We try to represent each number inside the square root as a product of a square and another number.
a) 7√32 - 5√2 + √8
√32 = √(16 *2) = √16 * √2 = 4* √2 = 4√2
√8 = √(4 *2) = √4 * √2 = 2* √2 = 2√2
7√32 - 5√2 + √8 = 7*(4√2) - 5√2 + 2√2 =
= 28√2 - 5√2 + 2√2 Factorize out √2
= (28 - 5 + 2)√2
= 25√2
b) 2√150 - 4√54 + 6√24
√150 = √(25 * 6) = √25 * √6 = 5*√6 = 5√6
√54 = √(9 * 6) = √9 * √6 = 3*√6 = 3√6
√24 = √(4 * 6) = √4 * √6 = 2*√6 = 2√6
2√150 - 4√54 + 6√24 = 2*(5√6) - 4*(3√6) + 6*(2√6)
= 2*5√6 - 4*3√6 + 6*2√6
= 10√6 - 12√6 + 12√6 Factorize √6
= (10 - 12 + 12)√6
= 10√6
There are 6 numbers total
17 * 6 = 102
10 + 12 + 16 + 20 + 26 = 84
p = 102-84 = 18
p = 18
It definetly is congruent.
Have a Great Day!!!
Answer:
None. The movement of these tectonic plates is likely caused by convection currents in the molten rock in Earth’s mantle below the crust.
Step-by-step explanation:
Plate tectonics is the scientific theory explaining the movement of the earth’s crust. It is widely accepted by scientists today. Recall that both continental landmasses and the ocean floor are part of the earth’s crust, and that the crust is broken into individual pieces called tectonic plates (Fig. 7.14). The movement of these tectonic plates is likely caused by convection currents in the molten rock in Earth’s mantle below the crust. Earthquakes and volcanoes are the short-term results of this tectonic movement. The long-term result of plate tectonics is the movement of entire continents over millions of years (Fig. 7.18). The presence of the same type of fossils on continents that are now widely separated is evidence that continents have moved over geological history.
Information found on:
<u>https://manoa.hawaii.edu/exploringourfluidearth/node/1348#:~:text=Plate%20tectonics%20is%20the%20scientific,movement%20of%20the%20earth's%20crust.&text=The%20movement%20of%20these%20tectonic,results%20of%20this%20tectonic%20movement.</u>
