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Alona [7]
1 year ago
5

Drag the tiles to the boxes to form correct pairs. Not all tiles will be used. Match the pairs of polynomials to their products.

(xy + 9y + 2) and (xy – 3) x2y2 + 3x2y – 7xy – 27x – 18 (2xy + x + y) and (3xy2 – y) 6x2y3 – 2xy2 + 3x2y2 – xy + 3xy3 – y2 (x – y) and (x + 3y) x3y + 3x2 + 3x2y2 + 7xy – 6 (xy + 3x + 2) and (xy – 9) x2 – 9y2 (x2 + 3xy – 2) and (xy + 3) (x + 3y) and (x – 3y)
Mathematics
1 answer:
andreyandreev [35.5K]1 year ago
5 0

The products of the polynomials are:

  • (xy + 9y + 2) * (xy - 3) = x²y² - xy + 9xy² - 27y - 6
  • (2xy + x + y) * (3xy² - y) = 6x²y³ - 2xy² + 3x²y² -xy + 3xy³- y²
  • (x - y) * (x + 3y) = x² + 2xy + 3y²
  • (xy + 3x + 2) * (xy – 9)  = x²y² - 7xy + 3x²y - 27x  - 18
  • (x² + 3xy - 2) * (xy + 3)  = x³y + 3x² + 3x²y² + 7xy - 6
  • (x + 3y) * (x – 3y) = x² - 9y²

<h3>How to evaluate the products?</h3>

To do this, we multiply each pair of polynomial as follows:

<u>Pair 1: (xy + 9y + 2) and (xy – 3)</u>

(xy + 9y + 2) * (xy - 3)

Expand

(xy + 9y + 2) * (xy - 3) = x²y² - 3xy + 9xy² - 27y + 2xy - 6

Evaluate the like terms

(xy + 9y + 2) * (xy - 3) = x²y² - xy + 9xy² - 27y - 6

<u>Pair 2: (2xy + x + y) and (3xy² - y)</u>

(2xy + x + y) * (3xy² - y)

Expand

(2xy + x + y) * (3xy² - y) = 6x²y³ - 2xy² + 3x²y² -xy + 3xy³- y²

<u>Pair 3: (x – y) and (x + 3y) </u>

(x - y) * (x + 3y)

Expand

(x - y) * (x + 3y) = x² + 3xy - yx + 3y²

Evaluate the like terms

(x - y) * (x + 3y) = x² + 2xy + 3y²

<u>Pair 4: (xy + 3x + 2) and (xy – 9) </u>

(xy + 3x + 2) * (xy – 9)

Expand

(xy + 3x + 2) * (xy – 9)  = x²y² - 9xy + 3x²y - 27x + 2xy - 18

Evaluate the like terms

(xy + 3x + 2) * (xy – 9)  = x²y² - 7xy + 3x²y - 27x  - 18

<u>Pair 5: (x² + 3xy - 2) and (xy + 3) </u>

(x² + 3xy - 2) * (xy + 3)

Expand

(x² + 3xy - 2) * (xy + 3)  = x³y + 3x² + 3x²y² + 9xy - 2xy - 6

Evaluate the like terms

(x² + 3xy - 2) * (xy + 3)  = x³y + 3x² + 3x²y² + 7xy - 6

<u>Pair 6: (x + 3y) and (x – 3y)</u>

(x + 3y) * (x – 3y)

Apply the difference of two squares

(x + 3y) * (x – 3y) = x² - 9y²

Read more about polynomials at:

brainly.com/question/4142886

#SPJ1

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1 4/5

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3 years ago
In parallelogram ABCD, AD = 12 in, m∠C = 46º, m∠DBA = 72º. Find the area of ABCD
dmitriy555 [2]

Answer:

The area of   parallelogram ABCD  is78.42 \mathrm{in}^{2}

Explanation:

Given:

AD = 12 in

m \angle C=46^{\circ}

m \angle D B A=72^{\circ}

To Find:

The area of   parallelogram ABCD=?  

Solution:

When we construct the parallelogram with the given data, we get a parallelogram formed by 12 cm as one side and an angle with 46 degrees.  

The area of the parallelogram can be calculated by a b * \sin (a n g l e)

Substituting the value of a=12  we have

\text { Area of parallelogram }=12 * \text { bsin } 46

<u>To find  the value of b, </u>

We know that area of a triangle can be expressed as,

\text { Area of triangle }=(A b / 2) \sin (\text {angle})

So,

(12 * B D / 2) * \sin 46=(A B * B D / 2) * \sin 72

Cancelling BD and 2 on both sides we get,  

12 * \sin 46=A B * \sin 72

A B=12 * \frac{\sin 46}{\sin 72}

Therefore,

b=\frac{12 \sin 46}{\sin 72}

Substituting the value of b,

=12 *\left(\frac{12 \sin 46}{\sin 72}\right) * \sin 46

=78.42  

So the area of the parallelogram is78.42 \mathrm{in}^{2}

6 0
3 years ago
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Vanyuwa [196]

y=mx+b

first find the y intercept or b or x=0

b=5

now find the slope

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m=3/2

the equation is D. y=3/2x+5

3 0
2 years ago
Solve the system using substitution.<br> 2x = 5y + 14<br> x = 5y
andrew-mc [135]

Answer:

<h2>y = 2.8</h2><h2>x = 14</h2>

Step-by-step explanation:

To solve an equation, we can only have one variable. In this case, we are given the system 2x = 5y + 14. However, we are given the value of x in terms of y. We can substitute 10y in for 2x and solve.

10y = 5y + 14

First, we need to get all the variables on one side of the equation, so we subtract 5y.

5y = 14

Divide by 5

y = 14/5 or 2 4/5 or 2.8

Now for the x part.

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Subtract 1x

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Now we check our answer.

2(14) = 5(2.8) + 14

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28 = 28

Because 28 equals 28, our solutions are correct.

7 0
3 years ago
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