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3 years ago

Solve x2+4x=1 by Completing the square

Mathematics

1 answer:

Viefleur [7K]3 years ago

7 0

Answer:

x = -2 ±√5

Step-by-step explanation:

You want to complete the square by adding the square of half the coefficient of the linear term:

x^2 + 4x + (4/2)^2 = 1 + (4/2)^2

(x +2)^2 = 5 . . . . . simplify

x +2 = ±√5 . . . . . . take the square root

x = -2 ±√5 . . . . . . subtract 2. This is the solution.

For the problem in the picture, replace x with p in the above.

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3 years ago

Rockwell hardness of pins of a certain type is known to have a mean value of 50 and a standard deviation of 1.2.a. If the distri

zalisa [80]

Answer:

$P(\= X \ge 51 ) =0.0062$

$P(\= X \ge 51 ) = 0$

Step-by-step explanation:

From the question we are told that

The mean value is $\mu = 50$

The standard deviation is $\sigma = 1.2$

Considering question a

The sample size is n = 9

Generally the standard error of the mean is mathematically represented as

$\sigma_x = \frac{\sigma }{\sqrt{n} }$

=> $\sigma_x = \frac{ 1.2 }{\sqrt{9} }$

=> $\sigma_x = 0.4$

Generally the probability that the sample mean hardness for a random sample of 9 pins is at least 51 is mathematically represented as

$P(\= X \ge 51 ) = P( \frac{\= X - \mu }{\sigma_{x}} \ge \frac{51 - 50 }{0.4 } )$

$\frac{\= X -\mu}{\sigma } = Z (The \ standardized \ value\ of \ \= X )$

$P(\= X \ge 51 ) = P( Z \ge 2.5 )$

=> $P(\= X \ge 51 ) =1- P( Z < 2.5 )$

From the z table the area under the normal curve to the left corresponding to 2.5 is

$P( Z < 2.5 ) = 0.99379$

=> $P(\= X \ge 51 ) =1-0.99379$

=> $P(\= X \ge 51 ) =0.0062$

Considering question b

The sample size is n = 40

Generally the standard error of the mean is mathematically represented as

$\sigma_x = \frac{\sigma }{\sqrt{n} }$

=> $\sigma_x = \frac{ 1.2 }{\sqrt{40} }$

=> $\sigma_x = 0.1897$

Generally the (approximate) probability that the sample mean hardness for a random sample of 40 pins is at least 51 is mathematically represented as

$P(\= X \ge 51 ) = P( \frac{\= X - \mu }{\sigma_x} \ge \frac{51 - 50 }{0.1897 } )$

=> $P(\= X \ge 51 ) = P(Z \ge 5.2715 )$

=> $P(\= X \ge 51 ) = 1- P(Z < 5.2715 )$

From the z table the area under the normal curve to the left corresponding to 5.2715 and

=> $P(Z < 5.2715 ) = 1$

$P(\= X \ge 51 ) = 1- 1$

=> $P(\= X \ge 51 ) = 0$

5 0

2 years ago

What is the solution set for the inequality 4−5g > 39 Question 3 options: g < −7 g>7 g<7 g > −7.

neonofarm [45]

Answer:

g < -7

General Formulas and Concepts:
Algebra I

Equality Properties

Multiplication Property of Equality
Division Property of Equality
Addition Property of Equality
Subtraction Property of Equality

Terms/Coefficients

Step-by-step explanation:

*Note:

When dividing or multiplying both sides of the inequality by a negative, flip the inequality sign.

Step 1: Define

Identify.

4 - 5g > 39

Step 2: Solve for g

[Subtraction Property of Equality] Subtract 4 on both sides: -5g > 35
[Division Property of Equality] Divide -5 on both sides: g < -7

∴ any number g less than -7 would work as a solution to the inequality.

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Topic: Algebra I

Unit: Inequalities

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2 years ago

The mass of a proton in scientific notation is 1.6 x 10-24 grams. What is the mass of a proton in standard form

borishaifa [10]

Answer:

Step-by-step explanation:

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3 years ago

What transformation is used to create this frieze pattern?

Lesechka [4]

Answer:

glide reflection

Step-by-step explanation:

got it right on the test!

5 0

2 years ago