The perimeter of a rectangle is (8x + 7y) feet, give two possible dimensions of the rectangle
1 answer:
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Answer:
x = 4
Step-by-step explanation:
Since the triangle is right use Pythagoras' identity to solve for x
The square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is
(x + 3)² + (4(x + 2))² = 25² ← expand parenthesis on left side
x² + 6x + 9 + 16(x+ 2)² = 625
x² + 6x + 9 + 16(x² + 4x + 4) = 625
x² + 6x + 9 + 16x² + 64x + 64 = 625 ← simplify left side
17x² + 70x + 73 = 625 ( subtract 625 from both sides )
17x² + 70x - 552 = 0 ← in standard form
with a = 17, b = 70, c = - 552
Using the quadratic formula to solve for x
x = ( - 70 ± ) / 34
= ( - 70 ± ) / 34
= - 70 ± ) / 34
= - 70 ± 206 ) / 34
x = = - 8.1176....
or x = = 4
However, x > 0 ⇒ x = 4
Hence
x + 3 = 4 + 3 = 7 and
4(4 + 2) = 24
The triangle is a 7- 24- 25 right triangle
Answer:
Step-by-step explanation:
Let d represent the rate of temperature decrease in degrees Celsius per day from Monday to Thursday.
As temperature decreased at a constant rate in the next 3 days, so the rate of temperature will decrease 3d degree Celsius in 3 days.
We are told that the pool was open on Monday. The high temperature was on Monday. So the decrease in temperature from Monday to Thursday will be
.
We have been given that the swimming pool is open when the high temperature is higher than .
As the pool was closed on Thursday. This means that temperature on Thursday was less than or equal to 20 degree Celsius. We can represent this information in an inequality as:
Therefore, the inequality can be used to determine the rate of temperature decrease in degrees Celsius per day, d, from Monday to Thursday.