The solution of the given equation is (3,6). The correct option is B.(3,6)
<h3>Given equations,</h3>
![y=x+3.......(1)\\4x+y=18.....(2)](https://tex.z-dn.net/?f=y%3Dx%2B3.......%281%29%5C%5C4x%2By%3D18.....%282%29)
<h3>How to solve the equations?</h3>
putting the value of y from equation (1) in equation (2) , we get
![4x+x+3=18\\](https://tex.z-dn.net/?f=4x%2Bx%2B3%3D18%5C%5C)
![5x=18-3\\5x=15\\x=3](https://tex.z-dn.net/?f=5x%3D18-3%5C%5C5x%3D15%5C%5Cx%3D3)
substitute the value of x=3 in equation (1) we get,
![y=3+3\\y=6](https://tex.z-dn.net/?f=y%3D3%2B3%5C%5Cy%3D6)
Hence, the solution of given equation is (3,6).
So, the correct option is B.
For more details about the system of equations, follow the link:
brainly.com/question/12895249
When a linear equation is in the form y = mx + c, the c, or constant, is the intercept on the y axis, meaning it crosses the y axis at (0, 1).
The gradient (1/3 in this case) is how much the y increments (or decrements) per increase of 1 of the value of x.
This would mean that there would be one point at (0, 1), and another at (3, 2). Draw a line from these two points and beyond, and that is the graph sketched.
Answer:
a.2nd quarter with 9 goals
b. 4.8 goals
c. 4 goals
Step-by-step explanation:
a. The mode is defined as the most appearing data point or the data point with the highest frequency..
From our data(for away goals):
- 1st quarter-2
- 2nd quarter-9
- 3rd quarter-7
- 4th quarter-4
Hence, the 2nd quarter has the mode for away goals with 9 goals.
b. Mean is defined as the average of a set of data points.
#We calculate the totals goals per quarter, sum over all quarters then divide by the number of games, 10:
![\bar x=\frac{1}{n}\sum{x_i}\\1^{st }_g=Away+Home=5+2=7\\\\2^{nd}_g=Away+Home=4+9=13\\\\3^{rd}_g=Away+Home=8+7=15\\\\4^{th}_g=Away+Home=9+4=13\\\\\bar x=\frac{1}{n}\sum{x_i}=\frac{1}{10}(7+13+15+13)=4.8](https://tex.z-dn.net/?f=%5Cbar%20x%3D%5Cfrac%7B1%7D%7Bn%7D%5Csum%7Bx_i%7D%5C%5C1%5E%7Bst%20%7D_g%3DAway%2BHome%3D5%2B2%3D7%5C%5C%5C%5C2%5E%7Bnd%7D_g%3DAway%2BHome%3D4%2B9%3D13%5C%5C%5C%5C3%5E%7Brd%7D_g%3DAway%2BHome%3D8%2B7%3D15%5C%5C%5C%5C4%5E%7Bth%7D_g%3DAway%2BHome%3D9%2B4%3D13%5C%5C%5C%5C%5Cbar%20x%3D%5Cfrac%7B1%7D%7Bn%7D%5Csum%7Bx_i%7D%3D%5Cfrac%7B1%7D%7B10%7D%287%2B13%2B15%2B13%29%3D4.8)
Hence, the mean number of goals per quarter is 4.8 goals
c. To find the number of more home goals than away goals, we subtract from their summations as:
![g_m=\sum{g_h}-\sum{g_a}\\\\=(5+4+8+9)-(2+9+7+4)\\\\=26-22\\\\=4](https://tex.z-dn.net/?f=g_m%3D%5Csum%7Bg_h%7D-%5Csum%7Bg_a%7D%5C%5C%5C%5C%3D%285%2B4%2B8%2B9%29-%282%2B9%2B7%2B4%29%5C%5C%5C%5C%3D26-22%5C%5C%5C%5C%3D4)
Hence, there are 4 more home goals than away goals.
Answer:
224 with a remainder of 9