Recall the sum identity for cosine:
cos(a + b) = cos(a) cos(b) - sin(a) sin(b)
so that
cos(a + b) = 12/13 cos(a) - 8/17 sin(b)
Since both a and b terminate in the first quadrant, we know that both cos(a) and sin(b) are positive. Then using the Pythagorean identity,
cos²(a) + sin²(a) = 1 ⇒ cos(a) = √(1 - sin²(a)) = 15/17
cos²(b) + sin²(b) = 1 ⇒ sin(b) = √(1 - cos²(b)) = 5/13
Then
cos(a + b) = 12/13 • 15/17 - 8/17 • 5/13 = 140/221
Point G cannot be a centroid because GE is wider that JG or JG is shorter than GE. So in this diagram GE is wider than JG with 10 cm and 5 cm respectively based on this information Point G cannot be a centroid of triangle HJK. So the answer is point G cannot be a centroid because JG is shorter than GE.
Answer:
<h2>x = -2 (verified by algebra) ✅</h2>
Step-by-step explanation:
Since we are given the value of y, we can replace it with 5x + 7.
We now have: 3x + 5x + 7 = -9
We can now simplify by adding 3x and 5x to get 8x.
8x + 7 = -9
We can subtract 7
8x = -16
And now, we divide by 8
x = -2
We can check to make sure we are correct
3(-2) + 5 (-2) + 7 = -9
-6 + -10 + 7 = -9
-9 = -9 ✅
The answer is "A" for your question.
