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olganol [36]
3 years ago
5

7 square root of 3 end root minus 4 square root of 6 end root plus square root of 48 end root minus square root of 54

Mathematics
1 answer:
Levart [38]3 years ago
5 0
7\sqrt3-4\sqrt6+\sqrt{48}-\sqrt{54}\\\\=7\sqrt3-4\sqrt6+\sqrt{16\cdot3}-\sqrt{9\cdot6}\\\\=7\sqrt3-4\sqrt6+\sqrt{16}\cdot\sqrt3-\sqrt9\cdot\sqrt6\\\\=7\sqrt3-4\sqrt6+4\sqrt3-3\sqrt6\\\\=\boxed{11\sqrt3-7\sqrt6}
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In the diagram below, TUVW is a rectangle. Prove triangle TZW is congruent to triangle UZV.
otez555 [7]

Answer:

By S.S.S. congruence property;  ΔTZW ≅ ΔVZU

Step-by-step explanation:

Given:

TUVW is a rectangle.

To Prove : TZW ≅ UZV

Proof:

Since TUVW is a rectangle, and we know that opposite side of a rectangle is equal.

So,

TW = UV \ \ .\ .\ .\ .\ 1

And also TV and WU are the diagonals of the rectangle.

And the diagonals of rectangle bisects each other.

Therefore;

TZ=ZV.........\ 2\\\\WZ=ZU..........\ 3

Now In ΔTZW and ΔVZU

TW = UV (from 1)

TZ = ZV (from 2)

WZ = ZU (from 3)

So, by S.S.S. congruence property;

ΔTZW ≅ ΔVZU

Hence proved.

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