w represents width
4w represents length
d represents diagonal
w2 + (4w)2 = d2
w2 + 16w2 = d2
17w2 = d2
±w√17 = d
The diagonal is the width times √17.
Answer:
3(2x+2) = 6x + 6
Step-by-step explanation:
Those are algebra tiles, so it is saying (if you read across the top) 2x +2 then if you read down you have 3 units, so the dot means 2x + 2 multiplied by 3
If you write it in algebraic terms it is 3(2x+2) so the answer when you distribute is 3 (2x) + 3(2) so 6x + 6, and if you count the number of red rectangles you have 6 of them, hence the 6x, and if you cound the units in gray you have 6 of them, hence the 6.
Algebra tiles are used to demonstrate algebra concepts
Answer:
The third option listed: ![\sqrt[3]{2x} -6\sqrt[3]{x}\\](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B2x%7D%20-6%5Csqrt%5B3%5D%7Bx%7D%5C%5C)
Step-by-step explanation:
We start by writing all the numerical factors inside the qubic roots in factor form (and if possible with exponent 3 so as to easily identify what can be extracted from the root):
![7\sqrt[3]{2x} -3\sqrt[3]{16x} -3\sqrt[3]{8x} =\\=7\sqrt[3]{2x} -3\sqrt[3]{2^32x} -3\sqrt[3]{2^3x} =\\=7\sqrt[3]{2x} -3*2\sqrt[3]{2x} -3*2\sqrt[3]{x}=\\=7\sqrt[3]{2x} -6\sqrt[3]{2x} -6\sqrt[3]{x}](https://tex.z-dn.net/?f=7%5Csqrt%5B3%5D%7B2x%7D%20%20-3%5Csqrt%5B3%5D%7B16x%7D%20-3%5Csqrt%5B3%5D%7B8x%7D%20%3D%5C%5C%3D7%5Csqrt%5B3%5D%7B2x%7D%20%20-3%5Csqrt%5B3%5D%7B2%5E32x%7D%20-3%5Csqrt%5B3%5D%7B2%5E3x%7D%20%3D%5C%5C%3D7%5Csqrt%5B3%5D%7B2x%7D%20%20-3%2A2%5Csqrt%5B3%5D%7B2x%7D%20-3%2A2%5Csqrt%5B3%5D%7Bx%7D%3D%5C%5C%3D7%5Csqrt%5B3%5D%7B2x%7D%20%20-6%5Csqrt%5B3%5D%7B2x%7D%20-6%5Csqrt%5B3%5D%7Bx%7D)
And now we combine all like terms (notice that the only two terms we can combine are the first two, which contain the exact same radical form:
![7\sqrt[3]{2x} -6\sqrt[3]{2x} -6\sqrt[3]{x}=\\=\sqrt[3]{2x} -6\sqrt[3]{x}](https://tex.z-dn.net/?f=7%5Csqrt%5B3%5D%7B2x%7D%20%20-6%5Csqrt%5B3%5D%7B2x%7D%20-6%5Csqrt%5B3%5D%7Bx%7D%3D%5C%5C%3D%5Csqrt%5B3%5D%7B2x%7D%20-6%5Csqrt%5B3%5D%7Bx%7D)
Therefore this is the simplified radical expression:
The slope of the original line is 1 so the perpendicular slop is -1
