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ANTONII [103]
3 years ago
7

Why does using FOIL on polynomial expressions match so closely to integer multiplication?

Mathematics
1 answer:
dezoksy [38]3 years ago
7 0
<span> FOIL is a mnemonic rule for multiplying binomial (that is, two-term) algebraic expressions. </span>
<span>FOIL abbreviates the sequence "First, Outside, Inside, Last"; it's a way of remembering that the product is the sum of the products of those four combinations of terms. </span>

<span>For instance, if we multiply the two expressions </span>
<span>(x + 1) (x + 2) </span>
<span>then the result is the sum of these four products: </span>
<span>x times x (the First terms of each expression) </span>
<span>x times 2 (the Outside pair of terms) </span>
<span>1 times x (the Inside pair of terms) </span>
<span>1 times 2 (the Last terms of each expression) </span>
<span>and so </span>
<span>(x + 1) (x + 2) = x^2 + 2x + 1x + 2 = x^2 + 3x + 2 </span>
<span>[where the ^ is the usual way we indicate exponents here in Answers, because they're hard to represent in an online text environment]. </span>

<span>Now, compare this to multiplying a pair of two-digit integers: </span>
<span>37 × 43 </span>
<span>= (30 × 40) + (30 × 3) + (7 × 40) + (7 × 3) </span>
<span>= 1200 + 90 + 280 + 21 </span>
<span>= 1591 </span>

<span>The reason the two processes resemble each other is that multiplication is multiplication; the difference in the ways we represent the factors doesn't make it a fundamentally different operation. </span>
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Four gallons of paint are used to paint 20 chairs and 5 small tables.if each chair and table used the same amount of paint, how
Vinil7 [7]

Answer:

0.16 gallons of paint are used on each piece of furniture.

The answer lies between the whole numbers 0 and 1.

Step-by-step explanation:

we know that

Four gallons of paint are used to paint 20 chairs and 5 small tables.

if each chair and table used the same amount of paint

then

sum the total pieces of furniture

20+5=25 pieces

Find the unit rate

Divide the total gallons of paint used by the total pieces

\frac{4}{25}=0.16\ \frac{gallons}{piece}

therefore

0.16 gallons of paint are used on each piece of furniture.

The answer lies between the whole numbers 0 and 1.

7 0
3 years ago
Find the equation of the plane that is parallel to the vectors left angle 3 comma 0 comma 3 right angle and left angle 0 comma 1
Sholpan [36]

Answer:

x + 3y -z - 3 = 0      

Step-by-step explanation:

We have to find the equation of plane that is parallel to the vectors

\langle 3,0,3\rangle, \langle0,1,3\rangle

The plane also passes through the point (2,0,-1).

Hence, the equation of plane s given by:

\displaystyle\left[\begin{array}{ccc}x-2&y-0&z+1\\3&0&3\\0&1&3\end{array}\right]\\\\=(x-2)(0-3) - (y-0)(9-0) + (z+1)(3-0)\\=-3(x-2)-9y+3(z+1)\\\Rightarrow -3x + 6 - 9y + 3z + 3 = 0\\\Rightarrow 3x + 9y -3z -9 = 0\\\Rightarrow x + 3y -z - 3 = 0

It is the required equation of plane.

4 0
3 years ago
A bakery made 55 boxes of rolls. Each box holds 12 rolls. How many rolls were made in all?
Lerok [7]
In total 660 rolls were made in all
4 0
3 years ago
Find BC if BD = X + 29, AD = x = 39, AC = 20, and BC = x + 19
nalin [4]

Answer:

10 units

Step-by-step explanation:

We are given that

BD=x+29

AD=x+39

AC=20

BC=x+19

AC=AB+BC

20=AB+x+19

AB=20-x-19=1-x

AD=AB+BD

x+39=1-x+x+29

x=30-39=-9

Substitute the value of x=-9

Then , we get BC=-9+19=10 units

Answer: BC=10 units

5 0
2 years ago
JL is a common tangent to circles M and K at point J. If angle MLK measures 61ᵒ, what is the length of radius MJ? Round to the n
Sladkaya [172]
3.122

The process to getting this comes in many steps. Firstly, you need to find the angles for JLK and MLJ. To find JLK use the arcsin function using the opposite side and the hypotenuse. 

Arcsin(Opp/Hype) = JLK
Arcsin(.5) = JLK
30 degrees = JLK

This means MLJ = 31 degrees since they add up to 61 degrees. 

Now we need to find the length of LJ, which we can do using the Pythagorean Theorem. 

3^2 + JL^2 = 6^2
9 + JL^2 = 36
JL^2 = 27
JL = \sqrt{27}

Now that we have the angle of MLJ and the length of JL, we can use the tangent function to find MJ.

Tan(angle) = opp/adj
Tan(31) = MJ/\sqrt{27}
\sqrt{27}Tan(31) = MJ
3.122 = MJ
7 0
3 years ago
Read 2 more answers
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