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Mathematics

2 answers:

snow_tiger [21]4 years ago

6 0

Explanation:

It can help to draw your own figure with the right angles better represented. You will notice that right triangles PQR and PRS share side RS. PQ is the hypotenuse of one of them; RS is the hypotenuse of the other.

We can write two equations that make use of the Pythagorean theorem:

PQ² = PR² +RQ²

RS² = QS² +RQ²

Then we can swap sides of the first equation and subtract the second equation. This gives ...

(PR² +RQ²) -(RS²) = (PQ²) -(QS² +RQ²)

Adding RQ², we can write this as ...

PR² -RS² +2RQ² = PQ² -QS²

The given relationship PR > RS means that PR² -RS² will be positive, so the left side of this equation must be positive.

Since PQ² - QS² is a positive number, PQ > QS.

Mandarinka [93]4 years ago

6 0

Step-by-step explanation:

In the right triangle PQR we have the side PQ is the hypotenuse then

PQ > PR

and since PR > RS (given) then PQ > RS (1)

In the right triangle QRS we have the side RS is the hypotenuse then

RS > QS (2)

finally ,

(1) + (2) give us PQ > QS

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Choose the correct graph of the given system of equations. y + 2x = −1 3y − x = 4 graph of two lines that intersect at the point

ELEN [110]

The system of equations has one solution (-1, 1)

<h3>Graph of system of linear equations </h3>

From the question, we are to graph the given system of equations.

The given system of equation is

y + 2x = −1

3y − x = 4

The graph of the given system of equations is shown below.

From the graph, we can observe that the solution to the given system of equation is given by two lines that intersect at the point (-1, 1).

Hence, the system of equations has one solution (-1, 1)

Learn more on Graph of linear equations here: brainly.com/question/14323743

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