(2.38•10^4)+ (6.75•10^3)=
10^3( 23.8+6.75)=
10^3• 30.55 ~
3.06•10^4
Answer:
noayuda cepo bro weynecesto ayda con mi ta no ac reupor to qdo esta ingen ules la eKaty rrypei
Step-by-step explanation:
The distributive property is used to solve the given problem,
Given
Equation; ![\rm -8(x-3y-9) = -8x+24y+72](https://tex.z-dn.net/?f=%5Crm%20-8%28x-3y-9%29%20%3D%20-8x%2B24y%2B72)
<h3>What is distributive property?</h3>
The distributive property says that the sum of two or more addends multiplied by a number gives you the same answer as distributing the multiplier, multiplying each addend separately, and adding the products together.
Therefore,
By applying distributive property in the equation;
![\rm -8(x-3y-9) \\\\ =- 8 \times x+(-8)\times (-3y)-8\times (-9)\\\\= -8x+24y+72](https://tex.z-dn.net/?f=%5Crm%20-8%28x-3y-9%29%20%5C%5C%5C%5C%20%3D-%208%20%5Ctimes%20x%2B%28-8%29%5Ctimes%20%28-3y%29-8%5Ctimes%20%28-9%29%5C%5C%5C%5C%3D%20-8x%2B24y%2B72)
Hence, the distributive property is used to solve the given problem,
To know more about Distributive property click the link given below.
brainly.com/question/13130806
Option A:
![\left[\begin{array}{c}x\\y\\\end{array}\right]=\left[\begin{array}{cc}3 & -5 \\-1 & 2 \end{array}\right] \left[\begin{array}{c}15\\18\\\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7Dx%5C%5Cy%5C%5C%5Cend%7Barray%7D%5Cright%5D%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D3%20%26%20-5%20%5C%5C-1%20%26%202%20%5Cend%7Barray%7D%5Cright%5D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D15%5C%5C18%5C%5C%5Cend%7Barray%7D%5Cright%5D)
Solution:
Given system of equations are
![\left\{\begin{array}{r}2 x+5 y=15 \\x+3 y=18\end{array}\right.](https://tex.z-dn.net/?f=%5Cleft%5C%7B%5Cbegin%7Barray%7D%7Br%7D2%20x%2B5%20y%3D15%20%5C%5Cx%2B3%20y%3D18%5Cend%7Barray%7D%5Cright.)
We can write this equation in matrix form.
Isolate the variables in the equation.
![\left[\begin{array}{cc}2&5\\1&3\\\end{array}\right] \left[\begin{array}{c}x\\y\\\end{array}\right]=\left[\begin{array}{c}15\\18\\\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D2%265%5C%5C1%263%5C%5C%5Cend%7Barray%7D%5Cright%5D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7Dx%5C%5Cy%5C%5C%5Cend%7Barray%7D%5Cright%5D%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D15%5C%5C18%5C%5C%5Cend%7Barray%7D%5Cright%5D)
Where ![A=\left[\begin{array}{cc}2&5\\1&3\\\end{array}\right] , X= \left[\begin{array}{c}x\\y\\\end{array}\right] \ \text{and} \ B =\left[\begin{array}{c}15\\18\\\end{array}\right]](https://tex.z-dn.net/?f=A%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D2%265%5C%5C1%263%5C%5C%5Cend%7Barray%7D%5Cright%5D%20%2C%20X%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7Dx%5C%5Cy%5C%5C%5Cend%7Barray%7D%5Cright%5D%20%20%5C%20%5Ctext%7Band%7D%20%5C%20B%20%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D15%5C%5C18%5C%5C%5Cend%7Barray%7D%5Cright%5D)
This is in the form of AX = B.
– – – (1)
Let us first calculate inverse of A.
![$A^{-1}=\frac{1}{a d-b c}\left[\begin{array}{cc}d & -b \\-c & a\end{array}\right]](https://tex.z-dn.net/?f=%24A%5E%7B-1%7D%3D%5Cfrac%7B1%7D%7Ba%20d-b%20c%7D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7Dd%20%26%20-b%20%5C%5C-c%20%26%20a%5Cend%7Barray%7D%5Cright%5D)
![$A^{-1}=\frac{1}{2\times 3-5 \times1}\left[\begin{array}{cc}3 & -5 \\-1 & 2 \end{array}\right]](https://tex.z-dn.net/?f=%24A%5E%7B-1%7D%3D%5Cfrac%7B1%7D%7B2%5Ctimes%203-5%20%5Ctimes1%7D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D3%20%26%20-5%20%5C%5C-1%20%26%202%20%5Cend%7Barray%7D%5Cright%5D)
![$A^{-1}=\frac{1}{6-5 }\left[\begin{array}{cc}3 & -5 \\-1 & 2 \end{array}\right]](https://tex.z-dn.net/?f=%24A%5E%7B-1%7D%3D%5Cfrac%7B1%7D%7B6-5%20%7D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D3%20%26%20-5%20%5C%5C-1%20%26%202%20%5Cend%7Barray%7D%5Cright%5D)
![$A^{-1}=\frac{1}{1 }\left[\begin{array}{cc}3 & -5 \\-1 & 2 \end{array}\right]](https://tex.z-dn.net/?f=%24A%5E%7B-1%7D%3D%5Cfrac%7B1%7D%7B1%20%7D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D3%20%26%20-5%20%5C%5C-1%20%26%202%20%5Cend%7Barray%7D%5Cright%5D)
![$A^{-1}=\left[\begin{array}{cc}3 & -5 \\-1 & 2 \end{array}\right]](https://tex.z-dn.net/?f=%24A%5E%7B-1%7D%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D3%20%26%20-5%20%5C%5C-1%20%26%202%20%5Cend%7Barray%7D%5Cright%5D)
Substitute this in (2), we get
![\left[\begin{array}{c}x\\y\\\end{array}\right]=\left[\begin{array}{cc}3 & -5 \\-1 & 2 \end{array}\right] \left[\begin{array}{c}15\\18\\\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7Dx%5C%5Cy%5C%5C%5Cend%7Barray%7D%5Cright%5D%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D3%20%26%20-5%20%5C%5C-1%20%26%202%20%5Cend%7Barray%7D%5Cright%5D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D15%5C%5C18%5C%5C%5Cend%7Barray%7D%5Cright%5D)
Hence option A is the correct answer.
The range is the output or the y values in the case of this function. The only y value on this function is 1 therefore the range is 1