Answer: 10:55
Step-by-step explanation:
Taking statement at face value and the simplest scenario that commencing from 08:00am the buses take a route from depot that returns bus A to depot at 25min intervals while Bus B returns at 35min intervals.
The time the buses will be back at the depot simultaneously will be when:
N(a) * 25mins = N(b) * 35mins
Therefore, when N(b) * 35 is divisible by 25 where N(a) and N(b) are integers.
Multiples of 25 (Bus A) = 25, 50, 75, 100, 125, 150, 175, 200 etc
Multiples of 35 (Bus B) = 35, 70, 105, 140, 175, 210, 245 etc
This shows that after 7 circuits by BUS A and 5 circuits by Bus B, there will be an equal number which is 175 minutes.
So both buses are next at Depot together after 175minutes (2hr 55min) on the clock that is
at 08:00 + 2:55 = 10:55
Answer:
smaller (t) = 2 and this in coordinates form (2,0)
larger (t) = 15 and this in coordinates form (15,0)
the vertex of the parabola = 
or in decimals (8.5, 42.25)
Step-by-step explanation:
- For the zeros of the function take each bracket and make it equal to zero.
SMALLER (t):
(t-2)=0
(add 2 for both sides)
t=2
LARGER (t):
(t-15)=0
(add 15 for both sides)
t=15
- For the vertex of the parabola you do:
step1: expand the brackets:
f(t)=-(t-2)(t-15)
f(t)= 
step2: define a,b and c using the expression 
:
a= -1 (the coefficient of 
)
b= 17 (the coefficient of t)
c= -30 (the single number without a letter)
step3: sub the values in the formula 
to find the x coordinate of the vertex :
= 
= 
or in decimals 8.5
step4: sub the value of t (the x-coordinate) in equation f(t):
f(t)=
f ( ) = - 
+ 17× - 30
= 
+ 
-30
=
or in decimals 42.25
(THIS IS A PICTURE OF THE GRAPH↓)
Answer:
x=9
Step-by-step explanation:
2x+10=28
2x=18
x=9
Substitution:
2x + (6(1/2x - 6)) = 19
2x + 3x - 36 = 19
5x - 36 = 19
+ 36
5x = 55
÷ 5
x = 11
y = (1/2 × 11) - 6
y = 5.5 - 6
y = -0.5
Elimination:
y = 1/2x - 6
- y
0 = 1/2x - 6 - y
+ 6
1/2x - y = 6
3x - 6y = 36
2x + 6y = 19
(add)
5x = 55
÷ 5
x = 11
y = (1/2 × 11) - 6
y = 5.5 - 6
y = -0.5
I hope this helps! Let me know if you need me to explain why I did some things :)
