Y=5x+42
subtract 5x from both sides
-5x+y=42
multiply by -1
5x-y=-42
In standard form, Ax+By=C, the variable A cannot be a negative. However, this is not an option so go with c.
the key is to write
as
which can be easily seen as an area of a rectangle with one side length n and the other (n+1). That explains the rectangle made of dots - 3 x 4
Now you only have half of them because of the 1/2. So that explains the lower "triangle" of dots being greyed out - they do not count in the area (upper triangle). So the count of the dark dots corresponds to the original expression.
For n=5 you can draw a similar rectangular matrix with 5 x 6 dots. And count only the upper triangular part.
Answer:
![2\sqrt{5}](https://tex.z-dn.net/?f=%202%5Csqrt%7B5%7D%20)
Step-by-step explanation:
Use the distance formula.
Subtract the x-coordinates and square the difference.
3 - 7 = -4; (-4)^2 = 16
Subtract the y-coordinates and square the difference.
4 - 2 = 2; 2^2 = 4
Add the differences and take the square root of the sum.
16 + 4 = 20; sqrt(20) = sqrt(4 * 5) = 2sqrt(5)
distance = 2sqrt(5)
You can use the distance formula which does the same thing.
![d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}](https://tex.z-dn.net/?f=%20d%20%3D%20%5Csqrt%7B%28x_2%20-%20x_1%29%5E2%20%2B%20%28y_2%20-%20y_1%29%5E2%7D%20)
![d = \sqrt{(7 - 3)^2 + (2 - 4)^2}](https://tex.z-dn.net/?f=%20d%20%3D%20%5Csqrt%7B%287%20-%203%29%5E2%20%2B%20%282%20-%204%29%5E2%7D%20)
![d = \sqrt{(4)^2 + (-2)^2}](https://tex.z-dn.net/?f=%20d%20%3D%20%5Csqrt%7B%284%29%5E2%20%2B%20%28-2%29%5E2%7D%20)
![d = \sqrt{16 + 4}](https://tex.z-dn.net/?f=%20d%20%3D%20%5Csqrt%7B16%20%2B%204%7D%20)
![d = \sqrt{20}](https://tex.z-dn.net/?f=%20d%20%3D%20%5Csqrt%7B20%7D%20)
![d = \sqrt{4 \times 5}](https://tex.z-dn.net/?f=%20d%20%3D%20%5Csqrt%7B4%20%5Ctimes%205%7D%20)
![d = \sqrt{4} \times \sqrt{5}](https://tex.z-dn.net/?f=%20d%20%3D%20%5Csqrt%7B4%7D%20%5Ctimes%20%5Csqrt%7B5%7D%20)
![d = 2\sqrt{5}](https://tex.z-dn.net/?f=%20d%20%3D%202%5Csqrt%7B5%7D%20)
A. 41 + 16=57 40+17= 57
b. 79 + 14=93 80+13= 93
c. 580+355=935 600+335=935
d. 174+620=794 194+600=794
e. 378+210=588 388+200=588
Here you go, hope this helps! :)
Answer:
this is the answer please give brainliest