Answer:
-9
Step-by-step explanation:for sure
Answer:
m∠C = 26°
m∠D = 108°
m∠E = 46°
Step-by-step explanation:
Set up the equation adding the expressions together to equal 180 (sum of all angles in a triangle)
(2x) + (x+3) + (5x-7) = 180
Remove the parentheses
2x + x+ 3 + 5x - 7 = 180
Add like terms
8x - 3 -7 = 8x -4 = 180
8x - 4 = 180
Add 4 on each side to cancel it out on the right
8x - 4 = 180
+4 = +4
8x = 184
Divide each side by 8 to get the variable by itself
8/8 =1 184/8 = 23
x = 23
Substitute x in eac expression
2x = 2(23) = 46°
x + 3 = 23 + 3 = 26°
5x - 7 = 5(23) - 7 = 115 -7 = 108
Chek it by adding all the degrees to make sure it equals 180
46 + 26 + 108 = 72 + 108 = 180
Answer:
D. Pythagorean
Step-by-step explanation:
Given the identity
cos²x - sin²x = 2 cos²x - 1.
To show that the identity is true, we need to show that the left hand side is equal to right hand side or vice versa.
Starting from the left hand side
cos²x - sin²x ... 1
According to Pythagoras theorem, we know that x²+y² = r² in a right angled triangle. Coverting this to polar form, we have:
x = rcostheta
y = rsintheta
Substituting into the Pythagoras firnuka we have
(rcostheta)²+(rsintheta)² = r²
r²cos²theta+r²sin²theta = r²
r²(cos²theta+sin²theta) = r²
(cos²theta+sin²theta) = 1
sin²theta = 1 - cos²theta
sin²x = 1-cos²x ... 2
Substituting equation 2 into 1 we have;
= cos²x-(1-cos²x)
= cos²x-1+cos²x
= 2cos²x-1 (RHS)
This shows that cos²x -sin²x = 2cos²x-1 with the aid of PYTHAGORAS THEOREM
