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emmainna [20.7K]
3 years ago
6

Marie has a rectangular board 12 inches by 16 inches around which she wants to put a uniform border of sherlls. if she has enoug

h shells for a border whose area is 128 determine the width of the border
Mathematics
1 answer:
Ede4ka [16]3 years ago
5 0
Area of rectangular board = length (inches) x width (inches) = 12" x 16" = 192 in²

Area of the border is given as 128 in²

Adding the area of the board and the border gives (192 + 128)in² = 320 in²

Set this up as the algebraic equation (x + 12)(x + 16) = 320 and solve for x:

Remember to use the FOIL method, which is multiplying the terms in the order of first, outer, inner, last.

x² + 12x + 16x + 192 = 320

x² + 28x + 192 - 320 = 0

x² + 28x - 128 = 0

solve for the two x values:

(x + 32)(x - 4) = 0, and knowing we only need the positive x value

x = 4 or 4 inches is the width of the border



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Ymorist [56]
Area of the rectangle minus area of 2 circles

Area of rectangle is 8x16
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Answer is:
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3 years ago
I NEED HELP PLEASE, THANKS! :) Determine the zeros for and the end behavior of f(x) = x(x – 4)(x + 2)^4.
Amiraneli [1.4K]

Answer:  a) zeros: x = {0, 4, -2}

               b) as x → ∞,  y → ∞

                   as x → -∞,  y → ∞

<u>Step-by-step explanation:</u>

I think you mean (a) find the zeros and (b) describe the end behavior

(a) Find the zeros by setting each factor equal to zero and solving for x:

      x (x - 4) (x + 2)⁴ = 0

  • x = 0   Multiplicity of 1  --> odd multiplicity so it crosses the x-axis
  • x = 4  Multiplicity of 1  --> odd multiplicity so it crosses the x-axis
  • x = -2 <u>Multiplicity of 4 </u> --> even multiplicity so it touches the x-axis

                       Degree  =  6

(b) End behavior is determined by the following two criteria:

  1. Sign of Leading Coefficient (Right side): Positive is ↑, Negative is ↓
  2. Degree (Left side): Even is same direction as right side, Odd is opposite direction of right side

Sign of the leading coefficient is Positive so right side goes UP

                                                                        as x → ∞,  y → ∞

Degree of 6 is Even so Left side is the same direction as right (UP)

                                                                        as x → -∞,  y → ∞

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Answer:

  B, C

Step-by-step explanation:

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The only other fact that must be true is that segments on the left side of the diagram are proportional to those (corresponding) on the right. (This is a property of the angle bisector.) There is nothing that says the sides must be equal, or that the triangle is isosceles.

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Answer:

No

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