The area of a rectangle is 54x^9 y^8 square yards. if the length of the rectangle is 6x^3 y^4 which expression represents the width of the rectangle in yards?

jack knows a=l*w, so he writes the following equation:
54x^9 y^8= 6x^3 y^4*w
he divides both sides by the length:
(54x^9 y^8)/(6x^3 y^4 )=9 x^12 y^12

error:

correct solution:

➷ Error: When he divided both sides by the length, he didn't subtract the exponents. Instead on subtracting the exponents, he added them - which is incorrect.

Correct solution: 54x^9 y^8 / 6x^3 y^4 = 9x^6 y^4

The width is 9x^6 y^4

(This is based on the rule that when you divide values with exponents, you have to subtract the exponents)

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Error: He added the exponents of the variables. The exponents must be subtracted.

Correct solution:

Step-by-step explanation:

According the quotient property of exponents, when you divide two powers with equal base, you must subtract the exponents.

Therefore, keeping the property above on mind, you have:

Therefore, you have that the width of the rectangle is the shown below:

it would take 7/10 of an hour too fill the pool.

step-by-step explanation:

the system of inequalities is

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

the equation of the dashed line is

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

the equation of the solid line is

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

step 3

the system of inequalities is