Answer:
x = - 1 ± 2i
Step-by-step explanation:
we can use the discriminant b² - 4ac to determine the nature of the roots
• If b² - 4ac > , roots are real and distinct
• If b² - 4ac = 0, roots are real and equal
• If b² - ac < 0, roots are not real
for x² + 2x + 5 = 0
with a = 1, b = 2 and c = 5, then
b² - 4ac = 2² - (4 × 1 × 5 ) = 4 - 20 = - 16
since b² - 4ac < 0 there are 2 complex roots
using the quadratic formula to calculate the roots
x = ( - 2 ± ) / 2
= (- 2 ± 4i ) / 2 = - 1 ± 2i
Let:
Vj = Speed of jane
Vm = Speed of mike
d = distance
t = time
Jane travels 7 mph less than 2 times as fast as Mike, therefore:
Vj = 2Vm - 7
Remeber:
distance = speed*time
Distance traveled by mike:
d=Vm*t = Vm*6
Distance traveled by jane:
d + 198 = Vj*6
where:
Vj = 2Vm - 7
d + 198 = (2Vm-7)*6
Now, let:
d=Vm*6 (1)
d + 198 = (2Vm-7)*6 (2)
Replace (1) into (2)
6Vm + 198 = 12Vm - 42
Subtract 6Vm from both sides:
6Vm + 198 - 6Vm = 12Vm - 42 - 6Vm
198 = 6Vm - 42
Add 42 to both sides:
198 + 42 = 6Vm - 42 + 42
240 = 6Vm
Divide both sides by 6:
240/6 = 6Vm/6
40 = Vm
Vm = 40mph
Replace Vm into this equation Vj = 2Vm - 7 :
Vj = 2(40) - 7 = 80 - 7 = 73mph
Answer:
y = 108°
Step-by-step explanation:
Since, line AB is parallel to line CD,
By the definition of corresponding angles,
m∠FPB = m∠FQD
(2x + 16)° = (3x - 12)°
3x - 2x = 16 + 12
x = 28
(3x - 12) = 3(28) - 12
= 72°
m∠FQD + m∠EQD = 180° [Linear pair of angles]
72° + y = 180°
y = 180 - 72
y = 108°
