Which equation can be solved using the expression (-3)+-/(3)^2+4(10)(2) divided by 2(10) for x? a)10x2 = 3x + 2 b)2 = 3x + 10x2 c)3x = 10x2 – 2 d)10x2 + 2 = –3x

B

Step-by-step explanation:

is a quadratic formula where a = 10, b = 3, and c = -2

⇒ 10x² + 3x - 2 = 0

Now let's look at the options provide and put them in standard form:

a) 10x² = 3x + 2

   10x² - 3x - 2 = 0

This is NOT the same as our answer above

b) 2 = 3x + 10x²

   0 = 10x² + 3x - 2

This IS the same as our answer above!!!

No need to check C and D because we already found the answer.

there are lots of ways.   pick's theorem tells us if the vertices are lattice points the area a is

a = b/2 + i - 1

where b is the number of boundary lattice points and i is the number of interior lattice points.

in the figure i count b=16, i=50 so

a = 8 + 50 - 1 = 57

let's try the shoelace formula.   the area is half the sum of the cross products of the sides.  

a(-2,6)   -2(2)-6(-5) = 26

b(-5,2)   -5(-3) - 2(-2) = 19

c(-2,-3) -2(-3) - (-3)(4) = 18

d(4,-3)   4(3) - (-3)(5) = 27

e(5,3)   5(3) - 3(1) = 12

f(1,3)     1(6) - 3(-2) = 12

a(-2,6)

each of the cross products is twice the area of the triangle with the associated side and one vertex the origin. so the area of abo=26/2=13.

area = (1/2) (26 + 19 +   18 + 27 + 12 + 12) = 57

that checks!