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3 years ago

Solve the quadratic equation x2 - x = 30 by completing the square

Mathematics

1 answer:

kap26 [50]3 years ago

5 0

Answer:

Step-by-step explanation:

Given

x² - x = 30

To complete the square

add ( half the coefficient of the x- term )² to both sides

x² + 2(- $\frac{1}{2}$ )x + $\frac{1}{4}$ = 30 + $\frac{1}{4}$

(x - $\frac{1}{2}$ )² = $\frac{121}{4}$

Take the square root of both sides

x - $\frac{1}{2}$ = ± $\sqrt{\frac{121}{4} }$ = ± $\frac{11}{2}$

Add $\frac{1}{2}$ to both sides

x = $\frac{1}{2}$ ± $\frac{11}{2}$ , thus

x = $\frac{1}{2}$ - $\frac{11}{2}$ = - 5

x = $\frac{1}{2}$ + $\frac{11}{2}$ = 6

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A quality analyst of a tennis racquet manufacturing plant investigates if the length of a junior's tennis racquet conforms to th

Burka [1]

Answer:

Confidence interval : $21.506$ to $24.493$

Step-by-step explanation:

A quality analyst selects twenty racquets and obtains the following lengths:

21, 25, 23, 22, 24, 21, 25, 21, 23, 26, 21, 24, 22, 24, 23, 21, 21, 26, 23, 24

So, sample size = n =20

Now we are supposed to find Construct a 99.9% confidence interval for the mean length of all the junior's tennis racquets manufactured at this plant.

Since n < 30

So we will use t-distribution

Confidence level = 99.9%

Significance level = α = 0.001

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X=21, 25, 23, 22, 24, 21, 25, 21, 23, 26, 21, 24, 22, 24, 23, 21, 21, 26, 23, 24

Sample mean = $\bar{x}=\frac{\sum x}{n}$

Sample mean = $\bar{x}=\frac{21+25+23+22+24+21+25+21+23+ 26+ 21+24+22+ 24+23+21+ 21+ 26+23+ 24}{20}$

Sample mean = $\bar{x}=23$

Sample standard deviation = $\sqrt{\frac{\sum(x-\bar{x})^2}{n-1}}$

Sample standard deviation = $\sqrt{\frac{(21-23)^2+(25-23)^2+(23-23)^2+(22-23)^2+(24-23)^2+(21-23)^2+(25-23)^2+(21-23)^2+(23-23)^2+(26-23)^2+(21-23)^2+(24-23)^2+(22-23)^2+(24-23)^2+(23-23)^2+(21-23)^2+(21-23)^2+(26-23)^2+(23-23)^2+(24-23)^2}{20-1}}$