The Triangle Sum Theorem states that the sum of the angles of a triangle equal 180°.
Therefore,
45° + 62° + k = 180
107° + k = 180
k = 73°
The value of k is 73°
Answer:
D) The third side could be 4 meters long.
Step-by-step explanation:
The third side of a triangle must be greater than the difference and less than the sum of the other two sides.
5-4=1
5+4=9
So the third side must be GREATER THAN 1 and LESS THAN 9. (1<x<9)
Therefore, the answer can't be A or C. The second one <em>could </em>be correct, depending on how much less than 4 it is. But the last one is definitely correct.
Use the Cosine Rule to find this
cos <B = [b^2 - a^2 - c^2] / -2ac
= [ 4^2 - 10^2 - 11^2] / -2*10*11
= 0.93182
so m < B = 21.3 degrees to nearest tenth. Answer
Answer:
(- 1, 8 ) and (5, 2 )
Step-by-step explanation:
Given the 2 equations
y = - x + 7 → (1)
y = 0.5(x - 3)² → (2)
Substitute y = 0.5(x - 3)² into (1)
0.5(x - 3 )² = - x + 7 ← expand and simplify left side
0.5(x² - 6x + 9) = - x + 7 ( multiply both sides by 2 )
x² - 6x + 9 = - 2x + 14 ( subtract - 2x + 14 from both sides )
x² - 4x - 5 = 0 ← in standard form
(x - 5)(x + 1) = 0 ← in factored form
Equate each factor to zero and solve for x
x - 5 = 0 ⇒ x = 5
x + 1 = 0 ⇒ x = - 1
Substitute these values into (1) for corresponding values of y
x = 5 : y = - 5 + 7 = 2 ⇒ (5, 2 )
x = - 1 : y = 1 + 7 = 8 ⇒ (- 1, 8 )
