well, since we know that there are 180° in π radians, how many degrees will it be in 345°?
![\begin{array}{ccll} degrees&radians\\ \cline{1-2} 180&\pi \\ 345&x \end{array}\implies \cfrac{180}{345}~~ = ~~\cfrac{\pi }{x}\implies \cfrac{12}{23}~~ = ~~\cfrac{\pi }{x} \\\\\\ 12x=23\pi \implies x=\cfrac{23\pi }{12}](https://tex.z-dn.net/?f=%5Cbegin%7Barray%7D%7Bccll%7D%20degrees%26radians%5C%5C%20%5Ccline%7B1-2%7D%20180%26%5Cpi%20%5C%5C%20345%26x%20%5Cend%7Barray%7D%5Cimplies%20%5Ccfrac%7B180%7D%7B345%7D~~%20%3D%20~~%5Ccfrac%7B%5Cpi%20%7D%7Bx%7D%5Cimplies%20%5Ccfrac%7B12%7D%7B23%7D~~%20%3D%20~~%5Ccfrac%7B%5Cpi%20%7D%7Bx%7D%20%5C%5C%5C%5C%5C%5C%2012x%3D23%5Cpi%20%5Cimplies%20x%3D%5Ccfrac%7B23%5Cpi%20%7D%7B12%7D)
8x + 3y = 20.50
-
4x+5y=22.50
=
4x-2y=-2, so you have to divide each number by 2, then
2x-y=-1, so
-y=-1-2x /-1, y=1+2x, then replace it with one original equation like the first one for instance:
8x+3(1+2x)=20.50, then
8x+3+6x=20.50, then
14x=20.50-3
14x=17.5
x=1.25, then solve y:\
y=1+2*(1.25)
y=1+2.5
y=3.5,
So answer is x=1.25, and y=3.5
Answer:
The coordinates of M are (2,-8)
Step-by-step explanation:
The coordinates of the point that divides the line segment joining
to
in the ratio m:n is given by:
![(\frac{mx_2+nx_1}{m+n},\frac{my_2+ny_1}{m+n})](https://tex.z-dn.net/?f=%28%5Cfrac%7Bmx_2%2Bnx_1%7D%7Bm%2Bn%7D%2C%5Cfrac%7Bmy_2%2Bny_1%7D%7Bm%2Bn%7D%29)
If A is at (-4,-2) and B is at (4. -10) and the ratio is 3:1.
Then
![(\frac{3(4)+1(-4)}{3+1},\frac{3(-10)+1(-2)}{3+1})](https://tex.z-dn.net/?f=%28%5Cfrac%7B3%284%29%2B1%28-4%29%7D%7B3%2B1%7D%2C%5Cfrac%7B3%28-10%29%2B1%28-2%29%7D%7B3%2B1%7D%29)
![(\frac{8}{4},\frac{-32}{4})](https://tex.z-dn.net/?f=%28%5Cfrac%7B8%7D%7B4%7D%2C%5Cfrac%7B-32%7D%7B4%7D%29)
The coordinates of M are (2,-8)
A) x^2 +x -30 = 0 is factored by looking for two factors of 30 that differ by 1. We know ... 30 = 1*30 = 2*15 = 3*10 = 5*6The last two factors differ by 1, so we can factor the trinomial as (x +6)(x -5) = 0
b) The solutions are found by finding values of x that make these factors zero. The only way the product will be zero is if one or more of the factors is zero. x + 6 = 0 x = -6 . . . . . subtract 6
x - 5 = 0 x = 5 . . . . . add 5
The solutions are x = -6 or x = 5These are the values of x that will satisfy the equation (make it true). What they mean depends on the meaning of the variable and the situation the equation is a model of.