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sweet-ann [11.9K]
3 years ago
12

X(x+3) + 34 = (x +5)(x+2)

Mathematics
1 answer:
My name is Ann [436]3 years ago
4 0
X(x + 3) + 34 = (x + 5)(x + 2)

First, expand to remove parentheses. 
x^{2} + 3x + 34 =  x^{2} + 2x + 5x + 10
Second, add '2x + 5x' to get '7x'.
x^{2} + 3x + 34 =  x^{2}  + 7x + 10
Third, cancel out 'x^{2}' on both sides.
3x + 34 = 7x + 10
Fourth, subtract '3x' from both sides.
34 = 7x + 10 - 3x
Fifth, subtract '7x - 3x' to get '4x'.
34 = 4x + 10
Sixth, subtract '10' from both sides.
34 - 10 = 4x
Seventh, subtract '34 - 10' to get '24'.
24 = 4x
Eighth, divide both sides by '4', leaving the 'x' by itself.
\frac{24}{4} =x
Ninth, since '24 ÷ 4 = 6', simplify the fraction to '6'.
6 = x
Tenth, switch your sides to get the answer.
x = 6

Answer: x = 6

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113.7-2.154\frac{9.1}{\sqrt{29}}=110.06    

113.7+2.154\frac{9.1}{\sqrt{29}}=117.34    

And the 96% confidence is given by (110.06; 117.34)

Step-by-step explanation:

Information given

\bar X=113.7 represent the sample mean

\mu population mean (variable of interest)

s=9.1 represent the sample standard deviation

n=29 represent the sample size  

Confidence interval

The confidence interval for the mean is given by the following formula:

\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}   (1)

The degrees of freedom are given by:

df=n-1=29-1=28

The Confidence is 0.96 or 96%, the significance is \alpha=0.04 and \alpha/2 =0.02, and the critical value would be t_{\alpha/2}=2.154

Replacing the info we got:

113.7-2.154\frac{9.1}{\sqrt{29}}=110.06    

113.7+2.154\frac{9.1}{\sqrt{29}}=117.34    

And the 96% confidence is given by (110.06; 117.34)

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