In the figure below, $\triangle ZAX$ is equilateral and has perimeter $30$.

What is the exact area of the quadrilateral $FLAX$? Explain how you determined your answer.

[asy]
pair f=(0,sqrt(3)); pair l=(2,sqrt(3)); pair a=(2,0); pair x=(0,0);
pair z=(f+l)/2;
dot(f); dot(l); dot(a); dot(x); dot(z);
draw(x--f--l--a--x--z--a);
draw(rightanglemark(x, f,l,5));
draw(rightanglemark(f, l,a,5));
draw(rightanglemark(l, a,x,5));
draw(rightanglemark(a, x,f,5));
label("$F$",f, NW);
label("$Z$",z, N);
label("$L$",l, NE);
label("$A$",a, SE);
label("$X$",x, SW);
[/asy]

d, x=8

step-by-step explanation:

simplifying

4x + -5 = 2x + 11

reorder the terms:

-5 + 4x = 2x + 11

reorder the terms:

-5 + 4x = 11 + 2x

solving

-5 + 4x = 11 + 2x

solving for variable 'x'.

move all terms containing x to the left, all other terms to the right.

add '-2x' to each side of the equation.

-5 + 4x + -2x = 11 + 2x + -2x

combine like terms: 4x + -2x = 2x

-5 + 2x = 11 + 2x + -2x

combine like terms: 2x + -2x = 0

-5 + 2x = 11 + 0

-5 + 2x = 11

add '5' to each side of the equation.

-5 + 5 + 2x = 11 + 5

combine like terms: -5 + 5 = 0

0 + 2x = 11 + 5

2x = 11 + 5

combine like terms: 11 + 5 = 16

2x = 16

divide each side by '2'.

savings account is an account only used for saving money. this acts as an emergency source of funding for an individual. answer a would result in the money in his account to grow as it specifically states that interest is compounded daily at the rate of 2%

step-by-step explanation:

the battle of gettysburg is considered the "high water mark" of the confederacy because it marked the greatest advance of the confederate forces against the union.

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