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miss Akunina [59]
3 years ago
13

Use the identity (x^2+y^2)^2=(x^2−y^2)^2+(2xy)^2 to determine the sum of the squares of two numbers if the difference of the squ

ares of the numbers is 5 and the product of the numbers is 6.
Mathematics
1 answer:
marissa [1.9K]3 years ago
5 0

Answer:

Step-by-step explanation:

(x^2+y^2)^2=(x^2)^2+2x^2y^2+(y^2)^2

Adding and substracting 2x^2y^2

We get

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

And we know a^2-2ab+b^2=(a-b)^2

So we identify (x^2)^2 as a^2 ,(y^2)^2 as b^2 and -2x^2y^2 as - 2ab. So we can rewrite (x^2+y^2)^2=(x^2 - y^2)^2 + 2x^2y^2 + 2x^2y^2= (x^2 - y^2)^2+4x^2y^2= (x^2 - y^2)^2+2^2x^2y^2

Moreever we know (a·b·c)^2=a^2·b^2·c^2 than means 2^2x^2y^2=(2x·y)^2

And (x^2+y^2)^2=(x^2 - y^2)^2 + (2x·y)^2

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The ice cream shop sells sundaes for $2 each and banana splits for $3 each. One day, the shop sold 8 more sundaes than banana sp
Nataliya [291]

Answer:

$82 sundaes

$74 banana split

Step-by-step explanation:

Step one :

Given data

Cost of sundaes =$2 each

Cost of banana split =$3 each

Let the number of sundaes bought be x

And the number of banana split bought be y

The total is x+y

The shop sold 8 more Sundaes than the Banana split

x=8+y—-------1

Total amount made = $156

Therefore the system of equation for the situation is

x=8+y----—----------1

2x+3y=156---------2

But x=8+y

8+y+y=156

8+2y=156

2y=156-8

2y=148

Divide both sides by 2

y=148/2

y=74

On That day they sold $74 banana split

And also they sold x=8+74=$82 sundaes

4 0
2 years ago
The mean of five numbers is 25, what is their sum?
zubka84 [21]

125 is the answer.

A mean of vie numbers is 25. If it is 25, the numbers must be 25. So, since there is 5 of 25, multiply 25 by 5. Then, the answer would be 125.

There is also another way to do it. Set-up your equation.

x/5=25.

Now flip it to make the equation a multiplication problem.

25×5=x

Once you solve the equation, you should get 125 is the answer.

3 0
3 years ago
Could someone help? please the deadline is in 20 min!!!
Zepler [3.9K]

Answer:

7.$95 8. $112.50

Step-by-step explanation:

7.

50 divided by 100 is 0.5, then times by 90 is 45.

45 plus 50 is 95.

8.

$150/4=$37.50

$150-$37.50=$112.50

5 0
3 years ago
Solve for x.<br> 7y-6y-19=13
Hitman42 [59]

Answer:

Y=32

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
If two lines are perpendicular, which statement must be true? A.The slopes of the two lines are equal. B.The slopes of the two l
dangina [55]

Answer:

Option D is correct that is The Slopes of two lines are negative reciprocals.

Step-by-step explanation:

Perpendicular lines are the lines which intersect each other at right angle or make 90° angle with each other.

we that the Slope of perpendicular lines are equal to -1

Therefore, Option D is correct that is The Slopes of two lines are negative reciprocals.

5 0
3 years ago
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