Hi there! The answer is g(x) = 4^x.
The function g(x) is an exponential function, and these functions grow faster than linear or quadratic formulas.
Hello :
all n in N ; n(n+1)(n+2) = 3a a in N or : <span>≡ 0 (mod 3)
1 ) n </span><span>≡ 0 ( mod 3)...(1)
n+1 </span>≡ 1 ( mod 3)...(2)
n+2 ≡ 2 ( mod 3)...(3)
by (1), (2), (3) : n(n+1)(n+2) ≡ 0×1×2 ( mod 3) : ≡ 0 (mod 3)
2) n ≡ 1 ( mod 3)...(1)
n+1 ≡ 2 ( mod 3)...(2)
n+2 ≡ 3 ( mod 3)...(3)
by (1), (2), (3) : n(n+1)(n+2) ≡ 1×2 × 3 ( mod 3) : ≡ 0 (mod 3) , 6≡ 0 (mod)
3) n ≡ 2 ( mod 3)...(1)
n+1 ≡ 3 ( mod 3)...(2)
n+2 ≡ 4 ( mod 3)...(3)
by (1), (2), (3) : n(n+1)(n+2) ≡ 2×3 × 4 ( mod 3) : ≡ 0 (mod 3) , 24≡ 0 (mod3)
Step 1
<u>Find the slope of the given line</u>
we have

Isolate the variable y
Subtract
both sides


Divide by
both sides

the slope of the given line is

Step 2
Find the equation of the line that passes through the point
and is parallel to the given line
we know that
if two lines are parallel, then their slopes are equal
The equation of the line into point-slope form is equal to

we have

substitute in the equation


or 
therefore
<u>the answer is</u>
or

Hi there!

We are given the equation:
x² - 2y = 7
To verify if each ordered pair is apart of the function, we can plug in their respective x and y values:
1. (5)² - 2(8) = 7
25 - 16 = 9 ≠ 7. This is NOT correct.
2. (-1)² - 2(-3) = 7
1 + 6 = 7. This is correct.
3. (-4)² - 2(-11.5) = 7
16 + 23 = 39 ≠ 7. This is NOT correct.
4. (1.2)² - 2(-2.78) = 7
1.44 +5.56 = 7. This is correct.
Thus, only 1 and 4 are the correct answers.
In radical form, the shortest distance from ( -4 , 4 ) and the line y = -2x + 6 is
2√5 units.
Attached below is the calculation to arrive at the answer as well as a graph.