Answer:
Length of garden will be 30 metres.
Step-by-step explanation:
Let the Width of garden be x metres.
then,
Length of garden will be (x+6) metres.
Area = Length × Breadth
720 = x X (c+6)
720 = x²+6x
0 = x²+6x-720
As we can see above equation is a quadratic equation in the form of ax²+bx+C.
so,
![= \frac{ - b ± \sqrt{{b}^{2} - 4ac} }{2a} \\ = \frac{ - 6 ± \sqrt{{6}^{2} - 4 \times 1 \times - 720} }{2} \\ = \frac{ - 6 ± \sqrt{36 + 2880} }{2} \\ = \frac{ - 6 ± \sqrt{2916} }{2} \\ = \frac{ - 6 ± 54}{2}\\= \frac{-6+54}{2} ... \frac{ - 6 - 54}{2} \\ = \frac{48}{2} ... \frac{ - 60}{2} \\ = 24... - 30](https://tex.z-dn.net/?f=%20%3D%20%20%5Cfrac%7B%20-%20b%20%C2%B1%20%20%5Csqrt%7B%7Bb%7D%5E%7B2%7D%20-%204ac%7D%20%20%7D%7B2a%7D%20%20%5C%5C%20%3D%20%20%20%5Cfrac%7B%20-%206%20%C2%B1%20%20%20%5Csqrt%7B%7B6%7D%5E%7B2%7D%20-%204%20%5Ctimes%201%20%5Ctimes%20%20-%20720%7D%20%20%7D%7B2%7D%20%20%5C%5C%20%3D%20%20%20%20%5Cfrac%7B%20-%206%20%C2%B1%20%20%5Csqrt%7B36%20%2B%202880%7D%20%7D%7B2%7D%20%20%5C%5C%20%20%3D%20%20%20%5Cfrac%7B%20-%206%20%C2%B1%20%20%5Csqrt%7B2916%7D%20%7D%7B2%7D%20%20%5C%5C%20%20%3D%20%20%20%5Cfrac%7B%20-%206%20%C2%B1%2054%7D%7B2%7D%5C%5C%3D%20%5Cfrac%7B-6%2B54%7D%7B2%7D%20...%20%5Cfrac%7B%20-%206%20-%2054%7D%7B2%7D%20%20%5C%5C%20%20%3D%20%20%5Cfrac%7B48%7D%7B2%7D%20...%20%5Cfrac%7B%20-%2060%7D%7B2%7D%20%20%5C%5C%20%20%3D%2024...%20-%2030)
One of the Roots of the Quadratic equation is 24 and other is -30.
And as we know width of any garden cannot be negative so the width of garden will be 24 metres.
As we got the width,
adding 6 to it will give us the Length,
So,
24 metres + 6 = 30 metres.
Length of the garden is 30 metres.
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Answer:
73%
Step-by-step explanation:
Let us have the original price as $100
A discount of 27% will be;
27/100 * 100 = $27
so, the value to be paid will be $100 - $27 = $73
Now, what percentage of $100 is the $73 that was paid
that would be;
73/100 * 100% = 73%
Answer:
__
0.333
Step-by-step explanation:
you divide 1.00 by 3. The 3s never end.
Answer:
The equipment will cost $1740.
Step-by-step explanation:
Let the Cost of equipment, furniture and decoration be x, y and z.
Now, According to question,
x + y + z = 3600 ...... (1) (cost of all items)
x = 500 + y (∵ equipment cost 500 more than furniture)
and y = 2z ( ∵ furniture twice as much as decoration)
so, z = y/2
Now substituting the value of x and z in eq (1)
![x + y + z = 3600](https://tex.z-dn.net/?f=%20x%20%2B%20y%20%2B%20z%20%3D%203600)
![500 + y + y + \frac{y}{2} = 3600](https://tex.z-dn.net/?f=500%20%2B%20y%20%2B%20y%20%2B%20%5Cfrac%7By%7D%7B2%7D%20%3D%203600)
![2y + \frac{y}{2} = 3600 - 500](https://tex.z-dn.net/?f=2y%20%2B%20%5Cfrac%7By%7D%7B2%7D%20%3D%203600%20-%20500)
![\frac{5y}{2} = 3100](https://tex.z-dn.net/?f=%5Cfrac%7B5y%7D%7B2%7D%20%3D%203100)
![y = \frac{3100\times 2}{5} = 1240](https://tex.z-dn.net/?f=y%20%3D%20%5Cfrac%7B3100%5Ctimes%202%7D%7B5%7D%20%3D%201240)
So, the cost of furniture (y) = 1240
∴ Cost of equipment = y + 500 = 1240 + 500 = 1740
Therefore the cost of equipment was $1740.
Answer:
35°, 70°, 75°
Step-by-step explanation:
The sum of the 3 angles in a triangle = 180° , then
x + 2x + 75 = 180
3x + 75 = 180 ( subtract 75 from both sides )
3x = 105 ( divide both sides by 3 )
x = 35
2x = 2 × 35 = 70°
The angles in the Δ are 35°, 70°, 75°