Answer:
3.8m
Step-by-step explanation:
Since Lara is putting lace trim around the border of a circular tablecloth, by the time she finishes she has covered the circumference.
The circumference of a circle is calculated using:
![C=\pi \: d](https://tex.z-dn.net/?f=C%3D%5Cpi%20%5C%3A%20d)
where d is the diameter of the circle.
It was given that the diameter of the circular table cloth is 1.2 meters.
![C=3.14 \times 1.2](https://tex.z-dn.net/?f=C%3D3.14%20%5Ctimes%201.2)
![C=3.768](https://tex.z-dn.net/?f=C%3D3.768)
Therefore the length of the lace she needed is 3.8m
Answer : 23.77
Pythagoras theorem states that in any right angled triangle , the sum of squares of base and perpendicular is equal to the square of hypotenuse .
- Here in the given figure , hypotenuse is 30.5 and perpendicular is 19.1 .
![\sf\longrightarrow (base)^2+(perpendicular)^2=hypotenuse^2\\](https://tex.z-dn.net/?f=%5Csf%5Clongrightarrow%20%28base%29%5E2%2B%28perpendicular%29%5E2%3Dhypotenuse%5E2%5C%5C)
- Substituting the respective values,
![\sf\longrightarrow x^2 +(19.1)^2 = (30.5)^2 \\](https://tex.z-dn.net/?f=%5Csf%5Clongrightarrow%20x%5E2%20%2B%2819.1%29%5E2%20%3D%20%2830.5%29%5E2%20%5C%5C)
![\sf\longrightarrow x^2 + 364.81 = 930.25 \\](https://tex.z-dn.net/?f=%5Csf%5Clongrightarrow%20x%5E2%20%2B%20364.81%20%3D%20930.25%20%5C%5C)
![\sf\longrightarrow x^2 = 930.25 -364.81\\](https://tex.z-dn.net/?f=%5Csf%5Clongrightarrow%20x%5E2%20%3D%20930.25%20-364.81%5C%5C)
![\sf\longrightarrow x^2 = 565.44\\](https://tex.z-dn.net/?f=%5Csf%5Clongrightarrow%20x%5E2%20%3D%20565.44%5C%5C)
![\sf\longrightarrow x=\sqrt{565.44} \\](https://tex.z-dn.net/?f=%5Csf%5Clongrightarrow%20x%3D%5Csqrt%7B565.44%7D%20%5C%5C)
![\sf\longrightarrow \underline{\boxed{\bf base (x) = 23.77 }} \\](https://tex.z-dn.net/?f=%5Csf%5Clongrightarrow%20%5Cunderline%7B%5Cboxed%7B%5Cbf%20base%20%28x%29%20%3D%2023.77%20%7D%7D%20%5C%5C)
Let me know if you have any queries in the comment section !
You combine like terms so 5x + 3x= 8x and 2y + 4y = 6y so it is 8x + 6y
The solution is B. (3,-2)