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prohojiy [21]
3 years ago
10

The length of a rectangle is nine inches more than its width. Its area is 486 square inches. Find the width and length of the re

ctangle.

Mathematics
1 answer:
Elan Coil [88]3 years ago
3 0

Answer:

  • width: 18 in
  • length: 27 in

Step-by-step explanation:

The relations between length (L) and width (W) are ...

  W +9 = L

  LW = 486

Substituting gives ...

  (W+9)W = 486

  W^2 +9W -486 = 0 . . . put in standard form

  (W +27)(W -18) = 0 . . . . factor

  W = 18 . . . .  the positive solution

The width of the rectangle is 18 inches; the length is 27 inches.

_____

<em>Comment on factoring</em>

There are a number of ways to solve quadratics. Apart from using a graphing calculator, one of the easiest is factoring. Here, we're looking for factors of -486 that have a sum of 9.

486 = 2 × 3^5, so we might guess that the factors of interest are -2·3² = -18 and 3·3² = 27. These turn out to be correct: -18 +27 = 9; (-18)(27) = -486.

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Yanka [14]
Hello,
Let's assume n,n+1,n+2,n+3,n+4 the 5 numbers

n+(n+1)+...+(n+4)=5n+10=265
5n=265-10
5n=255
n=51
The 5th number is 51+4=55

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3 years ago
Factor: 2x + 2y<br> Show work please
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2(x + y)

Step-by-step explanation:

You can pull out a 2 from the expression.

So divide 2x by 2 and 2y by 2.

2x/2 = x

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Answer:

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3 years ago
You would like to make a nutritious meal of eggs, edamame, and elbow macaroni. The meal should provide at least 40 g of carbohyd
arsen [322]

Answer:

2x + 12y + 43 ≥ 40

17x + 12y + 8z ≥ 20

14x + 6y + z ≤ 50

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y ≥ 0

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Step-by-step explanation:

given:

Cost Eggs = $2

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cost of  elbow Macaroni = $3

Lets eggs = x,

edamame = y

elbow macaroni = z

TC = 2x+5y+3z

Therefore;

2x + 12y + 43 ≥ 40

17x + 12y + 8z ≥ 20

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x ≥ 0

y ≥ 0

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the first objective is to make sure the total cost is subject to the required nutritional requirements.

So the total cost function (TC) is denoted by the number of servings multiplied for each costs. Eggs cost $2, edamame $5, and macaroni $3.

The problem subjects that each meal contains at least 40g of carbohydrates (this is the condition).

to get this we need to add what each meal component adds to the total, eggs add 2g of carbs, edamame 12g, and macaroni 43g.

Same should be done for protein, we require at least 20 grams of protein,  Eggs add 17g, edamame adds 12g, and macaroni adds 8g.

and lastly we don't want more than 50 grams of fat,  Eggs add 14g, edamame add 6g and macaroni 1g.

4 0
3 years ago
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