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2 years ago

I WILL GIVE BRAINLIEST

Mathematics

1 answer:

shusha [124]2 years ago

5 0

Answer:

x = -3

Step-by-step explanation:

$y\geq -\frac{2}{3} x-3\\
y\leq 3x+8$

$-\frac{2}{3} x-3=3x+8$

Add 2/3 x to both sides: $-3=\frac{11}{3}x+8$

Subtract 8 from both sides: $-11=\frac{11}{3}x$

Multiply both sides by 3: $-33=11x$

Divide both sides by 11: $x=-3$

Therefore, point of intersection between both lines is at point (-3, -1)

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3 years ago

A cargo grain leaves Chicago at noon travelling west at 120 km/h. At 2 pm, a passenger train leaves Chicago travelling east at 3

AfilCa [17]

Answer:

a) The trains will be 1520 km apart at 2:40 pm for the cargo train and at 4:40 pm for the passenger train.

b) At that time the cargo train has traveled 560.04 km and the passenger train has traveled 960.12 km.

Step-by-step explanation:

a) First, we need to find the distance traveled by the cargo train in the two hours before the passenger train leaves Chicago:

$x_{1} = v_{1}t_{1} = 120 km/h*2h = 240 km$

Now, we can find the time when the trains will be 1520 km apart:

$1520 km = (x_{1} + 240 km) + x_{2}$

Where 1 is for the cargo train and 2 is for the passenger train.

$1520 km = (v_{1}*t_{1} + 240 km) + v_{2}t_{2}$

Since we need to calculate the time when the trains are 1520 km apart, t₁ = t₂, so:

$1520 km = (v_{1}*t + 240 km) + v_{2}t$

$t = \frac{1520 km - 240 km}{120 km/h + 360 km/h} = 2.667h$

For the cargo train, it will be 1520 km apart from the passenger train at:

$t_{1} = 12 pm + 2 h + 40 min = 2:40 pm$

And for a passenger train, it will be 1520 km apart from the cargo train at:

$t_{2} = 2 pm + 2 h + 40 min = 4:40 pm$

Hence, the trains will be 1520 km apart at 2:40 pm for the cargo train and at 4:40 pm for the passenger train.

b) The distance traveled by both trains is given by:

$x_{1} = v_{1}*t + 240 km = 120 km/h*2.667 h + 240 km = 560.04 km$

$x_{2} = v_{2}*t = 360 km/h*2.667 h = 960.12 km$

Therefore, at that time the cargo train has traveled 560.04 km and the passenger train has traveled 960.12 km.

I hope it helps you!

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2 years ago