Raul has 56 bouncy balls
he puts the balls into red gift bags and green gift bags
so lets say he puts x number of balls into green gift bags
then we are told that he puts three times as many balls into red gift bags as he puts into green gift bags
so the number of balls he puts into red gift bags is - 3 * x = 3x
the total number of balls = 56
so we can write the following equation
x + 3x = 56
4x = 56
x = 56/4
x = 14
therefore the amount of balls he puts into green bags is - 14 balls
<h3>Answer: 14</h3>
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Work Shown:
Side note: The triangles are similar, which allows us to set up the proportion in step 1.
Answer:
Henry Clay believed that American democracy depended on “that great principle of compromise”. What did he mean? Do you agree? Why?12
Step-by-step explanation:
Principle: Law of Exponents - Combination of product to a power & power to a power. The first is when raising a product of two integers to a power, the power is distributed to each factor. In equation it is,
(xy)^a = (x^a)(y^a)
The latter is when raising the base with a power to a power, the base will remain the same and the powers will be multiplied. In equation it is,
(x^a)(x^b) = x^ab
Check:
f(x) = 5*(16)^.33x = 5*(8*2)^0.33x = 5*(8^0.33x)(2^0.33x) = 5*(2^x)*(2^0.33x) = 5*(2^1.33x)
f(x) = 2.3*(8^0.5x) = 2.3*(4*2)^0.5x = 2.3*(2^x)(2^0.5x) = 2.3*(2^1.5x)
f(x) = 81^0.25x = 3^x
f(x) = 0.75*(9*3)^0.5x = 0.75*(3^x)*(3^0.5x) = 0.75*3^1.5x
f(x) = 24^0.33x = (8*3)^0.33x = (2^x)*(3^0.33x)
Therefore, the answer is third equation.
<em>ANSWER: f(x) = 81^0.25x = 3^x</em>
Answer:
11.81
Step-by-step explanation:
5 1/4 per 20 min (1/3 of an hour)
5.25 (5 1/4) * 3 = 15.75 pounds per hour
$0.75 earned per pound
So, 15.75 * $0.75 = $11.81
