factorise by grouping method
(ax + by)^2 + (bx-ay)^2​

Part (1)

n is some positive integer. Let's say for now that n is even. So n = 2k, for some integer k

This means n-1 = 2k-1 is odd since subtracting 1 from an even number leads to an odd number.

Now multiply n with n-1 to get

n(n-1) = 2k(2k-1) = 2m

where m = k(2k-1) is an integer

The result 2m is even showing that n(n-1) is even

------------

Let's say that n is odd this time. That means n = 2k+1 for some integer k

And also n-1 = 2k+1-1 = 2k showing n-1 is even

Now multiply n and n-1

n(n-1) = (2k+1)(2k) = 2k(2k+1) = 2m

where m = k(2k+1) is an integer

We've shown that n(n-1) is even here as well.

------------

So overall, n(n-1) is even regardless if n is even or if n is odd.

Either n or n-1 will be even. If you multiply an even number with any number, the result will be even.

=======================================================

Part (2)

n is some positive integer

2n is always even since 2 is a factor of 2n

2n+1 is always odd because we're adding 1 to an even number. The sequence of integers goes even,odd,even,odd, etc and it does this forever.

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Another way to see how 2n+1 is odd is to divide 2n+1 over 2 and you'll find that we get (2n+1)/2 = 2n/2+1/2 = n+0.5

The 0.5 at the end is not an integer, so there's no way that (2n+1)/2 is an integer; therefore 2n+1 is odd.

Answer: x=10 y=5 = 15xy

Step-by-step explanation:

Answer:

I believe the answer is p = -7/5

Step-by-step explanation:

Here's the equation and the workthru of my logic:

-5 (p + 3/5) = -4

Divide both sides by -5 to remove the -5 from the left side of the equation,

p + 3/5 = -4/5,

Subtract 3/5 from both sides to solve for p,

p = -4/5-3/5

p = -7/5

Solution is -7/5

Hope this helps.

Good luck!

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Sum of the interior angles of any triangle is 180° .

Thus ;

[tex]y + 48° + 90° = 180°[/tex]

[tex]y + 138° = 180°[/tex]

Subtract sides 138°

[tex]y + 138° - 138° = 180° - 138° \\ [/tex]

[tex]y = 42°[/tex]

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-7/3

Step-by-step explanation: is the answer for odyssey ware

Answer:

Ari will think that Feeze Zone makes milkshakes with too much caramel.

Step-by-step explanation:

First off I took 3 ounces of caramel to 5 scoops of ice cream, which makes a ratio of 3/5.

Freeze Zone makes milkshakes with 6 ounces of caramel, so I multiplied the 3 and the 5 by two to get 6 ounces of caramel for the ratio.

once you multiply the ratio by two it becomes 6/10 and the milkshakes that Freeze Zone makes are 6/8, so they have more caramel than Ari likes.

Sorry if the explanation is a little confusing, I hope it helped :)

Answer:

The legs are a and b, the hypotenuse is c

Step-by-step explanation:

The legs of a right triangle are the two smaller sides. The hypotenuse is the longest side it is also always opposite of the 90-degree angle. If you need to find the lengths of sides remember the Pythagorean theorem, .

Answer:

yes the person above me is correct .

Step-by-step explanation:

good job :)

Answer:

224 ounces

Step-by-step explanation:

Answer:

34

Step-by-step explanation:

Ohio had 20

14 votes less than Texas (20 + 14)

