Answer: X = t or minus 4 square root 3 and X= 4 square root 3 Explanation: add 48 on both sides bring down x squared = 48 take the square root on both sides you get X= t or - 4 square root 3 and X=4 square root 3) Animex yw
Answer:
![(C)\left(-\dfrac{1 }{2},-\dfrac{\sqrt{3} }{2} \right)$ and \left(\dfrac{1 }{2},\dfrac{\sqrt{3} }{2} \right)](https://tex.z-dn.net/?f=%28C%29%5Cleft%28-%5Cdfrac%7B1%20%7D%7B2%7D%2C-%5Cdfrac%7B%5Csqrt%7B3%7D%20%7D%7B2%7D%20%5Cright%29%24%20and%20%5Cleft%28%5Cdfrac%7B1%20%7D%7B2%7D%2C%5Cdfrac%7B%5Csqrt%7B3%7D%20%7D%7B2%7D%20%5Cright%29)
Step-by-step explanation:
The reference angle is the angle that the given angle makes with the x-axis.
For an ordered pair to share the same reference angle, the x and y coordinates must be the same or a factor of each other.
From the given options:
![(A)\left(-\dfrac{\sqrt{3} }{2} ,-\dfrac{1 }{2}\right)$ and \left(-\dfrac{1 }{2},-\dfrac{\sqrt{3} }{2} \right)\\\\(B)\left(\dfrac{1 }{2},-\dfrac{\sqrt{3} }{2} \right)$ and \left(-\dfrac{\sqrt{3} }{2}, \dfrac{1 }{2}\right)\\\\(C)\left(-\dfrac{1 }{2},-\dfrac{\sqrt{3} }{2} \right)$ and \left(\dfrac{1 }{2},\dfrac{\sqrt{3} }{2} \right)\\\\(D)\left(\dfrac{\sqrt{3} }{2},\dfrac{1 }{2} \right)$ and \left(\dfrac{1 }{2},\dfrac{\sqrt{3} }{2} \right)](https://tex.z-dn.net/?f=%28A%29%5Cleft%28-%5Cdfrac%7B%5Csqrt%7B3%7D%20%7D%7B2%7D%20%2C-%5Cdfrac%7B1%20%7D%7B2%7D%5Cright%29%24%20and%20%5Cleft%28-%5Cdfrac%7B1%20%7D%7B2%7D%2C-%5Cdfrac%7B%5Csqrt%7B3%7D%20%7D%7B2%7D%20%5Cright%29%5C%5C%5C%5C%28B%29%5Cleft%28%5Cdfrac%7B1%20%7D%7B2%7D%2C-%5Cdfrac%7B%5Csqrt%7B3%7D%20%7D%7B2%7D%20%5Cright%29%24%20and%20%5Cleft%28-%5Cdfrac%7B%5Csqrt%7B3%7D%20%7D%7B2%7D%2C%20%5Cdfrac%7B1%20%7D%7B2%7D%5Cright%29%5C%5C%5C%5C%28C%29%5Cleft%28-%5Cdfrac%7B1%20%7D%7B2%7D%2C-%5Cdfrac%7B%5Csqrt%7B3%7D%20%7D%7B2%7D%20%5Cright%29%24%20and%20%5Cleft%28%5Cdfrac%7B1%20%7D%7B2%7D%2C%5Cdfrac%7B%5Csqrt%7B3%7D%20%7D%7B2%7D%20%5Cright%29%5C%5C%5C%5C%28D%29%5Cleft%28%5Cdfrac%7B%5Csqrt%7B3%7D%20%7D%7B2%7D%2C%5Cdfrac%7B1%20%7D%7B2%7D%20%5Cright%29%24%20and%20%5Cleft%28%5Cdfrac%7B1%20%7D%7B2%7D%2C%5Cdfrac%7B%5Csqrt%7B3%7D%20%7D%7B2%7D%20%5Cright%29)
We observe that only the pair in option C has the same x and y coordinate with the second set of points being a negative factor of the first term. Therefore, they have the same reference angle.
The answer is 3/2. you do this by subtracting 7 1/4 from the 8 3/4 and simplifying the 6/4!
