That point will be where the perpendicular line through the origin intersects the given line.
.. (-1/4)x = 4x +3
.. -3 = (17/4)x
.. -12/17 = x
The point on the given line that is closest to the origin is (-12/17, 3/17).
Answer:
x=15
Step-by-step explanation:
The given equation is
![-2x+4=-\frac{1}{3}x-21](https://tex.z-dn.net/?f=-2x%2B4%3D-%5Cfrac%7B1%7D%7B3%7Dx-21)
Here the variable is x and the terms with the variable are ![-2x \;and\; -\frac{1}{3}x.](https://tex.z-dn.net/?f=-2x%20%5C%3Band%5C%3B%20-%5Cfrac%7B1%7D%7B3%7Dx.)
Keep all the terms having variable on one side and all the constants terms on the other side as
![-2x+\frac{1}{3}x=-21 -4](https://tex.z-dn.net/?f=-2x%2B%5Cfrac%7B1%7D%7B3%7Dx%3D-21%20-4)
Now, simplify the above equation to get the value of x as
![-\frac{5}{3}x=-25 \\\\\Rightarrow \frac{5}{3}x=25 \\\\\Rightarrow x=\frac{25\times3}{5} \\\\\Rightarrow x=15 \\\\](https://tex.z-dn.net/?f=-%5Cfrac%7B5%7D%7B3%7Dx%3D-25%20%5C%5C%5C%5C%5CRightarrow%20%5Cfrac%7B5%7D%7B3%7Dx%3D25%20%5C%5C%5C%5C%5CRightarrow%20x%3D%5Cfrac%7B25%5Ctimes3%7D%7B5%7D%20%5C%5C%5C%5C%5CRightarrow%20x%3D15%20%20%5C%5C%5C%5C)
In this way, the value of x is 15.
A sequence of
![n](https://tex.z-dn.net/?f=n)
nucleotides would have
![32^n](https://tex.z-dn.net/?f=32%5En)
possibilities. To exclude repetitions, we count the number of combinations:
<span>Step 1: 1.125 = 1 125⁄1000</span><span> </span>
<span>Step 2: Simplify 1 125⁄1000 = 1 1⁄8</span><span> </span>
<span>
</span>
Answer:
$17
Step-by-step explanation:
initial cost + hourly rate (number of hours)
$5 + $3 x 4
$5 + $12
= $17