The correct answer would be the first and the last ones.
Answer:
0.5 m
Step-by-step explanation:
Given that the dimensions of the garden are 15 meters by 20 meters.
The area of the new garden (original garden + stone placed around the perimeter) is 336m².
Let d be the width of the border having stepping stones as shown in the figure. The shaded region in the figure is the area having stepping stones.
The area including the shaded region ![= (15+2d)(20+2d) m^2](https://tex.z-dn.net/?f=%3D%20%2815%2B2d%29%2820%2B2d%29%20m%5E2)
![\Rightarrow 336 = (15+2d)(20+2d) \\\\\Rightarrow 336 = 300+ 70 d +4d^2 \\\\\Rightarrow 4d^2 +70d+300-336=0 \\\\\Rightarrow 4d^2 +70d-36=0 \\\\\Rightarrow 2d^2 +35d-18=0 \\\\\Rightarrow 2d^2 +36d-d-18=0 \\\\\Rightarrow (2d-1)(d+18)=0 \\\\\Rightarrow (2d-1)=0, \; or \; (d+18) \\\\\Rightarrow d= 0.5\;or -18 \\\\](https://tex.z-dn.net/?f=%5CRightarrow%20336%20%20%3D%20%2815%2B2d%29%2820%2B2d%29%20%5C%5C%5C%5C%5CRightarrow%20336%20%20%3D%20300%2B%2070%20d%20%2B4d%5E2%20%5C%5C%5C%5C%5CRightarrow%204d%5E2%20%2B70d%2B300-336%3D0%20%5C%5C%5C%5C%5CRightarrow%204d%5E2%20%2B70d-36%3D0%20%5C%5C%5C%5C%5CRightarrow%202d%5E2%20%2B35d-18%3D0%20%5C%5C%5C%5C%5CRightarrow%202d%5E2%20%2B36d-d-18%3D0%20%5C%5C%5C%5C%5CRightarrow%20%282d-1%29%28d%2B18%29%3D0%20%5C%5C%5C%5C%5CRightarrow%20%282d-1%29%3D0%2C%20%5C%3B%20or%20%5C%3B%20%28d%2B18%29%20%5C%5C%5C%5C%5CRightarrow%20d%3D%200.5%5C%3Bor%20-18%20%5C%5C%5C%5C)
As the width of the stone border can't be a negative value, so taking the positive value.
Hence, the width of the stone border is 0.5 m.
So, the wi
Answer:
8.4 dollars
Step-by-step explanation:
The error is in the resolution of the proportion. In fact, the initial proportion is correct:
![\frac{5}{3.5}=\frac{12}{x}](https://tex.z-dn.net/?f=%5Cfrac%7B5%7D%7B3.5%7D%3D%5Cfrac%7B12%7D%7Bx%7D)
where x is the total cost. However, the following step of the resolution is wrong. In fact, the correct resolution is the following:
- Multiplying by x on both sides:
![\frac{5x}{3.5}=12](https://tex.z-dn.net/?f=%5Cfrac%7B5x%7D%7B3.5%7D%3D12)
- Multiplying by 3.5 no both sides:
![5 x = 12 \cdot 3.5 \\5x = 42](https://tex.z-dn.net/?f=5%20x%20%3D%2012%20%5Ccdot%203.5%20%5C%5C5x%20%3D%2042)
And now we can find x:
![x=\frac{42}{5}=8.4](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B42%7D%7B5%7D%3D8.4)
So, the total cost is 8.4 dollars.
Answer:
x = 11
y = 17
Step-by-step explanation:
5y and (7y - 34) are vertical angles which means they're equal to each other:
5y = 7y - 34
5y - 7y = -34
-2y = -34
y = 17
(8x + 7) and (9x - 4) are also vertical angles:
8x + 7 = 9x - 4
8x - 9x = -4 - 7
-x = -11
x = 11