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2 years ago

A bus travelled from location A to location B in 90 minutes. Calculate the speed of the bus in km/h

Mathematics

1 answer:

DaniilM [7]2 years ago

6 0

Speed is distance over time. There’s no distance in the question and the time is 1 hr 30 mins hence 1.5 hours.

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Solve the system by substitution: y = -3x + 10 y=-3x + 4 Please show the steps!

sergiy2304 [10]

Answer:

x=1, y=7

Step-by-step explanation:

y = -3x + 10 - first equation

y=-3x + 4 - second equation

rearrange the expression to

-3x-y= -10

3x-y= -4

pick an equation and simplify; lets pick the second equation

3x-y= -4

$\frac{3x}{3} = \frac{-4+y}{3}$

divide 3 by both sides

x= $\frac{-4+y}{3}$ - third equation

substitute the value of x into an equation; lets pick the first equation

-3x-y= -10

-3 $(\frac{-4+y}{3})$ - y = -10

simplify. -3 cancels 3 so we are left with

-1(-4+y)-y = -10

simplify

4-y-y= -10

4-2y= -10

subtract 4 from both sides

-2y= -10-4

-2y= -14

divide -2 by both sides

y=7

substitute the value of y, (y=7) in an equation, we are using the second equation

3x-y= -4

3x-7= -4

3x = -4+7

3x= 3

divide 3 by both sides

x=1

so the answer is x=1, y=7

5 0

3 years ago

Can I get help solving this graph please?

Daniel [21]

see the attached figure with the letters

1) find m(x) in the interval A,B
A (0,100) B(50,40) -------------- > p=(y2-y1(/(x2-x1)=(40-100)/(50-0)=-6/5
m=px+b---------- > 100=(-6/5)*0 +b------------- > b=100
mAB=(-6/5)x+100

2) find m(x) in the interval B,C
B(50,40) C(100,100) -------------- > p=(y2-y1(/(x2-x1)=(100-40)/(100-50)=6/5
m=px+b---------- > 40=(6/5)*50 +b------------- > b=-20
mBC=(6/5)x-20

3) find n(x) in the interval A,B
A (0,0) B(50,60) -------------- > p=(y2-y1(/(x2-x1)=(60)/(50)=6/5
n=px+b---------- > 0=(6/5)*0 +b------------- > b=0
nAB=(6/5)x

4) find n(x) in the interval B,C
B(50,60) C(100,90) -------------- > p=(y2-y1(/(x2-x1)=(90-60)/(100-50)=3/5
n=px+b---------- > 60=(3/5)*50 +b------------- > b=30
nBC=(3/5)x+30

5) find h(x) = n(m(x)) in the interval A,B
mAB=(-6/5)x+100
nAB=(6/5)x
then
n(m(x))=(6/5)*[(-6/5)x+100]=(-36/25)x+120
h(x)=(-36/25)x+120
find h'(x)
h'(x)=-36/25=-1.44

6) find h(x) = n(m(x)) in the interval B,C
mBC=(6/5)x-20
nBC=(3/5)x+30
then
n(m(x))=(3/5)*[(6/5)x-20]+30 =(18/25)x-12+30=(18/25)x+18
h(x)=(18/25)x+18
find h'(x)
h'(x)=18/25=0.72

for the interval (A,B) h'(x)=-1.44
for the interval (B,C) h'(x)= 0.72

 h'(x) = 1.44 ------------ > not exist

8 0

2 years ago

Х+ 2y = -1 2x – Зу = 12

yarga [219]

Use substitution method

4 0

3 years ago

How do you solve 3x+3y=-15 and -3x+y=3

Lilit [14]

Answer:

Step-by-step explanation:

Substitute x and y values for zero. Or

3 0

3 years ago

Alice and her friend Emma leave on different flights from the same airport. Alice's flight flies 100 miles due south, then turns

DaniilM [7]

9514 1404 393

Answer:

Emma's flight is farther from the airport

Step-by-step explanation:

Even without doing any detailed calculation, you can see on a graph that the larger turn Alice's flight makes keeps it closer to the airport.

Emma's flight is farther from the airport.

The distance can be calculated using the Law of Cosines. The angle of interest is the supplement of the turn angle. Since the leg distances are the same in each case, the only variable affecting the distance from the airport is the angle measure. Again, the larger the turn, the shorter the distance from the airport. If T is the turn angle, the distance is ...

d² = 100² +50² -2·100·50·cos(180° -T)

d² = 12500 +10000·cos(T) . . . . . . . using cos(180°-T) = -cos(T)

d = 100√(1.25+cos(T))

For Alice's 70° turn, the distance is ...

d = 100√(1.25+0.342) ≈ 126.18 mi

For Emma's 50° turn, the distance is ...

d = 100√(1.25 +0.643) ≈ 137.58 mi

Emma's flight is farther from the airport.

_____

The law of cosines formula is ...

c² = a² +b² -2ab·cos(C)

where triangle sides are lengths a, b, c and angle C is opposite side c.

3 0

2 years ago

A bus travelled from location A to location B in 90 minutes. Calculate the speed of the bus in km/h​

A bus travelled from location A to location B in 90 minutes. Calculate the speed of the bus in km/h