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3 years ago

Write the square of the binomial as a polynomial: (-1 1/3p + 6q)^2

Mathematics

1 answer:

Thepotemich [5.8K]3 years ago

5 0

Answer:

$\frac{16}{9}$ p² -16pq + 36q²

Step-by-step explanation:

Given

(- $\frac{4}{3}$ p + 6q)²

= (- $\frac{4}{3}$ p + 6q)(- $\frac{4}{3}$ p + 6q)

Each term in the second factor is multiplied by each term in the first factor, that is

- $\frac{4}{3}$ p(- $\frac{4}{3}$ p + 6q) + 6q(- $\frac{4}{3}$ p + 6q)

= $\frac{16}{9}$ p² - 8pq - 8pq + 36q² ← collect like terms

= $\frac{16}{9}$ p² - 16pq + 36q²

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The game of Connex contains one 4-unit piece, two identical 3-unit pieces, three identical 2-unit pieces and four identical 1-un

Aleks [24]

Answer: 277 ways

Step-by-step explanation:

Let’s start bycreating 10-unit pieces using the 4-unit piece.

The arrangements are:

1). 4-3-3 (3 permutations)

2). 4-3-2-1 = 4! = 24 permutations.

3). 4-3-1-1-1 (5*[4!/(3!1!)]

= 5*4

= 20permutations

4). 4-2-2-2 (4 permutations)

5). 4-2-2-1-1 (5 *[4!/(2!2!)]

= 5*6

= 30 permutations

6). 4-2-1-1-1-1(6*[5!/(4!1!)]

= 6*5

= 30 permutations

Let’s-consider the arrangements using one or more3-unit pieces and no 4-unit piece:

7). 3-3-2-2 (4!/(2!2!)

8). 3-3-2-1-1 (5*(4!/(2!2!)

= 5*6

= 30 permutations.

9). 3-3-1-1-1-1 (6!/(4!2!) = 0

10). 3-2-2-2-1 (5*4!/(3!1!)

= 5*4

= 20permutations

11). 3-2-2-1-1-1 (6*5!/(3!2!)

= 6*10

= 60 permutations

Finally we would look at the arrangements using only 1-and 2-unit pieces:

12). 2-2-2-1-1-1-1 (7!/(4!3!)

= 35 permutations

add them all up:

(3 + 24 + 20 + 4) + (30 + 30 + 6 + 30) + (15 + 20 + 60 + 35)

=51 + 96 + 130

= 277ways

5 0

2 years ago

<img src="https://tex.z-dn.net/?f=%20-%20y%20%3D%20%5Cfrac%7B2%7D%7B5%7Dx%20-%203" id="TexFormula1" title=" - y = \frac{2}{5}x -

raketka [301]

The first step to solving this equation is to change the signs on both sides of the equation
y = - $\frac{2}{5}$ x + 3
Since we don't know what x is but we do know why y is,, we will write our answer with the answer to y and x being left as undefined.
y = - $\frac{2}{5}$ x + 3, x ∈ R
Let me know if you have any further questions
:)

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3 years ago

2. At a particular snack stand, each dill pickle has 65 calories and each bag of

Naddika [18.5K]

Answer:

5 pickles and 1.4 bags of popcorn

Step-by-step explanation:

5x 65= 375

695 - 375= 370

370 ÷ 250 = 1.4

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2 years ago

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Dima020 [189]

Answer:

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2 years ago

Dora's car can travel 81 miles using 2.7 gallons of gas. At this rate, how far, in miles, can Dora travel using

Delvig [45]

Answer:

2190 miles

Step-by-step explanation:

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3 years ago