PLEASE HELP Part A: The area of a square is (9x2 + 24x + 16) square units. Determine the length of each side of the square by factoring the area expression completely. Show your work. (5 points)

Part B: The area of a rectangle is (16x2 − 25y2) square units. Determine the dimensions of the rectangle by factoring the area expression completely. Show your work. (5 points)

9514 1404 393

  A: (3x +4)

  B: (4x +5y) × (4x -5y)

Step-by-step explanation:

Part A:

Since we know the trinomial is a perfect square, we know the terms of each binomial factor are the square roots of the first and last terms of the trinomial.

  9x² +24x +16 = (√(9x²) +√16)² = (3x +4)²

The side of the square is 3x+4.

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Part B:

The difference of squares is factored like this:

  a²-b² = (a +b)(a -b)

The given area expression is the difference of squares with ...

  a = 4x, b = 5y

so, the factorization is ...

  16x² -25y² = (4x +5y)(4x -5y)

The dimensions of the rectangle are (4x+5y) by (4x-5y).

walter needs to make at least 5 more cookies but no more than 40. 5 ≤ x ≤ 40

step-by-step explanation:

20 ≤ x + 15 ≤ 55

subtract 15 from all parts

20-15 ≤ x + 15-15 ≤ 55-15

5 ≤ x ≤ 40

this means how many more cookies he has to make

walter needs to make at least 5 more cookies, but no more than 40 cookies; 5 ≤ x ≤ 40