Use the Completing the Square method to solve for x.

Mathematics

1 answer:

olga nikolaevna [1]3 years ago

6 0

Answer:

x = -1

x = -5

Step-by-step explanation:

y= (x+3)^2 - 4

(x + 3)^2 = x^2+6x+9

y = x^2 + 6x + 9 - 4

y = x^2 + 6x + 5

x^2 + 6x = -5

x^2 + 6x + 9 = -5+9 (6/2=3, 3^2 = 9) (add 9 to both sides)

(x + 3)^2 = 4

x + 3 = sqrt 4

x + 3 = +- 2

x + 3= 2. x = 2-3. x = -1

x + 3 = -2. x = -3-2. x = -5

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8.52 The heights of 2-year-old children are normally distributed with a mean of 32 inches and a standard deviation of 1.5 inches

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Answer:

Heights of 29.5 and below could be a problem.

Step-by-step explanation:

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the z-score of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

The heights of 2-year-old children are normally distributed with a mean of 32 inches and a standard deviation of 1.5 inches.

This means that $\mu = 32, \sigma = 1.5$