We can rearrange 3x+y=9 to look more conventional by subtracting 3x from both sides and making it y= -3x+9.
Now we want to find a line that is parallel to this and goes through the point (0,-4). We know that -3 is the slope. With this in mind, if we want the other line to be parallel then it must have the same slope so that they never intersect. This gives us one of the numbers we need for the second line.
This means our second equation is looking like; y= -3x+b. This means we need to find b (the y-intercept) but we are also given a point it must go through and this is (0,-4). We simply plug this in into our new equation we need to solve and we get ; -4 = -3(0) + b . "since 0 is the x and -4 is the y" . From this we get that b= -4. This means the equation of a line parallel is:
y = -3x-4
Answer:
I need more context then that but if its simply measured thats about an inch
Step-by-step explanation:
Answer:
Step-by-step explanation:
Part of the money spent = Part of money spent on clothes + part of money spent on books
![=\frac{1}{3}+\frac{1}{4}\\\\=\frac{1*4}{3*4}+\frac{1*3}{4*3}\\\\=\frac{4}{12}+\frac{3}{12}\\\\=\frac{4+3}{12}\\\\=\frac{7}{12}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B1%7D%7B3%7D%2B%5Cfrac%7B1%7D%7B4%7D%5C%5C%5C%5C%3D%5Cfrac%7B1%2A4%7D%7B3%2A4%7D%2B%5Cfrac%7B1%2A3%7D%7B4%2A3%7D%5C%5C%5C%5C%3D%5Cfrac%7B4%7D%7B12%7D%2B%5Cfrac%7B3%7D%7B12%7D%5C%5C%5C%5C%3D%5Cfrac%7B4%2B3%7D%7B12%7D%5C%5C%5C%5C%3D%5Cfrac%7B7%7D%7B12%7D)
7/12 part of her money was spent
Option D:
![\left(y^{2}+3 y+7\right)\left(8 y^{2}+y+1\right)=8 y^{4}+25 y^{3}+60 y^{2}+10y+7](https://tex.z-dn.net/?f=%5Cleft%28y%5E%7B2%7D%2B3%20y%2B7%5Cright%29%5Cleft%288%20y%5E%7B2%7D%2By%2B1%5Cright%29%3D8%20y%5E%7B4%7D%2B25%20y%5E%7B3%7D%2B60%20y%5E%7B2%7D%2B10y%2B7)
Solution:
Given expression is
.
<u>To find the product of the expression:</u>
![\left(y^{2}+3 y+7\right)\left(8 y^{2}+y+1\right)](https://tex.z-dn.net/?f=%5Cleft%28y%5E%7B2%7D%2B3%20y%2B7%5Cright%29%5Cleft%288%20y%5E%7B2%7D%2By%2B1%5Cright%29)
Multiply each term of the first term with each term of the 2nd term.
![=y^{2}\left(8 y^{2}+y+1\right) +3 y\left(8 y^{2}+y+1\right) +7\left(8 y^{2}+y+1\right)](https://tex.z-dn.net/?f=%3Dy%5E%7B2%7D%5Cleft%288%20y%5E%7B2%7D%2By%2B1%5Cright%29%20%2B3%20y%5Cleft%288%20y%5E%7B2%7D%2By%2B1%5Cright%29%20%2B7%5Cleft%288%20y%5E%7B2%7D%2By%2B1%5Cright%29)
Using the exponent rule: ![a^m \cdot a^n = a^{m+n}](https://tex.z-dn.net/?f=a%5Em%20%5Ccdot%20a%5En%20%3D%20a%5E%7Bm%2Bn%7D)
![=\left(8 y^{4}+y^3+y^2\right) +\left(24 y^{3}+3y^2+3y\right) +\left(56 y^{2}+7y+7\right)](https://tex.z-dn.net/?f=%3D%5Cleft%288%20y%5E%7B4%7D%2By%5E3%2By%5E2%5Cright%29%20%2B%5Cleft%2824%20y%5E%7B3%7D%2B3y%5E2%2B3y%5Cright%29%20%2B%5Cleft%2856%20y%5E%7B2%7D%2B7y%2B7%5Cright%29)
![=8 y^{4}+y^3+y^2+24 y^{3}+3y^2+3y+56 y^{2}+7y+7](https://tex.z-dn.net/?f=%3D8%20y%5E%7B4%7D%2By%5E3%2By%5E2%2B24%20y%5E%7B3%7D%2B3y%5E2%2B3y%2B56%20y%5E%7B2%7D%2B7y%2B7)
Arrange the terms with same power.
![=8 y^{4}+y^3+24 y^{3}+y^2+3y^2+56 y^{2}+7y+3y+7](https://tex.z-dn.net/?f=%3D8%20y%5E%7B4%7D%2By%5E3%2B24%20y%5E%7B3%7D%2By%5E2%2B3y%5E2%2B56%20y%5E%7B2%7D%2B7y%2B3y%2B7)
![=8 y^{4}+25 y^{3}+60 y^{2}+10y+7](https://tex.z-dn.net/?f=%3D8%20y%5E%7B4%7D%2B25%20y%5E%7B3%7D%2B60%20y%5E%7B2%7D%2B10y%2B7)
Hence option D is the correct answer.
![\left(y^{2}+3 y+7\right)\left(8 y^{2}+y+1\right)=8 y^{4}+25 y^{3}+60 y^{2}+10y+7](https://tex.z-dn.net/?f=%5Cleft%28y%5E%7B2%7D%2B3%20y%2B7%5Cright%29%5Cleft%288%20y%5E%7B2%7D%2By%2B1%5Cright%29%3D8%20y%5E%7B4%7D%2B25%20y%5E%7B3%7D%2B60%20y%5E%7B2%7D%2B10y%2B7)