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4 years ago

How does this polynomial identity work on numerical relationships? (y + x) (ax + b)

Mathematics

1 answer:

Serggg [28]4 years ago

3 0

Let us take 'a' in the place of 'y' so the equation becomes

(y+x) (ax+b)

Step-by-step explanation:

Step 1:

(a + x) (ax + b)

Step 2: Proof

Checking polynomial identity.

(ax+b )(x+a) = FOIL

(ax+b)(x+a)

ax^2+a^2x is the First Term in the FOIL

ax^2 + a^2x + bx + ab

(ax+b)(x+a)+bx+ab is the Second Term in the FOIL

Add both expressions together from First and Second Term

= ax^2 + a^2x + bx + ab

Step 3: Proof

(ax+b)(x+a) = ax^2 + a^2x + bx + ab

Identity is Found .

Trying with numbers now

(ax+b)(x+a) = ax^2 + a^2x + bx + ab

((2*5)+8)(5+2) =(2*5^2)+(2^2*5)+(8*5)+(2*8)

((10)+8)(7) =(2*25)+(4*5)+(40)+(16)

(18)(7) =(50)+(20)+(56)

126 =126

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the length of the rectangle is twice its width. write and solve a system of linear equations to find the length L and width W of

xz_007 [3.2K]

Answer:

2 ( m + 2 m) = 36 is the required linear equation

Length of the rectangle is 12 ft and width = 6 ft

Step-by-step explanation:

Let the width of the rectangle = m ft.

So, the length of the rectangle = 2m ft.

Perimeter of rectangle = 36 ft

Now, PERIMETER OF THE RECTANGLE = 2(LENGTH + WIDTH)

⇒2 ( m + 2m) = 36

or, 2 x 3m = 36

⇒ 6m = 36 , or m = 36/6

⇒ m =6 ft

So, the Width of the rectangle; = m = 6 ft

and the Length of the rectangle = 2 m = 2 x 6 = 12 ft.

5 0

3 years ago

4.5÷6= estimate the quotient

scZoUnD [109]

Answer:

0.75 - 0.8

Step-by-step explanation:

4.5/6 = 0.75

The closest number to round 0.75 to is 0.8

3 0

3 years ago

Read 2 more answers

A rectangular field is 95 meters long and 65 meters wide. Give the length and width of another rectangular field that has the sa

Lena [83]

Answer:

There are a ton of answers. For instance, 1m by 159m.

Step-by-step explanation:

The formula for the area is $a=l*w$ , where $l$ and $w$ are constants.

The formula for perimeter is $p=2l+2w$

The question wants another rectangle that has the same perimeter, but a smaller area.

The perimeter of the two fields has to be:

$p=(2*95)+(2*65)\\p=190+130\\p=320$

Thankfully, the question never specified how much smaller the area has to be. So let's go to the logical extreme and make it 1 meter wide. To conserve the perimeter, we'd have to add the removed 64 meters to the original 95 meters of length, resulting in a rectangle with a width of 1m and a length of 159m. This results in an area of exactly 159 $m^{2}$ . The original rectangle had an area of 6175 $m^{2}$ . Mission accomplished!

But why stop there? Let's go even further down this rabbit hole!

Instead of 1, why don't we take it several steps further and use 0.0000001? At that point, the length would end up being 159.9999999m.

The area would be 0.00001599999999 $m^{2}$ .

Let's go further!!

Width: 0.00000000000000000001

Length: 159.99999999999999999999

Area: 0.00000000000000000001599999999999999999999 (approximate).

One more, for old time's sake.

Width: 0.00000000000000000000000000000000000000000000000001m

Length: 159.99999999999999999999999999999999999999999999999999m

Area: 0.00000000000000000000000000000000000000000000000015999999999999999999999999999999999999999999999999999 $m^{2}$

At that point, there's so little area in the plot of land that you could claim it has no area!

5 0

3 years ago

Select the expression that makes the equation true (−3⋅10 3 )⋅(4⋅10 6 ) select 2 answers

scZoUnD [109]

The answer is letter c , because if you multiply the number 4 that is outside with the third power you will get 12 and with the second power you will get 8 and base number stays the same. As an answer you’ll get the same numbers as the expression

5 0

3 years ago

A contract between a manufacturer and a consumer of light bulbs specifies that the mean lifetime of the bulbs must be at least 1

Alex17521 [72]

Answer:

Follows are the solution to the given points:

Step-by-step explanation:

In point a:

In this sense, describe what type of error I will be.

Type I error: to conclude that perhaps the mean bulb life would be less than three hours when it becomes (at least) 3 hours.

In point b:

Describe throughout this context what the Type II error becomes.

An error of type II: never assuming that its bulbs' mean lifetime is much less than 3 hours. three hours at least

In point c:

What error — type I and type II — would further impact the interaction between the manufacturer and the customer?

A Type II error is probably further problematic because it means that even the buyer will buy bulbs that do not last long.

4 0

3 years ago