B. Why does using FOIL on polynomial expressions match so closely to integer

1 answer:

7 0

FOIL is a mnemonic rule for multiplying binomial (that is, two-term) algebraic expressions.
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.

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

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

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.

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svetlana [45]

Answer:

0.73

Step-by-step explanation:

There are 100 total squares, and 73 are highlighted

73/100 = 0.73

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3 years ago

mary has 39 square feet of patio bricks. each square brick has sides 1 foot long. what is the greatest perimeter of a rectangle

bearhunter [10]

-- The smallest perimeter you can make with a certain area
is a circle.

-- The NEXT smallest perimeter with the same area is a square.

 With 1-ft by 1-ft square bricks, the shortest perimeter she could
make would be by using her bricks to make it as square as possible.
Without cutting bricks into pieces, the best she could do would be

 (13 bricks) x (3 bricks) .

= (13-ft) x (3-ft)

 Perimeter = (2 x length) + (2 x width)

 = (2 x 13-ft) + (2 x 3-ft)

 = (26-ft) + (6-ft) = 32 feet <== shortest perimeter.

-- Then, the more UNSQUARE you make it, the more perimeter
it takes to enclose the same area. That means Mary has to make
a rectangle as long and skinny as she can.

The longest perimeter she can make (without cutting bricks into
pieces) is (39 bricks) x (1 brick) .

 = (39-ft) x (1-ft) .

Perimeter = (2 x length) + (2 x width)

 = (2 x 39-ft) + (2 x 1-ft)

 = (78-ft) + (2-ft) = 80 feet .

What she'll have then is a brick path, 39 feet long and 1 foot wide,
and when you walk on it, you'll need to try hard to avoid falling off
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4 years ago

An account earns simple interest. $1800 at 6.5% for 30 months

Vikentia [17]

A = P(1 + rt)

Where:

A = Total Accrued Amount (principal + interest)
P = Principal AmountI = Interest Amount
r = Rate of Interest per year in decimal;
r = R/100
R = Rate of Interest per year as a percent;
R = r * 100
t = Time Period involved in months or years

Calculation:

First, converting R percent to r a decimal
r = R/100 = 6.5%/100 = 0.065 per year,
putting time into years for simplicity,
30 months ÷ 12 months/year = 2.5 years,
then, solving our equation

A = 1800(1 + (0.065 × 2.5)) = 2092.5 
A = $ 2,092.50

The total amount accrued, principal plus interest,
from simple interest on a principal of $ 1,800.00
at a rate of 6.5% per year
for 2.5 years (30 months) is $ 2,092.50.

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Ksju [112]

The measure of PRQ is 46 degrees.

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3 years ago

Simplify by dividing (-3/8) -5/9

Elodia [21]

Answer:

$\frac{-27}{40}$