The equation 9+12m=6+15(m-1) models the following situation: Movie-rental company A

Mathematics

1 answer:

Marizza181 [45]3 years ago

5 0

Answer:

Start by distributing the 15 to the (m-1). 9+12m=6+15m-15. Then combine like terms. 9+12m=15m-9. Next move the variable all to one side, it doesn't matter which variable you choose. I'll use 12m so when I subtract I am still left with a postive coefficient. To move the 12m we subtract it from both sides of the equation. We are left with 9=3m-9. Next we isolate the m by canceling out the 9. We do this by adding 9 to both sides. We are left with 18=3m. Finally, to completely isolate the m, we must divide both sides by the coefficient, 3. The result is 6=m. The answer is 6 months. You can check this by plugging 6 back into the equation where there is an m. (sorry for the long answer)

Step-by-step explanation:

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Solve for x.<br><br>-6x - 29 = 5x - 7

vodomira [7]

Answer:

x = -2

Step-by-step explanation:

-6x - 29 = 5x - 7

Add -6x to both sides

-29 = 11x - 7

Add 7 on both sides

-22 = 11x

Divide

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7 0

4 years ago

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Two cars are driving towards an intersection from perpendicular directions.

FrozenT [24]

For a better understanding of the solution provided here please find the diagram in the attached file.

In the diagram, A is the intersection. B is the position of the first car and C is the position of the second car. As can be clearly seen, as per the directions given in the question, the cars and the intersection make a right triangle.

The distance between the first car and the intersection is $x$ and the distance between the second car and the intersection is $y$ . The distance between the two cars is depicted by $s$ . As we can see, $s$ is the hypotenuse of the right triangle. At the given instance the distances are 8 meters and 6 meters respectively. Thus, by the Pythagorean Theorem the hypotenuse will be:

$s=\sqrt{8^2+6^2}= \sqrt{100}=10$ ...............(Equation 1)

Now, we know that at any instant the Pythagorean Theorem holds and so we will have, in general:

$s^2=x^2+y^2$

Now, implicitly differentiating the above formula with respect to time, we get:

$2s\frac{ds}{dt}=2x \frac{dx}{dt}+2y \frac{dy}{dt}$

This can be further simplified by dividing both the sides by the common factor 2 as:

$s\frac{ds}{st}=x \frac{dx}{dy}+y\frac{dy}{dt}$ .................(Equation 2)

As we can see from the questions and the diagram, $\frac{dx}{dt}=-2 m/s$ and $\frac{dy}{dt}=-9 m/s$ . The negative sign is there because the distances y and x are reducing as the cars approach the intersection.