Hello There!
Dividing a fraction is the same thing as multiplying by its reciprocal.
This means that
÷
is the same as multiplying
by
.
So basically when you divide you leave the first fraction alone but the second fraction in this case, 5/12 you would flip the number on top and the number on bottom to 12/5.
HAVE A GREAT DAY!
Answer:
Step-by-step explanation:
To find the area subtract the area of the semicircle from the area of the rectangle.
Although the line isn’t there, if you imagine there is one, then you will see that you form a rectangle which is the same line as the semicircle’s diameter.
The area of rectangle is:
⇒ ![A = lw](https://tex.z-dn.net/?f=A%20%3D%20lw)
⇒ ![A = (14)(8)](https://tex.z-dn.net/?f=A%20%3D%20%2814%29%288%29)
⇒ ![A = 112cm^{2}](https://tex.z-dn.net/?f=A%20%3D%20112cm%5E%7B2%7D)
The area of the semicircle;
⇒ ![A = \frac{1}{2}\pi r^{2}](https://tex.z-dn.net/?f=A%20%3D%20%5Cfrac%7B1%7D%7B2%7D%5Cpi%20r%5E%7B2%7D)
⇒ ![A = \frac{1}{2}\pi (7)^{2}](https://tex.z-dn.net/?f=A%20%3D%20%5Cfrac%7B1%7D%7B2%7D%5Cpi%20%287%29%5E%7B2%7D)
*Note here that the radius is half the diameter, so it is 7cm, not 14cm
⇒ ![A = 76.97cm^{2}](https://tex.z-dn.net/?f=A%20%3D%2076.97cm%5E%7B2%7D)
Finally subtract the two areas;
⇒ ![A = 112 - 76.97](https://tex.z-dn.net/?f=A%20%3D%20112%20-%2076.97)
⇒ ![A = 35.03cm^{2}](https://tex.z-dn.net/?f=A%20%3D%2035.03cm%5E%7B2%7D)
Answer:
Step-by-step explanation:
y=-1
Answer:
b) √200 = 10√2
Step-by-step explanation:
Here, the given expression is: √200
Simplifying the given expression, we get:
200 = 2 x 2 x 2 x 5 x 5
⇒ 200 = (2)² x (5) ² x 2
Taking ROOT both sides, we get:![\sqrt{200} = \sqrt{(2)^{2} \times (5)^{2} \times 2}\\\implies \sqrt{200} = \sqrt{(2)^{2} } \times \sqrt{(5)^{2} } \times \sqrt{(2) } = 2 \times 5 \times \sqrt{2}\\ = 10 \sqrt {2}\\\implies \sqrt{200} = 10 \sqrt {2}](https://tex.z-dn.net/?f=%5Csqrt%7B200%7D%20%20%3D%20%5Csqrt%7B%282%29%5E%7B2%7D%20%20%5Ctimes%20%285%29%5E%7B2%7D%20%20%5Ctimes%20%202%7D%5C%5C%5Cimplies%20%5Csqrt%7B200%7D%20%3D%20%5Csqrt%7B%282%29%5E%7B2%7D%20%7D%20%5Ctimes%20%5Csqrt%7B%285%29%5E%7B2%7D%20%7D%20%5Ctimes%20%20%5Csqrt%7B%282%29%20%7D%20%20%3D%202%20%5Ctimes%205%20%5Ctimes%20%5Csqrt%7B2%7D%5C%5C%20%3D%2010%20%5Csqrt%20%7B2%7D%5C%5C%5Cimplies%20%5Csqrt%7B200%7D%20%20%3D%20%2010%20%5Csqrt%20%7B2%7D)
Hence, √200 = 10√2
Answer:
The equation of the new line is ![y = -2x - 3](https://tex.z-dn.net/?f=y%20%3D%20-2x%20-%203)
Step-by-step explanation:
Reflecting a function over the x-axis:
Suppose we have a function y = f(x)
Suppose y' is the function y, reflected over the x-axis. Their relation is:
y' = -y
In this question:
Line with equation ![y = 2x + 3](https://tex.z-dn.net/?f=y%20%3D%202x%20%2B%203)
Reflection over the x-axis:
We have that:
![y = -(2x + 3) = -2x - 3](https://tex.z-dn.net/?f=y%20%3D%20-%282x%20%2B%203%29%20%3D%20-2x%20-%203)
The equation of the new line is ![y = -2x - 3](https://tex.z-dn.net/?f=y%20%3D%20-2x%20-%203)