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True [87]
3 years ago
7

Factor the following polynomial completely. -x 2 y 2 + x 4 + 4y 2 - 4x 2

Mathematics
2 answers:
zlopas [31]3 years ago
5 0

Answer:

(x + y)(x - y) (x + 2)(x - 2)

Step-by-step explanation:

-x^2 y^2 + x^4 + 4y^2 - 4x^2

Lets rearrange the terms

x^4 -x^2 y^2 - 4x^2 + 4y^2

Then we group first two terms and last two terms

(x^4 -x^2 y^2)+(- 4x^2 + 4y^2)

Factor out each group

x^2(x^2 - y^2) - 4 (x^2 - y^2)

(x^2 - y^2)(x^2 - 4)

Apply formula a^2 - b^2 = (a+b)(a-b)

(x + y)(x - y) (x + 2)(x - 2)

fgiga [73]3 years ago
3 0
<span>-x^2 y^2 + x^4 + 4y^2 - 4x^2
= </span>x^4 -x^2 y^2 - 4x^2 + 4y^2<span>
= x^2 (x^2 - y^2) - 4 (x^2 - y^2)
= (x^2 - y^2)(x^2 - 4)
= (x + y)(x - y) (x + 2)(x - 2) (....using a^2 - b^2 = (a+b)(a-b) )

hope it helps</span>
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laila [671]

Answer:

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3 years ago
Sketch the region R defined by 1≤ x≤ 2 and 0≤ y≤ 1/x^3
steposvetlana [31]
On the attachment, there is the graph for the region "R" and the calculations for the value a and b. 

the theory is that you have to choose a value that is between the range and assume that this value will divide the area into two equal parts. This is done for x = a

For
"y" you have to change the integral from dx to dy and you have to divide the region into 2 parts, given that the area cannot be calculated by 1 integral equation, so you proceed to calculate the rectangular area and take this area into consideration, for the same procedure as before. 

Then you calculate again the value y = b and that's it.

5 0
3 years ago
Look below to help please
laiz [17]
The larger box is 5x bigger than the smaller one.

6 0
3 years ago
A solution containing 12% alcohol is to be mixed with a solution containing 4% alcohol to make 20 gallons of solution containing
stepan [7]

Answer:

Step-by-step explanation:

Given that a solution containing 12% alcohol is to be mixed with a solution containing 4% alcohol to make 20 gallons of solution containing 9% alcohol.

Let x gallons of 12% alcohol be mixed with y gallons of 4% alcohol.

Total gallons= x+y = 20

Alcohol content in the total mixture = 0.12x+0.04y =9% of x+y

0.12x+0.4y=0.09(20)\\12x+4y = 180

b) Two equations are

x+y = 20\\12x+4y = 180

c) This is of the form Ax = B

where A =\left[\begin{array}{ccc}1&1\\12&4\end{array}\right]

Inverse is \frac{1}{4-12} \left[\begin{array}{ccc}4&-1\\-12&12\end{array}\right]\\=\frac{-1}{8} \left[\begin{array}{ccc}4&-1\\-12&12\end{array}\right]\\

Solution set is A inverse *B

= x \    12.5\\y  \     7.5

7 0
3 years ago
The enrollment at Ousley Jr. High School dropped by 60 students over a 5-year period. What is the average yearly drop in enrollm
Snezhnost [94]

Answer:

The average yearly drop in enrollment is 12.

Step-by-step explanation:

The average refers to the central value in a group of numbers and with the information provided, you can find the average by dividing the number of students that dropped out of the school by the number of years over which that ocurred:

number of students= 60

number of years= 5

60/5=12

According to this, the answer is that the average yearly drop in enrollment is 12.

3 0
3 years ago
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