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Ann [662]
2 years ago
6

Acellus

Mathematics
1 answer:
kipiarov [429]2 years ago
7 0

By taking the product of the two fractions we will see that the number that goes in the green box is a 6.

<h3>How to add two fractions?</h3>

We only can add two fractions if we have the same denominator in both of them, here we want to transform -2/3 in an equivalent fraction, such that the denominator is 9, so we multiply both the numerator and denominator by 3.

So we need to solve:

\frac{-2}{3}*\frac{3}{3} = \frac{-2*3}{3*3}  = \frac{-6}{9}

From that, we can conclude that the number that goes in the green box is 6.

If you want to learn more about fractions, you can read:

brainly.com/question/11562149

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The first quartile of the data set represented by the box plot is (8, 9, 12,14) . The median of the data set is (8, 12,16,19)
Andrei [34K]
The first quartile is 12. The median is 16!
7 0
2 years ago
Read 2 more answers
Solve the system of equations by finding the reduced row-echelon form of the augmented matrix for the system of equations.
Anuta_ua [19.1K]

Answer:

c

Step-by-step explanation:

First, we can transform this into a matrix. The x coefficients will be the first ones for each row, the y coefficients the second column, etc.

\left[\begin{array}{cccc}1&-2&3&-2\\6&2&2&-48\\1&4&3&-38\end{array}\right]

Next, we can define a reduced row echelon form matrix as follows:

With the leading entry being the first non zero number in the first row, the leading entry in each row must be 1. Next, there must only be 0s above and below the leading entry. After that, the leading entry of a row must be to the left of the leading entry of the next row. Finally, rows with all zeros should be at the bottom of the matrix.

Because there are 3 rows and we want to solve for 3 variables, making the desired matrix of form

\left[\begin{array}{ccc}1&0&0\\0&1&0\\0&0&1\end{array}\right] for the first three rows and columns. This would make the equation translate to

x= something

y= something

z = something, making it easy to solve for x, y, and z.

Going back to our matrix,

\left[\begin{array}{cccc}1&-2&3&-2\\6&2&2&-48\\1&4&3&-38\end{array}\right] ,

we can start by removing the nonzero values from the first column for rows 2 and 3 to reach the first column of the desired matrix. We can do this by multiplying the first row by -6 and adding it to the second row, as well as multiplying the first row by -1 and adding it to the third row. This results in

\left[\begin{array}{cccc}1&-2&3&-2\\0&14&-16&-36\\0&6&0&-36\end{array}\right]

as our matrix. * Next, we can reach the second column of our desired matrix by first multiplying the second row by (2/14) and adding it to the first row as well as multiplying the second row by (-6/14) and adding it to the third row. This eliminates the nonzero values from all rows in the second column except for the second row. This results in

\left[\begin{array}{cccc}1&0&10/14&-100/14\\0&14&-16&-36\\0&0&96/14&-288/14\end{array}\right]

After that, to reach the desired second column, we can divide the second row by 14, resulting in

\left[\begin{array}{cccc}1&0&10/14&-100/14\\0&1&-16/14&-36/14\\0&0&96/14&-288/14\end{array}\right]

Finally, to remove the zeros from all rows in the third column outside of the third row, we can multiply the third row by (16/96) and adding it to the second row as well as multiplying the third row by (-10/96) and adding it to the first row. This results in

\left[\begin{array}{cccc}1&0&0&-5\\0&1&0&-6\\0&0&96/14&-288/14\end{array}\right]

We can then divide the third row by -96/14 to reach the desired third column, making the reduced row echelon form of the matrix

\left[\begin{array}{cccc}1&0&0&-5\\0&1&0&-6\\0&0&1&-3\end{array}\right]

Therefore,

x=-5

y=-6

z=-3

* we could also switch the second and third rows here to make the process a little simpler

3 0
3 years ago
The volume of a rectangular prism is
Feliz [49]

Answer:

<em>h =  v/lw .</em>

Step-by-step explanation:

v=lwh

Divide both sides by lw:

v  / lw = h.

6 0
2 years ago
Five more than a half number is 6. find the number.
Artyom0805 [142]
First write the equation:
1/2x + 5 = 6

Then subtract five from both sides:

1/2x = 1

Multiply both sides by 2:

x = 2
7 0
2 years ago
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If f(1) = 160 and f(n + 1) = –2f(n), what is f(4)?
balandron [24]

Answer with Step-by-step explanation:

f(1) = 160 and f(n + 1) = –2f(n)

⇒ f(2)= -2×f(1)

        = -2×160

       = -320

⇒ f(3)= -2×f(2)

    = -2×(-320)

   = 640

⇒ f(4)= -2×f(3)

    = -2×640

   = -1280

Hence, Value of f(4) is:

- 1280

7 0
3 years ago
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