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2 years ago

Slope of (15,130) and (1,160)

Mathematics

2 answers:

Vedmedyk [2.9K]2 years ago

6 0

The formula of a slope:

$m=\dfrac{y_2-y_1}{x_2-x_1}$

We have the points (15, 130) amd (1, 160). Substitute:

$m=\dfrac{160-130}{1-15}=\dfrac{30}{-14}=-\dfrac{15}{7}$

lana66690 [7]2 years ago

5 0

Hi there! :)

Step-by-step explanation:

$Slope=\frac{Y_2-Y_1}{X_2-X_1}=\frac{RISE}{RUN}$

$\frac{160-130}{1-15}=\frac{30}{-14}=\frac{30/2}{-14/2}=\frac{15}{-7}=-\frac{15}{7}$

Therefore, the slope is -15/7.

Final answer is -15/7.

Hope this helps!

Have a nice day! :)

-Charlie

Thank you so much! :)

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2 years ago

a truck and a car drive uniformly among the expressway from city a to city b. The truck leaves at 09:15 am and arrives at 1:15 p

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the car overtake the truck at time 11:40 am.

Step-by-step explanation:

We have both vehicules going at constant speed from city a to city b. The distance is unknown, but can be written as d.

We will express the time in hours (and decimals of hours).

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The truck took t2-t1=13.25-9.25=4 to go from city a to b.

The average speed is then:

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We can write the equation for the position x(t) for the truck as:

$x(t)=x_0+v_t\cdot t=x_0+\dfrac{d}{4}t\\\\\\x(13.25)=x_0+\dfrac{d}{4}(13.25)=d\\\\x_0=d-3.3125d=-2.3125d\\\\\\x(t)=-2.3125d+0.25d\cdot t$

For the car we have:

- The arrival time is 12:45 am. This is t2=12.75.

- The starting time is 10 am. This is t1=10.

The car took t2-t1=12.75-10=2.75.

The average speed is then:

$v_c=\dfrac{\Delta x}{\Delta t}=\dfrac{d}{2.75}$

We can write the equation for the position x(t) for the car as:

$x(t)=x_0+v_c\cdot t=x_0+\dfrac{d}{2.75}t\\\\\\x(12.75)=x_0+\dfrac{d}{2.75}(12.75)=d\\\\x_0=d-4.6363d=-3.6363d\\\\\\x(t)=-3.6363d+0.3636d\cdot t$

The time at which the car overtake the car is the time when both vehicles have the same position:

$x(t)/d=-2.3125+0.25\cdot t = -3.6363+0.3636\cdot t\\\\-2.3125+3.6363=(0.3636-0.25)t\\\\1.3238=0.1136t\\\\t=1.3238/0.1136\approx11.65$

The car overtakes the truck at t=11.65 hours or 11:39 am.

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2 years ago

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Step-by-step explanation:

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