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3 years ago

The area of rectangle ABCD is 9 cm2 show that x2 +5x=3

Mathematics

1 answer:

Anastasy [175]3 years ago

4 0

Answer: x² + 5x = 3

Step-by-step explanation:Step-by-step explanation:

The rectangle has been divided into a square and three rectangles.

The area of

a square = (x)(x) = x²

a rectangle #1 = (2)(x) = 2x

a rectangle #2 = (3)(x) = 3x

a rectangle #3 = (2)(3) = 6

The area of a large rectangle is the sum of the square area and three rectangles, and is 9 cm². Therefore we have the equation:

x² + 2x + 3x + 6 = 9 subtract 6 from both sides

x² + 5x + 6 - 6 = 9 - 6

x² + 5x = 3

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A large koi pond is filled from a garden hose at the rate of 12 gal/min. Initially, the pond contains 200 gal of water.

Semmy [17]

a) The linear function that models the amount of water after t minutes is given by:

$V(t) = 200 + 12t$

b) It takes 92 minutes to completely fill the pond.

Item a:

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Filled at a rate of 12 gallons per minute, thus the linear function has a slope of 12.

Then, the function is:

$V(t) = 200 + 12t$

Item b:

It takes t minutes to fill the pond, t is found for which:

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