What is the relation between the variables in the equation a=lw? a. a varies directly as lw b. a varies jointly as lw c. a varies inversely as lw d. none of the above

Option b is correct.

The relation between the variables in the equation A=lw is;

A varies jointly as lw.

Explanation:

Variation problems states that involves a simple relationships or formulas, involving one variable being equal to one term.

Joint variation: If y varies jointly with respect to a and b,then the equation will be of the form y = kab where k is the constant.

Given the equation: A = lw.

Since, this equation would be the formula of area of rectangle with length l and width w.

If we change the width(w) of the rectangle, then the area changes(A),

Similarly, if we change the length(l) of the rectangle then the area(A) will also change.

Therefore, by the definition of Joint variation;

We can say that the area(A) of the rectangle varies jointly with the length and the width of the rectangle i.e,  A varies jointly as lw.

simplifying

5(x + -6) = 2(x + 3)

reorder the terms:

5(-6 + x) = 2(x + 3)

(-6 * 5 + x * 5) = 2(x + 3)

(-30 + 5x) = 2(x + 3)

reorder the terms:

-30 + 5x = 2(3 + x)

-30 + 5x = (3 * 2 + x * 2)

-30 + 5x = (6 + 2x)

solving

-30 + 5x = 6 + 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.

-30 + 5x + -2x = 6 + 2x + -2x

combine like terms: 5x + -2x = 3x

-30 + 3x = 6 + 2x + -2x

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

-30 + 3x = 6 + 0

-30 + 3x = 6

add '30' to each side of the equation.

-30 + 30 + 3x = 6 + 30

combine like terms: -30 + 30 = 0

0 + 3x = 6 + 30

3x = 6 + 30

combine like terms: 6 + 30 = 36

3x = 36

divide each side by '3'.

x = 12

simplifying

x = 12

this should .

answer: h=5.6 i don't really know how to put into words, so i though i would let you do that. i hope i was able to some

step-by-step explanation:

18 = 6(h)+1/2

18 = 6h+1/2

18-1 = 6h/2

17 = 3h

17/3 = h

h = 5.6