Answer:
A. 15, 20, and 25
Step-by-step explanation:
Note that 3-4-5 is a pythagorean triple via following:
Dividing 15, 20, and 25 by 5 nets you the pythagorean triple 3-4-5.
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Answer:
33.75 cubic inches of styrofoam can be placed inside the container.
Step-by-step explanation:
Based on given information, the volume of the prism (), in cubic inches, is determined by using this formula:
(1)
Where:
- Base of the triangular face, in inches.
- Height of the triangular face, in inches.
- Length of the prism, in inches.
If we know that ,
and
, then the volume of the prism is:
33.75 cubic inches of styrofoam can be placed inside the container.
Given:
The sequence is:
To find:
The formula for the nth term in the given sequence.
Solution:
We have,
The given sequence can be written as
The sign are alternative and the absolute value of each term can be defined by the expression , where n is a natural number.
So, the required formula is:
Therefore, the formula for nth term in the given sequence is .
Answer:
see explanation
Step-by-step explanation:
Given
9 - 225
← factor out 9 from each term
= 9( - 25
) ← difference of squares
Difference of squares factors in general as
a² - b² = (a - b)(a + b)
= (x² )² ⇒ a = x²
25 = (5
)² ⇒ b = 5
Hence
- 25
= ( -5
)(
+ 5
)
Thus
9 - 225
= 9 ( - 5
)(
+ 5
)