Answer:
![\frac{4\sqrt{6x}}{2x}](https://tex.z-dn.net/?f=%5Cfrac%7B4%5Csqrt%7B6x%7D%7D%7B2x%7D)
Explanation:
The problem we are given is
![4\sqrt{\frac{3}{2x}}](https://tex.z-dn.net/?f=4%5Csqrt%7B%5Cfrac%7B3%7D%7B2x%7D%7D)
We can write the square root of a fraction as a fraction with a separate radical for the numerator and denominator; this gives us
![4\times \frac{\sqrt{3}}{\sqrt{2x}}](https://tex.z-dn.net/?f=4%5Ctimes%20%5Cfrac%7B%5Csqrt%7B3%7D%7D%7B%5Csqrt%7B2x%7D%7D)
We can write the whole number 4 as the fraction 4/1; this gives us
![\frac{4}{1}\times \frac{\sqrt{3}}{\sqrt{2x}}\\\\=\frac{4\sqrt{3}}{\sqrt{2x}}](https://tex.z-dn.net/?f=%5Cfrac%7B4%7D%7B1%7D%5Ctimes%20%5Cfrac%7B%5Csqrt%7B3%7D%7D%7B%5Csqrt%7B2x%7D%7D%5C%5C%5C%5C%3D%5Cfrac%7B4%5Csqrt%7B3%7D%7D%7B%5Csqrt%7B2x%7D%7D)
We now need to "rationalize the denominator." This means we need to cancel the square root in the denominator. In order to do this, we multiply both numerator and denominator by √(2x); this is because squaring a square root will cancel it:
![\frac{4\sqrt{3}}{\sqrt{2x}}\times \frac{\sqrt{2x}}{\sqrt{2x}}\\\\=\frac{4\sqrt{3}\times \sqrt{2x}}{2x}](https://tex.z-dn.net/?f=%5Cfrac%7B4%5Csqrt%7B3%7D%7D%7B%5Csqrt%7B2x%7D%7D%5Ctimes%20%5Cfrac%7B%5Csqrt%7B2x%7D%7D%7B%5Csqrt%7B2x%7D%7D%5C%5C%5C%5C%3D%5Cfrac%7B4%5Csqrt%7B3%7D%5Ctimes%20%5Csqrt%7B2x%7D%7D%7B2x%7D)
When multiplying radicals, we can extend the radical over both factors:
![\frac{4\sqrt{3} \times \sqrt{2x}}{2x}\\\\=\frac{4\sqrt{3\times 2x}}{2x}\\\\=\frac{4\sqrt{6x}}{2x}](https://tex.z-dn.net/?f=%5Cfrac%7B4%5Csqrt%7B3%7D%20%5Ctimes%20%5Csqrt%7B2x%7D%7D%7B2x%7D%5C%5C%5C%5C%3D%5Cfrac%7B4%5Csqrt%7B3%5Ctimes%202x%7D%7D%7B2x%7D%5C%5C%5C%5C%3D%5Cfrac%7B4%5Csqrt%7B6x%7D%7D%7B2x%7D)
Answer:
x+12
Step-by-step explanation:
Answer:
y = 2x/3 + 0 for x < 0
y = -3x for x ≥ 0
Step-by-step explanation:
Blue line
line rises 2 units for each 3 units of run so slope is 2/3, intercept is 2
y = 2x/3 + 0 for x < 0
Red line
line falls 3 units for each 1 unit of run so slope is -3, y intercept is 0
y = -3x
Answer:
C
Step-by-step explanation:
The period of a sine function can be found by looking at the argument.
In the equation y = Sin (ax), ax is the argument, and period is 360/a.
For the function shown, y = Sin x, the period is 360/1 = 360. This means that the period is the number of months it takes to complete one cycle of the graph (take one point in the graph and run along the curve until the same point is reached).
<em>If we take January as the first point (y = 40) and run along until i come to same point, we are back to next years' January. Hence, the period is 12 months. </em><em>Answer choice C is right.</em>
Answer:
B. m![\geq 2\frac{1}{2}](https://tex.z-dn.net/?f=%5Cgeq%202%5Cfrac%7B1%7D%7B2%7D)
Step-by-step explanation:
![m\geq \frac{5}{2}](https://tex.z-dn.net/?f=m%5Cgeq%20%5Cfrac%7B5%7D%7B2%7D)