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11111nata11111 [884]

3 years ago

11

A perfect square trinomial can be represented by a square model with equivalent length and width. Which polynomial can be repres

ented by a perfect square model
x2 – 6x + 9

x2 – 2x + 4

x2 + 5x + 10

x2 + 4x + 16

2 answers:

olchik [2.2K]3 years ago

5 0

From the given options, x^2 - 6x + 9 = (x - 3)^2 is a perfect square.

nikdorinn [45]3 years ago

5 0

Answer:

Option A is the correct answer

Step-by-step explanation:

For a perfect square quadratic equation discriminant b²-4ac is zero.

<u>Option A</u>

x²-6x+9, a = 1 , b = -6 and c = 9

b²-4ac = 36 - 4 x 1 x 9 = 0

Correct answer.

<u>Option B</u>

x²-2x+4, a = 1 , b = -2 and c = 4

b²-4ac = 4 - 4 x 1 x 4 = -12

Wrong answer.

<u>Option C</u>

x²+5x+10, a = 1 , b = 5 and c = 10

b²-4ac = 25 - 4 x 1 x 10 = -15

Wrong answer.

<u>Option D</u>

x²+4x+16, a = 1 , b = 4 and c = 16

b²-4ac = 16 - 4 x 1 x 16 = -48

Wrong answer.

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Use decimals and fractions in the same equation showing the Commutative Property. Repeat for the Associative Property.

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For Commutative Property of Addition

Let us take a decimal number $2.14$ and a fraction $\frac{5}{20}$

Now, according to the Commutative property of Addition:

For any two numbers $a$ and $b$ :

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So, for $2.14$ and $\frac{5}{20}$

Let us add

$2.14+\frac{5}{20} = \frac{214}{100} +\frac{5}{20}$

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$\frac{5}{20} + 2.14 = \frac{5}{20} + \frac{214}{100}$

$= \frac{5 \times 5}{20 \times 5} +\frac{214}{100} \\ \\= \frac{25}{100} + \frac{214}{100} \\ \\= 0.25 + 2.14 \\ \\ = 2.39$

Therefore, $2.14+\frac{5}{20} = \frac{5}{20} + 2.14$

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For Associated Property of Addition

Let us take two same decimal numbers $2.14$ , $7.25$ and a fraction $\frac{5}{20}$

Now, according to the Associated property of Addition:

For any three numbers $a$ , $b$ and $c$

$a + (b+c) =(a+b) + c$

So, for $2.14$ , $7.25$ and $\frac{5}{20}$

The Left hand side:

$a + (b+c)$

$2.14 + (7.25 + \frac{5}{20}) = 2.14 + (\frac{725}{100} + \frac{5 \times 5}{20\times 5})$

$= 2.14 + (\frac{725}{100} + \frac{25 }{100})$

$= 2.14 + (\frac{750}{100} )$

$= \frac{214}{100} + \frac{750}{100}$

$= \frac{964}{100}$

$=9.64$

The Right hand side:

$(a + b )+c$

$(2.14 + 7.25 )+ \frac{5}{20}= ( 9.39 ) + \frac{5 }{20}$

$= 9.39 + \frac{5 \times 5 }{20 \times 5}$

$= 9.39 + \frac{25}{100}$

$= 9.39 + 0.25$

$= 9.64$

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$(2.14 + (7.25 + \frac{5}{20} )= (2.14 + 7.25 )+ \frac{5}{20}$

Therefore, $2.14+\frac{5}{20} = \frac{5}{20} + 2.14$

Hence, Associative Property of Addition is satisfied.

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