What is the prime factorization of -800?
1 answer:
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Answer:
The answer is True
Step-by-step explanation:
A <em>mathematical induction</em> consists in only 2 steps:
<u>First step</u>: Show the proposition is true for the first one valid integer number.
<u>Second step</u>: Show that if any one is true then the next one is true
Finally, if first step and second step are true, then the complete proposition is true.
So, given
First step: using and replacing n=2 (the first valid integer number >1)
As the result is an integer number, so the first step is true.
Second step: using any next number, , let it replace
As the First step is true, we know that
,
So let it replace in the previous expression
Finally
where the last expression is an integer number
So the second step is true, and the complete proposition is True
Answer:
Length of the shorter diagonal is 8.68 cm.
Step-by-step explanation:
Length of the side AB = 11 cm
Length of side BC = 5 cm
Angle between these sides, m∠ABC = 50°
By cosine rule in ΔABC,
AC² = AB² + BC² - 2AB.BC.cos B
AC² = (11)² + 5² - 2(11)(5)cos50°
AC² = 121 + 25 - 70.71
AC = √(75.29)
AC = 8.68 cm
By the property of parallelogram,
m∠B + m∠C = 180° [Interior consecutive angles]
50° + m∠C = 180°
m∠C = 130°
Similarly, In ΔBCD,
BD² = BC² + CD² - 2BC.CD.cos130°
BD² = (5)² + (11)² - 2(5)(11)cos130°
BD² = 25 + 121 + 70.71
BD² = 216.71
BD = 14.72 cm
Therefore, length of the shorter diagonal will be 14.72 cm.
