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Ne4ueva [31]
3 years ago
10

The distance from one corner of a rectangular garden to the other is 13 ft. The length of the garden is 7 ft longer than the wid

th. Write a quadratic equation to find the dimension of the garden. Solve the equation and find the area of the garden in square feet.
Mathematics
1 answer:
coldgirl [10]3 years ago
4 0

Answer:

  • dimensions: 12 ft by 5 ft
  • area: 60 ft²

Step-by-step explanation:

Let x represent the shorter dimension in feet. Then the longer one is x+7 and the Pythagorean theorem tells us the relation of these to the diagonal is ...

  x² + (x+7)² = 13²

  2x² +14x + 49 = 169 . . . . eliminate parentheses

  x² +7x -60 = 0 . . . . . subtract 169 and divide by 2

  (x +12)(x -5) = 0 . . . . factor the equation

  x = -12 or +5 . . . . . . . only the positive value of x is useful here.

The short dimension is 5 ft, so the long dimension is 12 ft. The area is their product, 60 ft².

_____

<em>Comment on finding the area</em>

The quadratic equation above can be rearranged and factored as ...

  x(x +7) = 60

Since the dimensions of the garden are x and (x+7), this product is the garden's area. This equation tells us the area is 60. We don't actually have to find the dimensions.

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daser333 [38]

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Answer: 40°

Explanation... since U is on a straight line and since GS is 140

180 - 140 = 40

<em>Hope it helps...</em>

3 0
3 years ago
If a and B are the zeros of the quadratic polynomial f(x) = x2- 5x + 4 find the value of 1/a+1/b-2ab
bearhunter [10]

Answer:

<h2>-27/4</h2>

Step-by-step explanation:

Given the quadratic polynomial given as g(x) = x²- 5x + 4, the zeros of the quadratic polynomial occurs at g(x) = 0 such that x²- 5x + 4 = 0.

Factorizing the resulting equation to get the roots

x²- 5x + 4 = 0

(x²- x)-(4 x + 4) = 0

x(x-1)-4(x-1) = 0

(x-1)(x-4) = 0

x-1 = 0 and x-4 = 0

x = 1 and x = 4

Since a and b are known to be the root then we can say a = 1 and b =4

Substituting the given values into the equation  1/a+1/b-2 ab , we will have;

= 1/1 + 1/4 - 2*1*4

= 1 + 1/4 - 8

= 5/4 - 8

Find the Lowest common multiple

= (5-32)/4

= -27/4

<em>Hence the required value is -27/4</em>

5 0
3 years ago
Put brackets in the calculation below to make it correct.<br><br> 15 - 4 x 2 + 1 = 3
bagirrra123 [75]
If you put brackets around (2+1), your method of working is: 
1) 15-4*(2+1)=3 
2) 15-4*3=3
3) 15-12=3
You don't need any more brackets, as the BIDMAS (brackets, Indices, division, multiplication, addition, subtraction) rule does the rest of the job for you. 
The answer is therefore: 15-4*(2+1)=3
3 0
2 years ago
In 2002, the Bookstore sold 1000 paperback books and 1500 hardback books. In 2003, the store sold 15% more paperback books and 5
ratelena [41]
Given:
2002 sold 1000 paperback books and 1500 hardback books for a total of 2,500 books.

2003 sold 15% more paperback books and 5% more hardback books.
1000 x 1.15 = 1,150 paperbacks
1500 x 1.05 = 1,575 hardbacks

1150 + 1575 = 2,725

2,725 - 2,500 = 225
225 / 2,500 = 0.09
0.09 x 100% = 9%  choice C

7 0
3 years ago
Write in vertex form<br> f(x)=x^2+12x+34
svp [43]

Answer:

(-6, -2)

Step-by-step explanation:

f(x) =  {x}^{2}  + 12x + 34

= f(x) =  {1x}^{2}  + 12x + 34

= a = 1, b = 12

= x =  -  \frac{12}{2 \times 1}

= x =  -  \frac{12}{2}

= x = -6

= f(x) =  {x}^{2}  + 12x + 34.. =  - 6

= f( - 6) =  - 2

= (-6, -2)

8 0
2 years ago
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