Floyd's contract consists of
(i) $200 per month fixed.
(i) $12 per album sold.
Let x = number of albums sold last month.
Because total earnings is $644, therefore
200 + 12x = 644
To find x, do the following:
Subtract 200 from each side.
12x = 644 - 200 = 444
Divide each side by 12.
x = 444/12 = 37
Answer:
The equation is 12x + 200 = 644.
The solution for x (number of albums sold) is 37.
24 slices because you would do three apples times eight slices so you would get 24 slices
The Linear inequality holds true for 21 ≥ x;
What is Linear Inequality?
The mathematical expression with unequal sides is known as inequality in mathematics. Inequality is referred to in mathematics when a relationship results in a non-equal comparison between two expressions or two numbers. In this instance, any of the inequality symbols, such as greater than symbol (>), less than symbol (), greater than or equal to a symbol (), less than or equal to a symbol (), or not equal to a symbol (), is used in place of the equal sign "=" in the expression. Polynomial inequality, rational inequality, and absolute value inequality are the various types of inequalities that can exist in mathematics. The symbols "" and ">" signify tight inequalities, while "" and "" signify slack inequalities.
In the given question, the given inequality given is:
-3(2x-11) ≥ 8x-9;
Solving the Inequality:
⇒-6x + 33 ≥ 8x - 9;
⇒33 + 9 ≥ 8x - 6x;
⇒ 42 ≥ 2x;
⇒ 21 ≥ x;
Hence,
The Linear inequality holds true for 21 ≥ x;
To learn more about Linear Inequality, visit:
brainly.com/question/24372553
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Let's work with 2-by-2 matrices so we're on the same page. The ideas will work for any appropriate matrices.
From the rule of matrix multiplication, we see:
![\left[\begin{array}{cc}a_{11} & a_{12} \\a_{21} & a_{22} \end{array}\right] \left[\begin{array}{cc}b_{11} & b_{12} \\b_{21} & b_{22} \end{array}\right] = \left[\begin{array}{cc} a_{11}b_{11} + a_{12}b_{21} & a_{11}b_{12} + a_{12}b_{22} \\ a_{21}b_{11} + a_{22}b_{21} & a_{21}b_{12} + a_{22} b_{22} \end{array}\right]](https://tex.z-dn.net/?f=%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7Da_%7B11%7D%20%26%20a_%7B12%7D%20%5C%5Ca_%7B21%7D%20%26%20a_%7B22%7D%20%5Cend%7Barray%7D%5Cright%5D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7Db_%7B11%7D%20%26%20b_%7B12%7D%20%5C%5Cb_%7B21%7D%20%26%20b_%7B22%7D%20%5Cend%7Barray%7D%5Cright%5D%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D%20a_%7B11%7Db_%7B11%7D%20%2B%20a_%7B12%7Db_%7B21%7D%20%26%20a_%7B11%7Db_%7B12%7D%20%2B%20a_%7B12%7Db_%7B22%7D%20%5C%5C%20a_%7B21%7Db_%7B11%7D%20%2B%20a_%7B22%7Db_%7B21%7D%20%26%20a_%7B21%7Db_%7B12%7D%20%2B%20a_%7B22%7D%20b_%7B22%7D%20%5Cend%7Barray%7D%5Cright%5D%20)
As you noted, we see the columns of B contributing to the rows of C. The question is, why would we ever have defined matrix multiplication this way?
Here's a nontraditional way of feeling this connection. We can define matrix multiplication as "adding multiplication tables." A multiplication table is made by starting with a column and a row. For example,

We then fill this table in by multiplying the row and column entries:
![\begin{array}{ccc} {} & [1] & [2] \\ 1| &1 & 2 \\ 2| & 2 &4 \end{array}](https://tex.z-dn.net/?f=%5Cbegin%7Barray%7D%7Bccc%7D%20%7B%7D%20%26%20%5B1%5D%20%26%20%5B2%5D%20%5C%5C%201%7C%20%261%20%26%202%20%5C%5C%202%7C%20%26%202%20%264%20%5Cend%7Barray%7D)
It's then reasonable to say that given two matrices A and B, we can construct multiplication tables by taking the columns of A and pairing them with the rows of B:
![\left[\begin{array}{cc}a_{11} & a_{12} \\a_{21} & a_{22} \end{array}\right] \left[\begin{array}{cc}b_{11} & b_{12} \\b_{21} & b_{22} \end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7Da_%7B11%7D%20%26%20a_%7B12%7D%20%5C%5Ca_%7B21%7D%20%26%20a_%7B22%7D%20%5Cend%7Barray%7D%5Cright%5D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7Db_%7B11%7D%20%26%20b_%7B12%7D%20%5C%5Cb_%7B21%7D%20%26%20b_%7B22%7D%20%5Cend%7Barray%7D%5Cright%5D%20)
![= \begin{array}{cc} {} & \left[\begin{array}{cc} b_{11} & b_{12}\end{array} \right]\\ \left[\begin{array}{c} a_{11} \\ a_{21} \end{array} \right] \end{array} +\begin{array}{cc} {} & \left[\begin{array}{cc} b_{21} & b_{22}\end{array} \right]\\ \left[\begin{array}{c} a_{12} \\ a_{22} \end{array} \right] \end{array}](https://tex.z-dn.net/?f=%3D%20%5Cbegin%7Barray%7D%7Bcc%7D%20%7B%7D%20%26%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D%20b_%7B11%7D%20%26%20b_%7B12%7D%5Cend%7Barray%7D%20%5Cright%5D%5C%5C%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D%20a_%7B11%7D%20%5C%5C%20a_%7B21%7D%20%5Cend%7Barray%7D%20%5Cright%5D%20%5Cend%7Barray%7D%20%2B%5Cbegin%7Barray%7D%7Bcc%7D%20%7B%7D%20%26%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D%20b_%7B21%7D%20%26%20b_%7B22%7D%5Cend%7Barray%7D%20%5Cright%5D%5C%5C%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D%20a_%7B12%7D%20%5C%5C%20a_%7B22%7D%20%5Cend%7Barray%7D%20%5Cright%5D%20%5Cend%7Barray%7D)
![= \left[\begin{array}{cc} a_{11} b_{11} & a_{11} b_{12} \\ a_{21} b_{11} & a_{21} b_{12} \end{array} \right] + \left[\begin{array}{cc} a_{12} b_{21} & a_{12} b_{22} \\ a_{22} b_{21} & a_{22} b_{22} \end{array} \right]](https://tex.z-dn.net/?f=%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D%20a_%7B11%7D%20b_%7B11%7D%20%26%20a_%7B11%7D%20b_%7B12%7D%20%5C%5C%20a_%7B21%7D%20b_%7B11%7D%20%26%20a_%7B21%7D%20b_%7B12%7D%20%5Cend%7Barray%7D%20%5Cright%5D%20%2B%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D%20a_%7B12%7D%20b_%7B21%7D%20%26%20a_%7B12%7D%20b_%7B22%7D%20%5C%5C%20a_%7B22%7D%20b_%7B21%7D%20%26%20a_%7B22%7D%20b_%7B22%7D%20%5Cend%7Barray%7D%20%5Cright%5D)
Adding these matrices together, we get the exact same expression as the traditional definition.