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stich3 [128]
2 years ago
12

Difference of squares gives which complex factors for the expression x^2+13

Mathematics
2 answers:
Serga [27]2 years ago
7 0

The Given Expression is : → x² + 13

  =  x² + (√13)²

=  x² - ( i √13)²  As , i²= -1 because , i = √-1

= (x - i√13)(x +√13)   → Using the formula , A² - B² = (A-B)(A+B)

Out of the four options Given : Option C →(x - i√13)(x +√13) is true regarding the expansion of function x² + 13.

fredd [130]2 years ago
7 0

Answer:

Option C.

Step-by-step explanation:

Shortest way to solve this question is to find the factors of the given expression.

The given expression is (x² + 13).

Now we have to factorize it.

(x² + 13) = x² + (√13)²

             = x² + [-(i)²√(13)²]  [Since i = √(-1)]

             = x² - (i√13)²

             = (x - i√3)(x + i√3) [Since (a² - b²) = (a + b)(a - b)]

Option C will be the answer.

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Al purchases a speedboat costing $24,500. State taxes are 5.5% and federal excise tax is 13%. What is the total purchase price?
trapecia [35]

Answer: The total purchase price is $ 29,032

Step-by-step explanation:

Hi, to solve this problem you have to solve the percentages of each taxes first.

So :

  • state taxes =$24,500 × 5.5% = $1,347.5
  • federal tax = $24,500 × 13% = $3,185

The next step is adding the taxes results to the speedboat cost.

so:

speedboat = $24,500

speedboat + taxes = $24,500 + $1,347.5 +$3,185 = $29,032

The total purchse price for the speedboat is $29,032.

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2 years ago
Julie is at the store buying groceries. She needs to get a quart of orange juice and some peaches. The quart of orange juice cos
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The answer is D
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1 year ago
Colin gets pic 'n mix when at the cinema and makes his bag up with 3 types of sweet. He pick:
Kisachek [45]

Answer: 2/3

Explanation: Assume that the number of smarties he picked is c.

Now, we are given that:

1- He picked 3 times as many cola bottles as smarties. This means that:

Number of cola bottles he picked = 3s

2- He picked twice as many smarties as marshmallows. This means that:

number of marshmallows he picked = 0.5s

Now to get the proportion o f cola bottles, we will divide the number of cola bottles by the total number of sweets as follows:

proportion of cola bottles =  

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1 year ago
A control chart is developed to monitor the analysis of iron levels in human blood. The lines on the control chart were obtained
sergejj [24]

Answer:

Step-by-step explanation:

Hello!

The variable is X: iron level on human blood.

It has a mean of μ= 51.50 mg/dl and a standard deviation of σ= 3.50 mg/dl.

According to the control chart, the process should be shut down for troubleshooting when the analysis shows values X[bar]≥ 53.42 mg/dl and X[bar]≤ 49.58 mg/dl

Warnings are received at levels X[bar]≥52.78 mg/dl and X[bar]≤ 50.22 mg/dl

The system works between levels 49.58<X[bar]<53.42 and works without warnings between 50.22<X[bar]<52.78.

Using these parameters you have to analyze if the lists of sample means to see which ones are within the working values are wich ones are outside this interval.

<u>Sample 1</u>

Min= 50.15

Max= 51.99

Mean= 51.61

Without warning 50.22<X[bar]<52.78

Without Action interval 49.58<X[bar]<53.42

<em>This sample's min value is below the lower limit of the warning interval but not low enough to reach action levels, the max value is within the working range.</em>

<em><u /></em>

<u>Sample 2 </u>

Min= 50.32

Max= 52.56

Mean= 51.16

Without warning 50.22<X[bar]<52.78

Without Action interval 49.58<X[bar]<53.42

<em>Both the max and min values of the sample are within the working range without warning.</em>

<em />

<u>Sample 3</u>

Min= 50.25

Max= 53.12

Mean= 51.83

Without warning 50.22<X[bar]<52.78

Without Action interval 49.58<X[bar]<53.42

<em>The max value of this sample is above the upper limit of the warning interval but does not surpass the upper bond of the troubleshoot interval. Min value is within working values.</em>

<em />

<u>Sample 4</u>

Min= 50.05

Max= 53.01

Mean= 51.70

Without warning 50.22<X[bar]<52.78

Without Action interval 49.58<X[bar]<53.42

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<u>Sample 5</u>

Min= 50.35

Max= 52.71

Mean= 51.37

Without warning 50.22<X[bar]<52.78

Without Action interval 49.58<X[bar]<53.42

<em>Both min and max values are within working levels without warnings.</em>

<em />

Considering that samples reaching warning levels should be shut down as a precaution, they are classified as:

Shutdown: Sample 1, 3 and 4

Do not shutdown: Sample 2 and 5.

I hope it helps!

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11Alexandr11 [23.1K]

Each child will get 1/4 of the sandwich.

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