34 electoral votes Texas had in 2004.

~~~Hope this helps~~~

HOPE THIS HELPS YOU...

The answer it's 95o UwU

Answer:

54

Step-by-step explanation:

Answer:

4.3 x 10^-9

Step-by-step explanation:

Convert to base 10 and move decimal 9 to right

Answer:

If we know that [tex]x = 1[/tex] and [tex]y = 9[/tex], the value of [tex]g[/tex] is 19.

Step-by-step explanation:

Let [tex]C(x,y) =(-2,12)[/tex] and [tex]D(x,y) =(4,6)[/tex], from Analytical Geometry and Linear Algebra we have that midpoint of CD is determined by:

[tex]M(x,y) = \frac{1}{2}\cdot C(x,y)+\frac{1}{2}\cdot D(x,y)[/tex] (Eq. 1)

[tex]M(x,y) = \frac{1}{2}\cdot (-2,12)+\frac{1}{2}\cdot (4,6)[/tex]

[tex]M(x,y) = (-1,6)+(2,3)[/tex]

[tex]M(x,y) =(-1+2,6+3)[/tex]

[tex]M(x,y)= (1,9)[/tex]

If we know that [tex]x = 1[/tex] and [tex]y = 9[/tex], the value of [tex]g[/tex] is 19.

Answer:

Step-by-step explanation:

the formula for calxulating the area if the isosceles triangle is expressed as;

[tex]A = \frac{1}{2}bh[/tex]

b is the base of the triangle

h is the altitude

Given

b = 16ft

h = 10ft

Substitute

A = 1/2 * 16 * 10

A = 8*10

A = 80ft²

Hence the area of the triangle is 80ft²

b) To get the measure of one side of the triangle, we will use the pythagoras theorem. Let s be the slant side

s² = h²+(b/2)²

s² = 10²+(16/2)²

s² = 10²+(8)²

s² =100+64

s² =164

s = √164

s = 12.8ft

Hence one side of the triangle is 12.8ft

Answer:

No

Step-by-step explanation:

-2 is a larger number than -5, if you were to plot these two numbers on a number line, -5 would be further to the left of 0 than -2, which makes it a smaller number. The sign < means less than. The statement being made is that -2 is less than -5, which is false.

Answer:

no

Step-by-step explanation:

I took a test and this question was on it and the answer was no.

Answer:

Me

Step-by-step explanation:

Because I am really good at math

Answer:

f(x) = |x + 2|

General Formulas and Concepts:

Transformations Graph: f(x) = a|bx - c|+ d

Step-by-step explanation:

Step 1: Define

We see a transformation from a parent function of the absolute value.

Parent Graph: f(x) = |x|

Step 2: Find equation of graph

We see the transformation moving horizontally 2 units to the left.

c = -2

f(x) = |x + 2|

Answer:rental cost for each movie =$3.75 and for video games = $5.5

Step-by-step explanation:

Step 1 Let the cost of movie = x

and cost of video game = y

Cost at  Ist Month for 6 movies and 5 video games for a total of $50 will  be

6x+ 5y= $50------- Equation 1

Cost at  2nd Month for 2 movies and 3 video games for a total of $24 will  be

2x+ 3y= $24--------  Equation 2

Step 2--- Solving

6x+ 5y= $50------- Equation 1

2x+ 3y= $24--------  Equation 2

Multiplying equation 2 by (3)

6x+ 5y= $50------- Equation 1

6x+ 9y= $72--------Equaton 3

subtracting  equation 1 from equation 3

9y-5y=22

4y= 22

y=22/4= 5.5

Putting the value of y = 5.5 in equation 1

6x+ 5y= $50

6x + 5(5.5)= $50

6x =50-27.5

6x=22.5

x=22.5/6

x =3.75

Therefore rental cost for each movie =$3.75 and for video games = $5.5

Answer:

1

Step-by-step explanation:

m=y2-y1/x2-x1

(-2)-2=(-4)

3-7=(-4)

-4/-4=1

hope this helps :3

if it did pls mark brainliest

Answer:

The answer is D.

Step-by-step explanation:

Domain describes the range of the x values that is true for a function. By looking at the graph, the possible values of x are between -8 and 3. Therefore the answer is: x such that [-8≤x≤3]

Answer:

-1/8

Step-by-step explanation:

MATH

Answer:

$32

Step-by-step explanation:

0.8*40

Answer:

117 cups

Step-by-step explanation:

two dozen cookies calls for 234cups of sugar

2 dozen cookies = 234 cups of sugar

How much sugar is needed to make one dozen cookies?

Let x = cups of sugar needed

1 dozen cookies = x cups of sugar

2 dozen cookies : 234 cups of sugar = 1 dozen cookies : x cups of sugar

2 : 234 = 1 : x

2 / 234 = 1 / x

Cross product

2*x = 234 * 1

2x = 234

x = 234 / 2

= 117 cups

Your options are wrong because none corresponds with the answer

Answer:

[tex]\frac{80}{1.94}[/tex]

Step-by-step explanation:

I hope this helps!

Answer:

Jillian had a cake and Ruby ate 2/3 of it. Jillian's friends then came over and consumed 3/4 of the kuchen, which Ruby already ate out of. How much of the cake is left?

Step-by-step explanation:

Just think about it with simpler numbers. What if the expression was (4 ÷ 2)? Then the word problem could be made quite easily. Following the previous example, simply replace the numbers (4 and 2) with the fractions given (1/3 and 3/4) and make a few tweaks for it to make more sense.

Good luck!

The total pizza left is 1/3 of the whole pizza. If the remainig student are to take 3/4 of the remaining, how much will each student take

Algebraic equations are ways we can solve real life apllications.

Given the division problem

1/3÷ 3/4 ​

This can be written usng this statement:

The total pizza left is 1/3 of the whole pizza. If the remainig student are to take 3/4 of the remaining, how much will each student take

Learn more on word problem here: https://brainly.com/question/21405634

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