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adoni [48]
3 years ago
7

Which expressions represent a quadratic expression in factored form?

Mathematics
1 answer:
Bingel [31]3 years ago
8 0

Answer:

3 and 4

Step-by-step explanation:

Well to start we have to know that they are asking us, a factorized form of a quadratic expression

a quadratic expression is of the form

ax ^ 2 + bx + c

Now the factored form is as follows            

 a ( x - x1 )  ( x - x2 )

Next, let's look at each of the options

In this case we lack a term with x since if we solve we have a linear equation

1.    5(x+9)

  5x + 45

In this case if we pay attention they are being subtracted instead of multiplying, so we will not get a quadratic function

2.    (x+4) - (x+6)

       -2

In this case we have everything we need, now let's try to solve

3.     (x-1) (x-1)

      x^2 - x - x + 1

      x^2 - 2x + 1       quadratic function

In this case we have everything we need, now let's try to solve

4.     (x-3) (x+2)

        x^2 -3x +2x -6

         x^2 -x - 6    quadratic function

In this case we have a quadratic function but we do not have it in its factored form since we can observe the x ^ 2

5.     x^2 + 8x

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Answer:

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Step-by-step explanation:

First create like dominators

2/3 -1/6  = 4/6 - 1/6

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4/6 - 1/6 = 3/6

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3/6 = 1/2

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\qquad {\: \:\bigstar \:  {\underline{\overline{\boxed{\bf{Information \: provided \:  with  \: us }}}}}\: \bigstar}

➻ In a group of 40 people, 27 can speak English and 25 can speak Spanish.

\qquad {\: \:\bigstar \:  {\underline{\overline{\boxed{\bf{What \: we \:  have  \: to \: find ? }}}}}\: \bigstar}

➻ The required number of people who can speak both English and Spanish .

\qquad {\: \:\bigstar \:  {\underline{\overline{\boxed{\bf{Assumption}}}}}\: \bigstar}

<u>Consider</u> ,

➻ A → Set of people who speak English.

➻ B → Set of people who speak Spanish

➻ A∩B → Set of people who can speak both English and Spanish

\qquad {\: \:\bigstar \:  {\underline{\overline{\boxed{\bf{Given}}}}}\: \bigstar}

  • ➻ n (A) = 27

  • ➻ n (B) = 25

  • ➻ n (A∪B) = 40

  • ➻ n(A∩B) = ?

\qquad {\: \:\bigstar \:  {\underline{\overline{\boxed{\bf{Now}}}}}\: \bigstar}

➻ n(A∪B) = n(A) + n (B) - n(A∩B)

➻ 40 = 27 + 25 - n (A∩B)

➻ 40 = 52 - n (A∩B)

➻ n (A∩B) = 52 - 40

➻ ∴ n (A∩B) = 12

\qquad {\: \:\bigstar \:  {\underline{\overline{\boxed{\bf{Therefore}}}}}\: \bigstar}

∴ Required Number of persons who can speak both English and Spanish are <u>12 .</u>

━━━━━━━━━━━━━━━━━━━━━━

\qquad {\: \:\bigstar \:  {\underline{\overline{\boxed{\bf{Verification}}}}}\: \bigstar}

➻ n(A∪B) = n(A) + n (B) - n(A∩B)

➻ 40 = 27 + 25 - 12

➻ 40 = 52 - 12

➻ 40 = 40

➻ ∴ L.H.S = R.H.S

━━━━━━━━━━━━━━━━━━━━━━

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