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blagie [28]
3 years ago
8

The isosceles triangles below are similar.

Mathematics
1 answer:
ohaa [14]3 years ago
4 0

Answer: a) 2:1. b) 3. c) Perimeter of ΔEFG=36 Perimeter of ΔHIJ=18. d) 2:1

Step-by-step explanation:

a) Find the ratio of GF and JI. 16:8. Simplify by dividing both by 8 to get 2:1.

b) Set up this equation: 6/16=x/8. Cross-multiply. 6*8=48. Divide by 16. 48/16=3.

c) First find the length of one half of GF by dividing 16 by 2. 16/2=8. Set up the Pythagorean theorem. 8^2+6^2=c^2. Square 8 and 6. 64+36=c^2. Add 64 and 36. 100=c^2. Find the square root of 100. c=10.

EF and EG both measure 10 since they are shown to be congruent. 10+10+16=36.

Next find the length of one half of JI by dividing 8 by 2. 8/2=4. Set up the Pythagorean theorem. Since we know x=3, it will be 4^2+3^2=c^2. Square both 4 and 3. 16+9=c^2. Add 16 and 9. 25=c^2. Find the square root of 25. c=5.

HJ and HI both measure 5 since they are congruent. 5+5+8=18.

d) Find the ratio of the perimeters of ΔEFG and ΔHIJ. 36:18. Simplify by dividing both by 6 to get 6:3. Simplify further by dividing both by 3 to get 2:1.

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marta [7]
The correct answer is:   [A]:  " 4x³ + x² − 11x + 15 " .

_______________________________________________________
<u>Note</u>:
_______________________________________________________

(6x³ − 4x + 5) − (2x³ − x² + 7x − 10) ;

=  (6x³ − 4x + 5) − 1(2x³ − x² + 7x − 10) ;
_________________________________________

Examine the following portion of the expression:
_________________________________________
    " − 1(2x³ − x² + 7x − 10) " ; 

=  (-1 * 2x³)  − (-1 * x²) + (-1 * 7x) − (-1 * 10) ; 

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= (-2x³)  + 1x² − 7x + 10 ; 

=   " − 2x³ + 1x² − 7x + 10 " ;

Now, bring down the other part:

 6x³  − 4x  +  5 − 2x³ + 1x² − 7x + 10 ;

Combine the "like terms" :

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+ 5 + 10 = + 15 ; 

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+ 1x² ( which equals:  " x² ") ; 
____________________________________________________
And rewrite:
____________________________________________________
   →  " 4x³ + x² − 11x + 15 " ; 

   →  which is:  Answer choice:  [A]:  " 4x³ + x² − 11x + 15 " .
____________________________________________________
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