Answer:
1 = 130° , 2 =50° , 3 = 85°, 4=45°
Step-by-step explanation:
1 =45 + 85 = 130 { sum of opposite interior angle equals exterior angle}
2 = 180 - 1 { angles on a straight line equals 180}
= 180 -130 = 50°
4 = 180 - 135 = 45° { angles on a straight line equals 180}
3 = 135 -2 { sum of opposite interior angles equals exterior angle; 3 + 2 = 135}
3 = 135-50 = 85°
Note : sum of opposite interior angles equals external exterior angle, let's prove it:
If we look at the triangle at the bottom left, we have :
85, 45 and r { let's denote r as the missing angle}
So 85 + 45 + r = 180° { sum of angles of a triangle}
By simple arithmetic
r = 180 - ( 85+45) = 180 - 130 = 50°
but r + 4 = 180° { sum of angles in a straight line equals 180°}
4 = 180 - 50 = 130°
So you see 4 is the exterior angle of the triangle opposite to 85° and 45° interior angles}
Answer: C
<u>Step-by-step explanation:</u>
∑ 8()⁽ⁿ⁻¹⁾ from n = 1 to n = 5
n = 1 → 8()⁽¹⁻¹⁾
= 8 =
n = 2 → 8()⁽²⁻¹⁾
= =
n = 3 → 8()⁽³⁻¹⁾
= =
n = 4 → 8()⁽⁴⁻¹⁾
= =
n = 5 → 8()⁽⁵⁻¹⁾
= =
Sum =
= 408.99
Answer:
(i) p = -7, q = -3
(ii) (-3/2, 0), (2, 0), (3, 0)
Step-by-step explanation:
Use long division (see picture).
When we divide by x − 1, we get a remainder of q + p + 20.
When we divide by x + 1, we get a remainder of 16 − q + p.
We know the first remainder is equal to 10 and the second remainder is equal to 12. Solving the system of equations:
10 = q + p + 20
12 = 16 − q + p
0 = q + p + 10
0 = 4 − q + p
0 = 14 + 2p
p = -7
q = -3
Therefore:
f(x) = 2x³ − 7x² − 3x + 18
Finding the zeros:
f(x) = 2x³ − 6x² − x² − 3x + 18
f(x) = 2x² (x − 3) − (x² + 3x − 18)
f(x) = 2x² (x − 3) − (x − 3) (x + 6)
f(x) = (x − 3) (2x² − (x + 6))
f(x) = (x − 3) (2x² − x − 6)
f(x) = (x − 3) (x − 2) (2x + 3)
The zeros are at x = -3/2, x = 2, and x = 3.
X y z, if it is a triangle= 180
if not, x+y+z cannot be answered, be more specific