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3 years ago

Solve the system of equations below. 5x + 2y = 9 2x - 3y = 15

Mathematics

1 answer:

riadik2000 [5.3K]3 years ago

3 0

Answer:

(3,-3)

y= -3

x= 3

Step-by-step explanation:

5x+2y=9

2x-3y=15

solve the equation

x=9/5-2/5y

2x-3y=15

substitute the value of x into an equation

2(9/5-2/5y)-3y=15

distribute

18/5-4/5y-3y=15

subtract -4/5 to -3

18/5-19/5y=15

subtract 18/5 from both sides

-19/5=57/5

divide both sides by -19/5

y= -3

substitute the value of y into an equation

x=9/5-2/5(-3)

distribute

x=9/5+6/5

add 9/5 to 6/5

x=3

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(3,-3)

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A submarine lies 3 kilometers from the path of a target ship. The sub’s torpedoes have a range of 5 kilometers. For what distanc

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The distance along the path of the ship be within the range of the torpedoes is 4 kilometers.

Explanation:

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Let AC denotes the the target ship would be within the range of the torpedoes.

The image attached below illustrates that the distance between submarine and the target ship and the range of the torpedoes.

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To determine the length of AB, let us use Pythagorean theorem,

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Substituting the values of BC = 3 and AC = 5, we have,

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3 years ago

A person standing at the edge of a cliff throws a rock upward from a height of 180ft above ground level with an initial velocity

taurus [48]

Answer: 8.73 ft/s

Step-by-step explanation:

We have the following equation that models the motion of the rock:

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Where $h(t)$ is the height of the rock at a time $t$ .

Now, if $h(t)=48 ft$ we can find $t$ and then the velocity of the rock at that height:

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Rearranging the equation:

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Multiplying the equation by -1:

$16t^{2}-64t-132=0$

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$t=\frac{-(-64)\pm\sqrt{(-64)^{2}-4(16)(-132)}}{2(16)}$

Choosing the positive result of the equation:

$t=5.5 s$

Since velocity $V$ is defined as the traveled distance $h(t)$ in a given time $t$ , we have:

$V=\frac{h(t)}{t}$

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3 years ago

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Tju [1.3M]

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