Let $abcd$ be a convex quadrilateral, and let $p$, $q$, $r$, $s$, $t$, $u$, $v$, and $w$ be the trisection points of the sides of $abcd$, as shown. [asy] unitsize(1 cm); pair a, b, c, d, p, q, r, s, t, u, v, w; a = (1,2); b = (4,3); c = (5,-1); d = (0,0); p = (2*a + b)/3; q = (a + 2*b)/3; r = (2*b + c)/3; s = (b + 2*c)/3; t = (2*c + d)/3; u = (c + 2*d)/3; v = (2*d + a)/3; w = (d + 2*a)/3; fill(a--q--r--c--u--v--cycle, gray(0.7)); draw(a--b--c--d--cycle); draw(q--r); draw(u--v); dot("$a$", a, nw); dot("$b$", b, ne); dot("$c$", c, se); dot("$d$", d, sw); dot("$p$", p, n); dot("$q$", q, n); dot("$r$", r, e); dot("$s$", s, e); dot("$t$", t, dir(270)); dot("$u$", u, dir(270)); dot("$v$", v, nw); dot("$w$", w, nw); [/asy] if the area of quadrilateral $abcd$ is 180, then find the area of hexagon $aqrcuv$.

a.   we have two

lines:   y = 4-x   and  

y = 8-x^-1

given two simultaneous equations that are both to be

true, then the solution is the points where the lines cross. the intersection is

where the two equations are equal. therefore the solution that works for both

equations is when

4-x = 8-x^-1

this is where the two lines will cross and that is the

common point that satisfies both equations.

b.   4-x = 8-x^-1

  x           4-x       8-x^-1

-3           7        

8.33

-2           6         8.5

-1           5         9

  0           4        

-

  1           3        

7

  2           2        

7.5

  3           1         7.67

the table shows that none of the x values from -3 to 3 is

the solution because in no case does

4-x = 8-x^-1

to find the solution we need to rearrange the equation to

find for x:

4-x = 8-x^-1

multiply both sides with x:

4x-x^2 = 8x-1

x^2+4x-1=0

x= -4.236, 0.236

therefore there are two points that satisfies the

equation.

find y:  

x=-4.236

y = 4-x   = 4 – (-4.236)

= 8.236

y = 8-x^-1 =   .236)^-1

= 8.236

x=0.236

  y = 4-x   = 4 – (0.236) = 3.764

y = 8-x^-1 =   8-(0.236)^-1

= 3.764

thus the two lines cross at 2 points:

(-4.236, 8.236) & (0.236, 3.764)

c.   to solve

graphically the equation 4-x = 8-x^-1

we would graph both lines: y = 4-x   and   y

= 8-x^-1

the point on the graph where the lines cross is the

solution to the system of equations.

just graph the points on part b on a cartesian coordinate

system and extend the two lines.   the

solution is, as stated, the point where the two lines cross on the graph.

step-by-step explanation:

mark brainliest!

answer: c.  

step-by-step explanation:

mixtures containing substances that get attracted to magnet can be separated using a magnet. we can separate iron from a mixture of sand and iron, as only iron attracts to the magnet.

this is the formula: v = the value of investment at the end of the time period

p = the principal amount (the initial amount invested)

r = the annual interest rate

n = the annual frequency of compounding (how many times a year interest is added)

t = the number of years the money is invested

^ means raise to the power of