Solve for q:
2 p - 1/q = r/q + 4
Bring 2 p - 1/q together using the common denominator q. Bring r/q + 4 together using the common denominator q:
(2 p q - 1)/q = (4 q + r)/q
Multiply both sides by q:
2 p q - 1 = 4 q + r
Subtract 4 q - 1 from both sides:
q (2 p - 4) = r + 1
Divide both sides by 2 p - 4:
Answer: q = (r + 1)/(2 p - 4)
<u>Answer:
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The factor of ![9 x^{4}+12 x^{3}+21 x^{2} \text { is } 3 x^{2}\left(3 x^{2}+4 x+7\right)](https://tex.z-dn.net/?f=9%20x%5E%7B4%7D%2B12%20x%5E%7B3%7D%2B21%20x%5E%7B2%7D%20%5Ctext%20%7B%20is%20%7D%203%20x%5E%7B2%7D%5Cleft%283%20x%5E%7B2%7D%2B4%20x%2B7%5Cright%29)
<u>Solution:
</u>
From question given that the equation is
![9 x^{4}+12 x^{3}+21 x^{2}](https://tex.z-dn.net/?f=9%20x%5E%7B4%7D%2B12%20x%5E%7B3%7D%2B21%20x%5E%7B2%7D)
We have to find the factors of the given equation.
By taking 3 as a common term in above expression,
![=3\left(3 x^{4}+4 x^{3}+7 x^{2}\right)](https://tex.z-dn.net/?f=%3D3%5Cleft%283%20x%5E%7B4%7D%2B4%20x%5E%7B3%7D%2B7%20x%5E%7B2%7D%5Cright%29)
By taking “x” as a common term in above expression, we get equation as
![=3 x\left(3 x^{3}+4 x^{2}+7 x\right)](https://tex.z-dn.net/?f=%3D3%20x%5Cleft%283%20x%5E%7B3%7D%2B4%20x%5E%7B2%7D%2B7%20x%5Cright%29)
Again taking “x” as a common term in above expression, we get
![=3 x^{2}\left(3 x^{2}+4 x+7\right)](https://tex.z-dn.net/?f=%3D3%20x%5E%7B2%7D%5Cleft%283%20x%5E%7B2%7D%2B4%20x%2B7%5Cright%29)
cannot be factorized.(imaginary roots)
Hence factor of ![9 x^{4}+12 x^{3}+21 x^{2} \text { is } 3 x^{2}\left(3 x^{2}+4 x+7\right)](https://tex.z-dn.net/?f=9%20x%5E%7B4%7D%2B12%20x%5E%7B3%7D%2B21%20x%5E%7B2%7D%20%5Ctext%20%7B%20is%20%7D%203%20x%5E%7B2%7D%5Cleft%283%20x%5E%7B2%7D%2B4%20x%2B7%5Cright%29)
Answer:
Step-by-step explanation:
Given that the difference of sample means of two populations is 108.7, and the standard deviation of the difference in sample means is 32.
H0: difference inmeans =0
Ha: difference inmeans not equal to 0
(Two tailed test)
Test statistic = mean difference/std deviation
![=\frac{108.7}{32}\\=3.40](https://tex.z-dn.net/?f=%3D%5Cfrac%7B108.7%7D%7B32%7D%5C%5C%3D3.40)
For 68% confidence level, }z}<1
Here z =3.40 >1
Hence reject null hypothesis
The difference between the means cannot be 0 and there is statistical evidence at 68% level to reject null hypothesis
B. 81 because the square root of 81 is 9
Answer:
not enough information. please show us a picture