Answer:
- 836
Step-by-step explanation:
Check out the attachment below:
Please Help ASAP!! Domain and range of function...
2 answers:
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Answer:
4 pounds of wooden blocks and 6 pounds of plastic bricks should be used.
Step-by-step explanation:
Let w = wooden block
Let p = plastic bricks
<u>Given the following data;</u>
Price of wooden block per pounds = $5
Price of plastic brick per pounds = $10
*Translating the word problem into an algebraic equation*
For the 10-pound mixture;
.........equation 1
For the $80 mixture;
..........equation 2
Solving the linear equation by using the substitution method;
Making w the subject in equation 1:
.......equation 3
Substituting "w" into equation 2;
Simplifying the equation, we have;
Rearranging the equation, we have;
p = 6 pounds (For the plastic brick).
To find w;
Substituting "p" into equation 3;
w = 4 pounds (For the wooden block).
Given
We can rewrite it in matrix form as:
![\left[\begin{array}{cccc}1&-1&2&4\\5&2&-1&3\\0&0&0&0\\0&0&0&0\end{array}\right] \left[\begin{array}{c}w\\x\\y\\z\end{array}\right] =\left[\begin{array}{c}0\\0\\0\\0\end{array}\right] \\ \\ \left[\begin{array}{cccc}1&-1&2&4\\5&2&-1&3\\0&0&0&0\\0&0&0&0\end{array}\right|\left.\begin{array}{c}0\\0\\0\\0\end{array}\right]\ \ \ \ \ -5R_1+R_2\rightarrow R_2](https://tex.z-dn.net/?f=%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D1%26-1%262%264%5C%5C5%262%26-1%263%5C%5C0%260%260%260%5C%5C0%260%260%260%5Cend%7Barray%7D%5Cright%5D%20%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7Dw%5C%5Cx%5C%5Cy%5C%5Cz%5Cend%7Barray%7D%5Cright%5D%20%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D0%5C%5C0%5C%5C0%5C%5C0%5Cend%7Barray%7D%5Cright%5D%20%5C%5C%20%20%5C%5C%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D1%26-1%262%264%5C%5C5%262%26-1%263%5C%5C0%260%260%260%5C%5C0%260%260%260%5Cend%7Barray%7D%5Cright%7C%5Cleft.%5Cbegin%7Barray%7D%7Bc%7D0%5C%5C0%5C%5C0%5C%5C0%5Cend%7Barray%7D%5Cright%5D%5C%20%5C%20%5C%20%5C%20%5C%20-5R_1%2BR_2%5Crightarrow%20R_2)
![\left[\begin{array}{cccc}1&-1&2&4\\0&7&-11&-17\\0&0&0&0\\0&0&0&0\end{array}\right|\left.\begin{array}{c}0\\0\\0\\0\end{array}\right]\ \ \ \ \ \frac{1}{7} R_2\rightarrow R_2 \\ \\ \left[\begin{array}{cccc}1&-1&2&4\\0&1&-\frac{11}{7}&-\frac{17}{7}\\0&0&0&0\\0&0&0&0\end{array}\right|\left.\begin{array}{c}0\\0\\0\\0\end{array}\right]\ \ \ \ \ R_1+R_2\rightarrow R_1](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D1%26-1%262%264%5C%5C0%267%26-11%26-17%5C%5C0%260%260%260%5C%5C0%260%260%260%5Cend%7Barray%7D%5Cright%7C%5Cleft.%5Cbegin%7Barray%7D%7Bc%7D0%5C%5C0%5C%5C0%5C%5C0%5Cend%7Barray%7D%5Cright%5D%5C%20%5C%20%5C%20%5C%20%5C%20%20%5Cfrac%7B1%7D%7B7%7D%20R_2%5Crightarrow%20R_2%20%5C%5C%20%20%5C%5C%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D1%26-1%262%264%5C%5C0%261%26-%5Cfrac%7B11%7D%7B7%7D%26-%5Cfrac%7B17%7D%7B7%7D%5C%5C0%260%260%260%5C%5C0%260%260%260%5Cend%7Barray%7D%5Cright%7C%5Cleft.%5Cbegin%7Barray%7D%7Bc%7D0%5C%5C0%5C%5C0%5C%5C0%5Cend%7Barray%7D%5Cright%5D%5C%20%5C%20%5C%20%5C%20%5C%20R_1%2BR_2%5Crightarrow%20R_1)
![\\ \\ \left[\begin{array}{cccc}1&0&\frac{3}{7}&\frac{11}{7}\\0&1&-\frac{11}{7}&-\frac{17}{7}\\0&0&0&0\\0&0&0&0\end{array}\right|\left.\begin{array}{c}0\\0\\0\\0\end{array}\right] \\ \\ \Rightarrow w= -\frac{3}{7} y- \frac{11}{7} z \\ x=\frac{11}{7} y+ \frac{17}{7} z \\ y=free \\ z=free \\ \\ =y\left\ \textless \ -\frac{3}{7},\frac{11}{7}1,0\right\ \textgreater \ +z\left\ \textless \ - \frac{11}{7},\frac{17}{7},0,1\right\ \textgreater \](https://tex.z-dn.net/?f=%20%5C%5C%20%20%5C%5C%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D1%260%26%5Cfrac%7B3%7D%7B7%7D%26%5Cfrac%7B11%7D%7B7%7D%5C%5C0%261%26-%5Cfrac%7B11%7D%7B7%7D%26-%5Cfrac%7B17%7D%7B7%7D%5C%5C0%260%260%260%5C%5C0%260%260%260%5Cend%7Barray%7D%5Cright%7C%5Cleft.%5Cbegin%7Barray%7D%7Bc%7D0%5C%5C0%5C%5C0%5C%5C0%5Cend%7Barray%7D%5Cright%5D%20%5C%5C%20%20%5C%5C%20%5CRightarrow%20w%3D%20-%5Cfrac%7B3%7D%7B7%7D%20y-%20%5Cfrac%7B11%7D%7B7%7D%20z%20%5C%5C%20x%3D%5Cfrac%7B11%7D%7B7%7D%20y%2B%20%5Cfrac%7B17%7D%7B7%7D%20z%20%5C%5C%20y%3Dfree%20%5C%5C%20z%3Dfree%20%5C%5C%20%20%5C%5C%20%3Dy%5Cleft%5C%20%5Ctextless%20%5C%20-%5Cfrac%7B3%7D%7B7%7D%2C%5Cfrac%7B11%7D%7B7%7D1%2C0%5Cright%5C%20%5Ctextgreater%20%5C%20%2Bz%5Cleft%5C%20%5Ctextless%20%5C%20-%20%5Cfrac%7B11%7D%7B7%7D%2C%5Cfrac%7B17%7D%7B7%7D%2C0%2C1%5Cright%5C%20%5Ctextgreater%20%5C%20)
Thus, the solution set is a span of
We can rewrite it in matrix form as:
Thus, the solution set is a span of