A⁴+b⁴=a²b² ,prove that a⁶+b⁶=0

Answers

Answer 1

Answer: $a^4+b^4=a^2b^2\n a^4-a^2b^2+b^4=0\n a^4-2a^2b^2+b^4+a^2b^2=0\n (a^2+b^2)^2=-a^2b^2$

The only possible option is that $a^2+b^2=0 \wedge a^2b^2=0\n$ and this condition is met only when $a=0 \wedge b=0$ .

$0^6+0^6=0\n 0=0$

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Part 1:For the following system of equations, write your own real world scenario that describes what is happening. Use complete sentences and correct grammar in your scenario.

Part 2:
Solve the system and explain what the results mean according to your scenario.

2x + y = 11
3x + 4y = 24
...?

Answers

Here are my answers to the given questions above:
Part 1. Here is my example of a real life scenario that describes what is happening. Let us say, I have 2 cookies and the bottle of milk costs 11 dollars, and 3 cookies and 4 bottles of milk cost 24 dollars.
Part 2.
y=11-2x
3x+4(11-2x)=24
3x+44-8x=24
-5x=-20
x=4
y=11-8
y=3
Therefore, each cookie costs 4 dollars, and a bottle of milk costs 3 dollars.
Hope this answer helps. Let me know if you need more help next time.

What is the slope of the line shown below (2 2) (4 8) a. 3 b. 1/3 c. -1/3 d. -3

Answers

Answer:

Option A.3

Step-by-step explanation:

If its rise over run the fraction should be right 2 up 6 makeing a fraction of

6/2 which equals 3

The line has a slope of 3

The area of a rectangle is 21 m squared, and the length of the rectangle is 1 m less than twice the width. Find the dimensions of the rectangle. Help?

Answers

This should be right because I checked it afterwards
Width=W
Length=2W-1
The equation is as follows
W(2W-1)=21
$2W^(2)$ -W=21
Subtract 21 from each side
$2W^(2)$ -W-21
Group them/put them in parentheses..can't think of the right word right now
(2W-7)(W+3)
-7=I7I
You only do this for the first parenthese, 7÷2W=3.5
W=3.5
If W=3.5 then 2W-1⇒2×3.5-1⇒7-1⇒6
Length=6
If W=3.5 and L=6, then W(2W-1)=21
3.5(2×3.5-1)=21
Solve in parentheses first
3.5(7-1)=21
3.5(6)=21
3.5×6=21
The width is 3.5
The length is 6

How do i solve 89 times 69

Answers

$89\cdot 69\n \n =\left( 90-1 \right) \left( 70-1 \right) \n \n =90\cdot 70-90-70+1$

$\n \n =6,300-160+1\n \n =6,140+1\n \n =6,141$

89 x 69 = 6141
hope this helps!!!!!!!!!!

I need help with 18 and 19 please

Answers

18) Angle WZY = 75/2 = 37.5(Angle subtended by an arc on any point on a circe is half the angle subtended at centre)
19) r = 4 ft
Area of the whole circle = (pi)r^2= 22/7 *4*4 = 50.28
Area of the sector = 75/360*50.28= 97.77 ft^2

Help me please ..........................

Answers

G(x)= (x-4)^2+1......

Answer: G(x)=(x-2)^2+1

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