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MrRa [10]
3 years ago
12

Factorize: a^4+2xa³+a²x²-y^4

Mathematics
2 answers:
Art [367]3 years ago
5 0

9514 1404 393

Answer:

  (a^2 +ax -y^2)·(a^2 +ax +y^2)

Step-by-step explanation:

This can be factored as the difference of squares.

  a^4 +2a^3x +a^2x^2 - y^4 = a^2(a+x)^2 - y^4

  = (a(a+x) -y^2)(a(a+x) +y^2)

  = (a^2 +ax -y^2)·(a^2 +ax +y^2)

mart [117]3 years ago
4 0

Answer:

(a^2+ax-y) (a^2+ax+y^2)

Step-by-step explanation:

a^4+2xa³+a²x²-y^4

(a^2+ax)^2-y^4

(a^2+ax-y) (a^2+ax+y^2)

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Mark owns Siberian Husky sled dogs. He knows from data collected over the years that the weight of the dogs is a normal distribu
kozerog [31]
Calculate the z-score for the given data points in the item using the equation,
 
                             z-score = (x - μ) / σ

where x is the data point, μ is the mean, and σ is the standard deviation.

Substituting,
             (47.7)     z-score = (47.7 - 52.5)/2.4 = -2

This translates to a percentile of 2.28%.

              (54.9)      z-score = (54.9 - 52.5)/2.4 = 1

This translates to a percentile of 84.13%. 

Then, subtract the calculate percentiles to give us the final answer of <em>81.85%.</em> 

Thus, 81.85% of the Siberian Husky sled dogs are expected to weigh between 47.7 and 54.9 lbs. 
8 0
3 years ago
If f(x)=sinx−1/cos2x, then limx→π2f(x) is equivalent to which of the following?
Harrizon [31]

Answer:

2

Step-by-step explanation:

Given g(x) = sin(x)-1/cos2(x), we are to find the limit if the function g(x) as g(x) tends to π/2

Substituting π/2 into the function

lim x-->π/2 sin(x)-1/cos 2(x)

= sin(π/2) - 1/cos(2)(π/2)

= 1 - 1/cosπ

= 1- 1/-1

= 1 -(-1)

= 1+1

= 2

Hence the limit of the function h(x) = sin(x)-1/cos2(x) as x--> π/2 is 2

8 0
3 years ago
In considering career options, Ella would like to enter an industry with at least 50% growth from 2000 to 2010. Based on the abo
AlladinOne [14]

Answer:

Industries below 50% growth are

Personnel supply services, Warehousing and storage, Water and sanitation, Management and public relations, Business services, Equipment rental and leasing.

Step-by-step explanation:

In the graph percentage change is on the x axis and on the y axis all industries have been mentioned.

All the industries on y axis have the span over x axis representing the growth and salaries.

Out of 10 top industries only four industries have the growth of 50% which is evident from the graph.Those industries are Health Services,Computer and data processing, Cable television services and Residential care. Rest six industries are below 60% growth.So Ella should consider these industries to join.

8 0
4 years ago
Read 2 more answers
Janeel has a 10-inch by 12-inch photograph. She wants to scan the photograph, then reduce the result
Vaselesa [24]

<u>Complete Question:</u>

Janeel has a 10 inch by 12 inch photograph. She wants to scan the photograph, then reduce the results by the same amount in each dimension to post on her Web site. Janeel wants the area of the image to be one eight of the original photograph. Write an equation to represent the area of the reduced image. Find the dimensions of the reduced image.

<u>Correct Answer:</u>

A) (10-x)(12-x)=15

B) Dimensions are : Length = 10-x = 3 inch , Breadth = 12-x = 5 inch

<u>Step-by-step explanation:</u>

a. Write an equation to represent the area of the reduced image.

Let the reduced dimensions is by x , So the new dimensions are

length=10-x\\breadth=12-x

According to question , Area of new image is :

⇒ Area = \frac{1}{8}Length(breadth)

⇒ Area = \frac{1}{8}(10)(12)

⇒ Area = 15

So the equation will be :

⇒ (10-x)(12-x)=15

b. Find the dimensions of the reduced image

Let's solve :  (10-x)(12-x)=15

⇒ 120-10x-12x+x^2=15

⇒ 120-22x+x^2=15

⇒ x^2-22x+105=0

By Quadratic formula :

⇒ x = \frac{-b \pm \sqrt{b^2-4ac} }{2a}

⇒ x = \frac{22 \pm8 }{2}

⇒ x = \frac{22 +8 }{2} , x = \frac{22 -8 }{2}

⇒ x = 15 , x =7

x = 15 is rejected ! as 15 > 10 ! Side can't be negative

⇒ x =7

Therefore, Dimensions are : Length = 10-x = 3 inch , Breadth = 12-x = 5 inch

5 0
3 years ago
How can you find the sample space of two or more events?
Korolek [52]

Answer:

Just multiply the total number of outcomes with the expected.

Step-by-step explanation:

Hope this helps!! :D

4 0
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