Answer:
slope= 3/2
Step-by-step explanation:
Answer: 13/6
Step-by-step explanation:
Based upon the previous sequence.
1.there is a constant decrease of two in the numerator
2. There is a constant increase of one in the denominator
to find the fourth number in the sequence I used One of the numbers from the previous to determine the answer.
17/4 — —> then I followed the pattern and determine what fraction 3 was . . before it was converted into a whole number.
which would be 15/5 —> Now considering equations that are written like this also mean division, because in this case division is possible the answer would be 3, which would make the whole number 3 instead of 15/3. considering it was an improper fraction.
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Now If 15/5 wasn’t converted into 3, The answer to the sequence would be 13/6. If you follow the pattern like I said before there is a certain amount of increase and decrease so 13/6 will be your answer. The only reason is not a whole number because 13 can’t be divided by six to get a whole number.
Answer:
The last one (x,y)->(x+3,y+5)
Step-by-step explanation:
Whenever you move the x coordinate it’s the opposite, for example translated 3 units the the left is +3 and translated 3 units to the right is -3.
Whenever you move the y coordinate it’s normal so up 5 units means +5 and down means -5.
Question:
Which expression is equivalent to
![\frac{\sqrt{2}}{\sqrt[3]{2}}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Csqrt%7B2%7D%7D%7B%5Csqrt%5B3%5D%7B2%7D%7D)
Answer:
![\frac{\sqrt{2}}{\sqrt[3]{2}} =2^{\frac{1}{6}} = \sqrt[6]{2}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Csqrt%7B2%7D%7D%7B%5Csqrt%5B3%5D%7B2%7D%7D%20%3D2%5E%7B%5Cfrac%7B1%7D%7B6%7D%7D%20%3D%20%5Csqrt%5B6%5D%7B2%7D)
Step-by-step explanation:
Given
Required
Simplify
From laws of indices;
![\sqrt[n]{x} =x^{\frac{1}{n}}](https://tex.z-dn.net/?f=%5Csqrt%5Bn%5D%7Bx%7D%20%3Dx%5E%7B%5Cfrac%7B1%7D%7Bn%7D%7D)
So, the expression can be rewritten as
![\frac{\sqrt{2}}{\sqrt[3]{2}} = \frac{{2^{\frac{1}{2}}}}{2^{\frac{1}{3}}}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Csqrt%7B2%7D%7D%7B%5Csqrt%5B3%5D%7B2%7D%7D%20%3D%20%5Cfrac%7B%7B2%5E%7B%5Cfrac%7B1%7D%7B2%7D%7D%7D%7D%7B2%5E%7B%5Cfrac%7B1%7D%7B3%7D%7D%7D)
Also, from laws of indices
So, the expression is further solved to:
![\frac{\sqrt{2}}{\sqrt[3]{2}} =2^{\frac{1}{2} - \frac{1}{3}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Csqrt%7B2%7D%7D%7B%5Csqrt%5B3%5D%7B2%7D%7D%20%3D2%5E%7B%5Cfrac%7B1%7D%7B2%7D%20-%20%5Cfrac%7B1%7D%7B3%7D)
Solve exponents as fraction
![\frac{\sqrt{2}}{\sqrt[3]{2}} =2^{\frac{3-2}{6}}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Csqrt%7B2%7D%7D%7B%5Csqrt%5B3%5D%7B2%7D%7D%20%3D2%5E%7B%5Cfrac%7B3-2%7D%7B6%7D%7D)
![\frac{\sqrt{2}}{\sqrt[3]{2}} =2^{\frac{1}{6}}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Csqrt%7B2%7D%7D%7B%5Csqrt%5B3%5D%7B2%7D%7D%20%3D2%5E%7B%5Cfrac%7B1%7D%7B6%7D%7D)
This can be rewritten as
