Answer: There are 7,677 streets named as " First Street" and 7, 189 streets named as "Main Street" .
Step-by-step explanation:
Let x be the number of streets named as First Street .
y be the number of streets named as Main Street.
AS per the given information, we have the following system of equations :
![x+y=14866-------------(1)\\\\x=488+y-------------(2)](https://tex.z-dn.net/?f=x%2By%3D14866-------------%281%29%5C%5C%5C%5Cx%3D488%2By-------------%282%29)
Substitute the value of x from (2) in (1) , we get
![488+y+y=14866\\\\ 2y =14866- 488\\\\ 2y=14378\\\\ y=7189](https://tex.z-dn.net/?f=488%2By%2By%3D14866%5C%5C%5C%5C%202y%20%3D14866-%20488%5C%5C%5C%5C%202y%3D14378%5C%5C%5C%5C%20y%3D7189)
Put value of y in (2), we get
![x=488+7189=7677](https://tex.z-dn.net/?f=x%3D488%2B7189%3D7677)
Hence , there are 7,677 streets named as " First Street" and 7, 189 streets named as "Main Street" .
Answer: x= acb/11 + 32/11
Step-by-step explanation:
Solve for x by simplifying both sides of the equation, then isolating the variable.
Answer:
![3x^2-10x+8=(x-x_1)(x-x_2)=(x-2)(x-\frac{4}{3})](https://tex.z-dn.net/?f=3x%5E2-10x%2B8%3D%28x-x_1%29%28x-x_2%29%3D%28x-2%29%28x-%5Cfrac%7B4%7D%7B3%7D%29)
Step-by-step explanation:
The general form of a quadratic polynomial is given by:
(1)
You have the following polynomial:
(2)
In order to complete the factorization you can use the quadratic formula, to obtain the roost of the polynomial. The quadratic formula is given by:
(3)
By comparing the equation (1) with the equation (2) you obtain:
a = 3
b = -10
c = 8
Then, you replace these values in the equation (3):
![x_{1,2}=\frac{-(-10)\pm \sqrt{(-10)^2-4(3)(8)}}{2(3)}\\\\x_{1,2}=\frac{10\pm2}{6}\\\\x_1=2\\\\x_2=\frac{4}{3}](https://tex.z-dn.net/?f=x_%7B1%2C2%7D%3D%5Cfrac%7B-%28-10%29%5Cpm%20%5Csqrt%7B%28-10%29%5E2-4%283%29%288%29%7D%7D%7B2%283%29%7D%5C%5C%5C%5Cx_%7B1%2C2%7D%3D%5Cfrac%7B10%5Cpm2%7D%7B6%7D%5C%5C%5C%5Cx_1%3D2%5C%5C%5C%5Cx_2%3D%5Cfrac%7B4%7D%7B3%7D)
Then, the factorization of the polynomial is:
![3x^2-10x+8=(x-x_1)(x-x_2)=(x-2)(x-\frac{4}{3})](https://tex.z-dn.net/?f=3x%5E2-10x%2B8%3D%28x-x_1%29%28x-x_2%29%3D%28x-2%29%28x-%5Cfrac%7B4%7D%7B3%7D%29)