In a basketball game, a regular basket was worth 2 points and a long-distance basket was worth 3 points. If there were 45 basket
1 answer:
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Answer:
Proved (See Explanation)
Step-by-step explanation:
Show that 3ⁿ⁺⁴ - 3ⁿ is divisible by 16.
This is done as follows
From laws of indices;
aᵐ⁺ⁿ = aᵐ * aⁿ.
So, 3ⁿ⁺⁴ can be written as 3ⁿ * 3⁴.
becomes
Factorize
3ⁿ * 5
5(3ⁿ)
<em>The expression can not be further simplified.</em>
<em>However, we can conclude that when 3ⁿ⁺⁴ - 3ⁿ is divisible by 16, because 5(3ⁿ) is a natural whole number as long as n is a natural whole number.</em>
Given Equation:
Let us remove parenthesis first.
In order to remove parenthesis, we need to distribute -4 over parenthesis (2/3 h -3).
Distributing -4 over (2/3 h -3), we get,
-4*2/3 h - 4*-3 = -8/3 h + 12.
Substituting this value in original equation, we get
Now, in order to make the equation easy to solve, we always remove fractions. In order to remove fraction, we need to find the lowest common denominator of all terms(lcd).
The fraction terms has 3 in denominators, so we could multiply each and every term by 3 to remove 3's from denominators.
Multiplying each equation by 3, we get,
On simplfying this step, we get
Combining like terms on left side, we get
-7h +36 = 2h -18.
Subtracting 36 from both sides, we get
-7h +36 -36= 2h -18-36.
-7h=2h-54
Subtracting 2h from both sides, we get
-7h-2h=2h-54-2h
-9h = -54
Dividing both sides by -9.
-9h/-9 = -54/-9
h = 6.
Therefore, final answer is h=6.