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saul85 [17]
3 years ago
5

PLEASE HELP I WILL MARK AS BRAINLIEST!!! HELP PLEASE!!!!!

Mathematics
1 answer:
Natasha2012 [34]3 years ago
4 0

Answer:

The answer would be x=7

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A café owner is designing a new menu and wants to include a decorative border around the outside of her food listings. Due to th
kipiarov [429]

The 13-in. by 9-in. rectangle where the food listings fit has an area of 13 in. * 9 in. = 117 in.^2

Adding 48 in.^2 for the border, the total area of the menu with the border will be 117 in.^2 + 48 in.^2 = 165 in.^2

The border has to have uniform width around the menu. We need to find the width of the border. Let the border be x inches wide. Then since you have a border at each of the 4 sides, the border will add 2x to the length of the rectangle and 2x to the width of the rectangle. The menu will have a length of 2x + 13 and a width of 2x + 9. The area of the larger rectangle must by 165 in.^2. The area of a rectangle is length times width, so we get our equation:

(2x + 13)(2x + 9) = 165

Multiply out the left side (use FOIL or any other method you know):

4x^2 + 18x + 26x + 117 = 165

4x^2 + 44x + 117 = 165

4x^2 + 44x - 48 = 0

Divide both sides by 4.

x^2 + 11x - 12 = 0

Factor the left side.

(x + 12)(x - 1) = 0

x + 12 = 0 or x - 1 = 0

x = -12 or x = 1

The solution x = -12 is not valid for our problem because the width of a border cannot be a negative number. Discard the negative solution.

The solution is x = 1.

Answer: The border is 1 inch wide.

Check. Add 2 inches to the length and width of the food listings rectangle to get 15 inches by 11 inches. A = 15 in. * 11 in.= 165 in.^2. Now subtract the area of the border, 48 in.^2, 165 in.^2 = 48 in.^2 = 117 in.^2, and you get the area of the 13-in. by 9-in. rectangle. This shows that our solution is correct.

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3 years ago
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Is there a way to simplify the process of plugging in factors through synthetic division to find the zeros of a polynomial? I am
Iteru [2.4K]
Yes you can use the discriminant of a quadratic/polynomial. For instance, if
b^2 - 4ac = 0 there is one real root. If b^2 - 4ac > 0 there are two real roots and ib^2 - 4ac < 0  there are no real roots

The discriminant comes from the quadratic equation, which is the following.
x = \frac{-b \pm \sqrt{b^2-4ac}}{2a}
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3 years ago
Which number produces a rational number when multiplied by 0.4
Katyanochek1 [597]
A, B and D are already rational numbers, 0.4 itself is a rational number, two rational numbers make a product of rational number. 
So A, B, D are the correct choices. 

Are you sure it asks for rational numbers, not irrational number?
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3 years ago
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Can someone please help me?
miss Akunina [59]

Answer:

c

Step-by-step explanation:

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What question is it because I can’t see it
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