How long is the shorter side of a rectangle when one side is 2 times longer then the other and the area is 15?
1 answer:
You might be interested in
Answer:
The slope is 3.
Step-by-step explanation:
A direct variation function will always go through the origin point (0, 0).
Therefore, we have the two points (0, 0) and (-2, -6).
We can use the slope formula to find the slope:
Substitute and evaluate:
Therefore, the slope of the function is 3.
To graph, simply plot (0, 0) and (-2, -6) and draw a line connecting them. This is shown below.
Find the powers
$a^{2}=5+2 \sqrt{6}$
$a^{3}=11 \sqrt{2}+9 \sqrt{3}$
The cubic term gives us a clue, we can use a linear combination to eliminate the root 3 term $a^{3}-9 a=2 \sqrt{2}$ Square $\left(a^{3}-9 a\right)^{2}=8$ which gives one solution. Expand we have $a^{6}-18 a^{4}-81 a^{2}=8$ Hence the polynomial $x^{6}-18 x^{4}-81 x^{2}-8$ will have a as a solution.
Note this is not the simplest solution as $x^{6}-18 x^{4}-81 x^{2}-8=\left(x^{2}-8\right)\left(x^{4}-10 x^{2}+1\right)$
so fits with the other answers.