Which number is equal to 10 Superscript negative 3? –1,000 –30 0.001 0.003

Karolina [17]

<u>Given</u>:

The given expression is $10^{-3}$

We need to determine the equivalent number.

<u>Equivalent expression:</u>

To determine the equivalent number, let us solve the expression $10^{-3}$

Thus, let us apply the exponent rule $a^{-b}=\frac{1}{a^{b}}$ , we get;

$10^{-3}=\frac{1}{10^{3}}$

Also, the term 10³ can be written as $10^{3}=1000$

Thus, we get;

$\frac{1}{1000}$

Dividing, we get;

0.001

Hence, the equivalent number is 0.001

Hence, Option c is the correct answer.

5 0

3 years ago

Read 2 more answers

How do you write 7 1 \12 as a whole number

Alex777 [14]

Answer: 7

Step-by-step explanation:

Write as a decimal

7 1/2 would be written as ~7.0833

Rounding a decimal to the nearest whole number

If you have a decimal that is greater than or equal to 5 in the tenths place then you round up. Ex: 5.8 would be rounded to 6, 1.5 would be rounded to 2.

If you have a decimal that is less than or equal to 4 in the tenths place then you round down. Ex: 5.1 would be rounded 5, 1.2 would be rounded to 1.

Since 0 is in the tenth’s place we round down to 7.

3 0

3 years ago