I need help with this

9514 1404 393

  A, B, D

Step-by-step explanation:

The "form factor" in the attached is the difference between the sum of the squares of the short sides and the square of the long side. If that difference is 0, the Pythagorean theorem is satisfied, and the triangle is a right triangle. When the difference is positive, the triangle is acute; negative, the triangle is obtuse.

As you can see, all but the third triangle are right triangles.

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Example calculation:

A: 5^2 +12^2 -13^ = 25 +144 -169 = 0

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I like to let a spreadsheet do the work when there are repetitive calculations. The formula and data only need to be entered once.

d. bc = 12 and ef = 16

step-by-step explanation:

we are given that δabc : δdef such that .

also, it is given that

so, from the options, we need that .

a.

b.

c.  

d.

as, we can see that only option d gives the same ratio as i.e. .

hence, the possible lengths are bc = 12 and ef = 16.

use the power rule  

( a b ) n = a n b n

to distribute the exponent.

apply the product rule to  

3 x 2 y 3 . ( 3 x 2 ) 2 ( y 3 ) 2

apply the product rule to  

3 x 2 . 3 2 ( x 2 ) 2 ( y 3 ) 2

raise  

3

to the power of  

2 . 9 ( x 2 ) 2 ( y 3 ) 2 multiply the exponents in   ( x 2 ) 2

.

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 2 ⋅ 2 ( y 3 ) 2

multiply  

2   by   2 . 9 x 4 ( y 3 ) 2

multiply the exponents in  

( y 3 ) 2 .

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 4 y 3

⋅

2

multiply  

3   by   2 . 9 x 4 y 6

step-by-step explanation: