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ozzi
2 years ago
7

Use the quadratic formula to solve 4x²-9x=2x²-2x-4

Mathematics
1 answer:
Georgia [21]2 years ago
5 0

4x^2-9x = 2x^2 -2x -4\\\\\implies 4x^2 -9x -2x ^2 +2x +4 =0\\\\\implies 2x^2 -7x +4=0\\\\\text{Apply quadratic formula,}~ x = \dfrac{-b \pm \sqrt{b^2 -4ac}}{2a}.\\\\\text{In this case,} ~a =2, b = -7 ~ \text{and}~ c =4\\\\\\x =\dfrac{-(-7) \pm \sqrt{(-7)^2 - 4 \cdot 2 \cdot 4}}{2(2)}\\\\\\\implies x = \dfrac{7 \pm \sqrt{17}}4\\\\\\\text{Hence,}~ x = \dfrac{7 +\sqrt{17}}4~ \text{and}~x = \dfrac{7 -\sqrt{17}}4

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Answer:

Sam is correct.

Step-by-step explanation:

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Scores of an IQ test have a​ bell-shaped distribution with a mean of 100 and a standard deviation of 13. Use the empirical rule
Yuri [45]

Answer:

(a) 68% of people has an IQ score between 87 and 113​.

(b) 5% of people has an IQ score less than 74 or greater than 126.

(c) 0.15% of people has an IQ score greater than 139​.

Step-by-step explanation:

Given information:Scores of an IQ test have a​ bell-shaped distribution,

mean = 100

standard deviation = 13

According to the empirical rule

68% data lies between \overline{x}-\sigma and \overline{x}+\sigma.

95% data lies between \overline{x}-2\sigma and \overline{x}+2\sigma.

99.7% data lies between \overline{x}-3\sigma and \overline{x}+3\sigma.

(a)

\overline{x}-\sigma=100-13=87

\overline{x}+\sigma=100+13=113

[\overline{x}-\sigma,\overline{x}+\sigma]=[87,113]

Using empirical rule we can say that 68% of people has an IQ score between 87 and 113​.

(b)

\overline{x}-2\sigma=100-2(13)=74

\overline{x}+2\sigma=100+2(13)=126

[\overline{x}-2\sigma,\overline{x}+2\sigma]=[74,126]

Using empirical rule we can say that 95% of people has an IQ score between 74 and 126​.

The percentage of people has an IQ score less than 74 or greater than 126 is

P = 1- percent of people has an IQ score between 74 and 126​.

P = 1- 95%

P = 5%

Therefore 5% of people has an IQ score less than 74 or greater than 126.

(c)

\overline{x}-3\sigma=100-3(13)=61

\overline{x}+3\sigma=100+3(13)=139

[\overline{x}-3\sigma,\overline{x}+3\sigma]=[61,139]

Using empirical rule we can say that 99.7% of people has an IQ score between 61 and 139​.

The percentage of people has an IQ score less than 61 or greater than 139 is

P = 1- percent of people has an IQ score between 61 and 139​.

P = 1- 99.7%

P = 0.3%

The percentage of people has an IQ score greater than 139​ is

P=\frac{1}{2}(0.3\%)=0.15\%

Therefore 0.15% of people has an IQ score greater than 139​.

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