6 3/4=6*4+3/4=24+3/4=27/4
z/12=27/4
4z=27*12
4z=324
z=81
Answer:
(-2, 3)
Step-by-step explanation:
the point B is
B(x,y)
x
AB (A to B) is twice BC ( B to C )
AB is 2 - x. BC is x - (-4)= x + 4
So
2-x=2 (x + 4)
2-x=2x + 8
3x = -6
x = -2
y
(Same logic as above)
AB is -5 -y. BC is u - 7
-5 -y = 2(y - 7)
-5 - y = 2y - 14
3y = 9
y= 3
the point is (-2, 3)
<span>This question is an annuity problem with cost of the car = $32,998, the present value of the annuity (PV) is given by the difference between the cost of the car and the down payment = $32,998 - $4,200 = $28,798. The monthly payments (P) = $525 and the number of number of years (n) = 5 years and the number of payments in a year (t) is 12 payments (i.e. monthly) The formula for the present value of an annuity is given by PV = (1 - (1 + r/t)^-nt) / (r/t) 28798 = 525(1 - (1 + r/12)^-(5 x 12)) / (r/12) 28798r / 12 = 525(1 - (1 + r/12)^-60) 28798r / (12 x 525) = 1 - (1 + r/12)^-60 2057r / 450 = 1 - (1 + r/12)^-60 Substituting option A (r = 37% = 0.37) 2057r / 450 = 2057(0.37) / 450 = 761.09 / 450 = 1.691 1 - (1 + r/12)^60 = 1 - (1 + 0.37/12)^-60 = 1 - 0.1617 = 0.8383 Therefore, r is not 37% Substituting option D (r = 3.7% = 0.037) 2057r / 450 = 2057(0.037) / 450 = 76.109 / 450 = 0.1691 1 - (1 + r/12)^60 = 1 - (1 + 0.037/12)^-60 = 1 - 0.8313 = 0.1687 Therefore, r is approximately 3.7%</span>
Answer:
10 km/hr
Step-by-step explanation:
Average speed = Total distance travelled / Total time taken
Ardi:
Total distance travelled = 70 km
Total time taken = 35 minutes = 35/60 hour
Average speed = Total distance travelled / Total time taken
= 70 km ÷ 35/60 hr
= 70 × 60/35
= 4,200/35
= 120 km/hr
Lei:
Total distance travelled = 585 km Total time taken = 9:05 - 13:35 = 4 hours 30 minutes
= 4.5 hours
Average speed = Total distance travelled / Total time taken
= 585 km / 4.5 hours
= 130 km/hr
Difference, in km/h, between the average speed of their trains = Lei's train - Ardi's train
= 130 km/hr - 120 km/hr
= 10 km/hr
