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3 years ago

Which statement about this system of equations is true? y=2/3x y=2/3x+3

Mathematics

1 answer:

KATRIN_1 [288]3 years ago

8 0

Answer:

1. The system has no solution

Step-by-step explanation:

No solution can only be possible when two lines are parallel to one another, thus never intersect and hence have no solution. In order to identify a two parallel lines, the slope of each must be equal to one another. Let's take a look at our equations:

y=2/3x,

y=2/3x+3

Here 2/3 acts as the slope provided it is a "coefficient" of x. This means that the system has no solution provided the similar slopes.

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Step-by-step explanation:

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3 years ago

Determine the length of the leg of a 45o – 45o – 90o triangle with a hypotenuse length of 15 inches. ( ANSWER NEEDS TO BE IN RED

SIZIF [17.4K]

Answer:

The lenghts of both legs: $\frac{15\sqrt{2}}{2}\ inches$

Step-by-step explanation:

By definition, when a triangle has angles that measures 45°, 45° and 90°, its legs are congruent.

Then, knowing the lenght of the hypotenuse, we can find the lenght (in inches) of any leg of the given triangle by applying the Trigonometric Identity $sin\alpha=\frac{opposite}{hypotenuse}$ :

$sin(45\°)=\frac{leg}{15}\\\\leg=\frac{15}{\sqrt{2}}$

Finally, simplifying, we get:

$leg=\frac{15(\sqrt{2})}{(\sqrt{2})(\sqrt{2})}=\frac{15\sqrt{2}}{2}$

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