Considering the perimeter of the rectangle, we have that the length is of 9 inches and the width is of 55 inches.
<h3>What is the perimeter of a rectangle?</h3>
The perimeter of a rectangle of length l and width w is given as follows:
P = 2(l + w).
The length is an odd integer and the width is <u>5 times the next consecutive odd integer,</u> hence:
l = x, w = 5(x + 2).
The perimeter is of 128 inches, hence:
128 = 2l + 2w
128 = 2x + 10(x + 2)
128 = 2x + 10x + 20
12x = 108
x = 9.
Hence the length is of 9 inches and the width is of 55 inches.
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The quantity of the liquid in Richard's tank after 20 minutes will be 120 gallons and in Jason's tank will be 240 gallons.
<h3>What are gallons?</h3>
A gallon is a British unit which is used for the measurement of liquids that is equal to eight pints. In Britain, it is equal to about 4.546 litres. In America, it is equal to about 3.785 litres.
It is given in the question that:-
Richard fills his pool at a rate of 6 gallons per minute.
Jason's pool already contains 200 gallons, and he fills it at a rate of 2 gallons per minute.
After 20 minutes the amount of liquid in the tank will be:-
For Richard = 6 gallons per minute. x 20 minutes= 120 gallons
For Jason= 2 gallons per minute x 20 =40 gallons
Jason has 200 gallons already in the tank
So it will become = 200+24=240 gallons.
Hence quantity of the liquid in Richard's tank after 20 minutes will be 120 gallons and in Jason's tank will be 240 gallons.
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The Lowest common multiple of 22 and 44 would be 22 because each of the numbers are divisible by it. So 22 / 22 = 1 and 44 / 22 = 2
The equation of the line containing (- 4,5) and perpendicular to the line 5x - 3y = 4 is y = -3 / 5 x + 13 / 5
<h3>How to find the equation of a line?</h3>
The equation of a line can be represented as follows:
y = mx + b
where
Therefore, the equation passes through (-4, 5) and perpendicular to 5x - 3y = 4
Hence,
perpendicular lines follows the rule below:
m₁m₂ = -1
Hence,
5x - 3y = 4
5x - 4 = 3y
y = 5/ 3 x - 4 / 3
m₁ = 5 / 3
5/3 m₂ = -1
m₂ = - 3 / 5
Hence,
using (-4, 5)
5 = - 3 / 5 (-4) + b
5 = 12 / 5 + b
b = 5 - 12 / 5 = 25 - 12 /5 = 13 / 5
Therefore,
y = -3 / 5 x + 13 / 5
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