The lengths of two sides of a triangle are shown.

side 1: 8x2 − 5x − 2

side 2: 7x − x2 + 3

the perimeter of the triangle is 4x3 − 3x2 + 2x − 6.

part b: what is the length of the third side of the triangle? show your work.

answer:

the perimeter of a shape is the total length of the side of the shape.

from the equation above, let say the length of the third side is y

(8x2 - 5x - 2) + (7x - x2 + 3) + y = 4x3 - 3x2 + 2x - 6

rearrange the equation and put like terms together, the we have

8x2 - x2 - 5x + 7x - 2 + 3 + y = 4x3 - 3x2 + 2x - 6

7x2 + 2x + 1 + y = 4x3 - 3x2 + 2x - 6

make y subject of formula;

y = 4x3 - 3x2 - 7x2 + 2x -2x - 6 - 1

y = 4x3 - 10x2 + 0 - 7

y = 4x3 - 10x2 - 7

the length of the third side is 4x3 - 10x2 - 7

(sin 42)/31. = sinx)/37

sinx = 37 (sin42)/31

= 37× 0.66/31 = 0.787

x= 51.9

other angle opposite to y = 180-51.9-42

= 180- 93.9 =86.1

so

sin42)/31 = sin 86.1)/y

0.021 = 0.997 /y

y= 0.997/0.021 =47.47

d. 8

step-by-step explanation:

the given radical expression is:

we can rewrite this as:

we express as square numbers to get;

the exponents will now cancel out to give.

the correct answer is d