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2 years ago

Define a polynomial that is a difference of squares. How do you know that it is the difference of squares? How is it factored?

Mathematics

1 answer:

yulyashka [42]2 years ago

8 0

Answer:

When an expression can be viewed as the difference of two perfect squares, i.e. a²-b², then we can factor it as (a+b)(a-b). For example, x²-25 can be factored as (x+5)(x-5). This method is based on the pattern (a+b)(a-b)=a²-b², which can be verified by expanding the parentheses in (a+b)(a-b).

Step-by-step explanation:

lol it’s on wassa name ;) mark me brainliest? Btw

Here you go, your equation should look a lot like this:

x²-16 -----> (x+4)(x-4).

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Select option that continues pattern? 3,-6,12,4,20

harkovskaia [24]

The pattern is - 8 so the answer is 12.

4 0

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

Which is the best estimate for the mass of a baseball? A. 25 grams B. 25 kilograms C. 225 kilograms D. 225 grams i need the answ

Paraphin [41]

Im going to say B but im not 100 percent sure

5 0

3 years ago

Read 2 more answers

Use the data in the table to answer the question. Citations are "speeding tickets." You may fill in the table to help you answer

Vikentia [17]

Answer:

Linear approximation is given by: $y = \frac{x}{5}+2$

Step-by-step explanation:

We are given the following information in the question:

Number of citations: 5 7.5 10 15 20

Outputs Residuals: 3 6 10 5 6

We have to find the linear approximation of the data that passes through the points (5, 3) and (20, 6).

Linear approximation is given by:

The equation of line is given by:

$(y-y_1) = \displaystyle\frac{y_2-y_2}{x_2-x_1}(x-x_1)$

where, $(x_1,y_1), (x_2.y_2)$ is the point through which the line passes.

The equation of line is:

$(y-3) = \displaystyle\frac{6-3}{20-5}(x-5)\\\\15(y-3)= 3(x-5)\\15y = 3x-15+45\\15y = 3x + 30\\y = \frac{x}{5}+2$

The above equation is the required linear approximation.

8 0

3 years ago

The sides of a rectangle are in the ratio 2:5. If the longer side of the rectangle is 25.5

Ksju [112]

Answer: The width of the rectangle is 10.2 inches, the perimeter is 71.4 inches, the area is 260.1 inches.

Step-by-step explanation:

25.5/5=5.1

5.1*2=10.2

The width is 10.2 inches

25.5*2+10.2*2=71.4

The perimeter is 71.4 inches

20.5*10.2=260.1

The area is 260.1

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3 years ago

Read 2 more answers