Answer:
= 6n - 4
Step-by-step explanation:
There is a common difference between consecutive terms in the sequence, that is
8 - 2 = 14 - 8 = 6
This indicates the sequence is arithmetic with n th term
= a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Here a₁ = 2 and d = 6 , thus
= 2 + 6(n - 1) = 2 + 6n - 6 = 6n - 4
Thus the formula representing the sequence is
= 6n - 4
Answer: x = 1/16
Step-by-step explanation:
Since the inverse of a Logarithm is an exponential function, we know that the final solution has to involve an exponential function somewhere in it.
1. log B(2) {x} = -4 || given
2. x = 2 ^ -4 || Logarithm rule that allows you to move the base of the logarithm to the base of the exponent on the other side. For example, if you had log B(5) {x} = 3, the base of 5 would move over to the other side and it would be raised to 3; x = 5^3.
3. x = (1) / (2^4) || Simplify. Use the negative exponent rule. This rule always leaves a numerator of 1, and a denominator of your exponent. In this case, it will be 2 ^ -4, so you will do 2^4 which is 16 and you will put that over 1. Resulting in your final answer of x = 1/16
Answer: 132
Step-by-step explanation:
The expression for the greatest common factor of 20 and 30 using the distributive property is 10(2 + 3)
Pounds of ice = 20
Number of cups = 30
The relation for the distributive property :
a × (b + c)
Expand ;
a × (b + c) = (a × b) + (a × c) = ab + ac
Finding the greatest common factor of 20 and 30 ;
(2 × 10) + (3 × 10)
According to the distributive property
(2 × 10) + (3 × 10) = 10(2 + 3)
Therefore, the expression for the greatest common factor is 10(2 + 3)
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