Answer:
![(1-\sqrt{2})a^2](https://tex.z-dn.net/?f=%281-%5Csqrt%7B2%7D%29a%5E2)
Step-by-step explanation:
Consider irght triangle PRS. By the Pythagorean theorem,
![PS^2=PR^2+RS^2\\ \\PS^2=a^2+a^2\\ \\PS^2=2a^2\\ \\PS=\sqrt{2}a](https://tex.z-dn.net/?f=PS%5E2%3DPR%5E2%2BRS%5E2%5C%5C%20%5C%5CPS%5E2%3Da%5E2%2Ba%5E2%5C%5C%20%5C%5CPS%5E2%3D2a%5E2%5C%5C%20%5C%5CPS%3D%5Csqrt%7B2%7Da)
Thus,
![MS=PS-PM=\sqrt{2}a-a=(\sqrt{2}-1)a](https://tex.z-dn.net/?f=MS%3DPS-PM%3D%5Csqrt%7B2%7Da-a%3D%28%5Csqrt%7B2%7D-1%29a)
Consider isosceles triangle MSC. In this triangle
![MS=MC=(\sqrt{2}-1)a.](https://tex.z-dn.net/?f=MS%3DMC%3D%28%5Csqrt%7B2%7D-1%29a.)
The area of this triangle is
![A_{MSC}=\dfrac{1}{2}MS\cdot MC=\dfrac{1}{2}\cdot (\sqrt{2}-1)a\cdot (\sqrt{2}-1)a=\dfrac{(\sqrt{2}-1)^2a^2}{2}=\dfrac{(3-2\sqrt{2})a^2}{2}](https://tex.z-dn.net/?f=A_%7BMSC%7D%3D%5Cdfrac%7B1%7D%7B2%7DMS%5Ccdot%20MC%3D%5Cdfrac%7B1%7D%7B2%7D%5Ccdot%20%28%5Csqrt%7B2%7D-1%29a%5Ccdot%20%28%5Csqrt%7B2%7D-1%29a%3D%5Cdfrac%7B%28%5Csqrt%7B2%7D-1%29%5E2a%5E2%7D%7B2%7D%3D%5Cdfrac%7B%283-2%5Csqrt%7B2%7D%29a%5E2%7D%7B2%7D)
Consider right triangle PTS. The area of this triangle is
![A_{PTS}=\dfrac{1}{2}PT\cdot TS=\dfrac{1}{2}a\cdot a=\dfrac{a^2}{2}](https://tex.z-dn.net/?f=A_%7BPTS%7D%3D%5Cdfrac%7B1%7D%7B2%7DPT%5Ccdot%20TS%3D%5Cdfrac%7B1%7D%7B2%7Da%5Ccdot%20a%3D%5Cdfrac%7Ba%5E2%7D%7B2%7D)
The area of the quadrilateral PMCT is the difference in area of triangles PTS and MSC:
![A_{PMCT}=\dfrac{(3-2\sqrt{2})a^2}{2}-\dfrac{a^2}{2}=\dfrac{(2-2\sqrt{2})a^2}{2}=(1-\sqrt{2})a^2](https://tex.z-dn.net/?f=A_%7BPMCT%7D%3D%5Cdfrac%7B%283-2%5Csqrt%7B2%7D%29a%5E2%7D%7B2%7D-%5Cdfrac%7Ba%5E2%7D%7B2%7D%3D%5Cdfrac%7B%282-2%5Csqrt%7B2%7D%29a%5E2%7D%7B2%7D%3D%281-%5Csqrt%7B2%7D%29a%5E2)
Answer: You would need 512 cubic centimetres
Step-by-step explanation: The first approach to this question would be to understand the properties of the shape given in the question.
If a cube has an edge with length 8 cm, then all edges measure 8 cm as well. That is one property of a cube. Hence, the length, width and height all measure 8 cm each.
The volume of a cube is given as follows;
V = L x W x H (and the answer is expressed as V³)
Since the length , width and height all measure 8 cm, the volume can simply be expressed as
V = L x L x L
V = L³
V = 8³
V = 512 cm³
Therefore to completely fill a cube with edge length of 8 cm you would need 512 cubic centimetres.