This ones a bit of a trick question, since whether the integers are even or odd doesn't really matter. What does matter, is that consecutive odd integers are 2 numbers apart (as are consecutive even integers).
So again, if the first of the odd integers is the variable n
the consecutive odd integers after it can be written as:
n+2 , n+4, etc...
So the sum of four consecutive odd integers can be written as:
sum = n + (n+2) + (n+4) + (n+6)
Simplify:
sum = 4n + 12
And finally rearrange to solve for n:
= n
This can also be written as:
- 3 = n
Whichever way you prefer.
It is 7 thousand and a bunch of random numbers
Answer:
y = 3
x = 1
y = 1.5
x = 2
Step-by-step explanation:
For the first x point, look at the graph where x is 0. When x is 0, y is 3. So the first one is 3. For the second one, there is a point on the graph where y is 4. Where y is 4, x is 1, so you the second answer is 1. For the third one, find the y point where x is -1. At the x value, -1, y is 1.5. For the last one, where y is 5, x is 2.
(x+y=31)2
2x-y=11
2x+2y=62
- 2x -y=11
3y=51
y=17
x+17=31
x=14
y-x=3
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>
