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:
k = 5
Step-by-step explanation:
The standard form of an equation representing proportionality is
y = kx ← k is the constant of proportionality
y = 5x ← is in standard form
with k = 5
X = short section of rope
4x = longer section of rope
x + 4x = 25
5x = 25
x = 5
…or in other words the shorter piece of rope is 5 feet long
Answer: 1,2 and 4
Step-by-step explanation:
factors of 12 are : 1,2,3,4,6,12
factors of 28 are :1,2,4,7,14,28
commom factors are= 1,2,4
1 yard is 3ft, so just multiply 2.5 with 3 and that gives u 7.5.
