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VARVARA [1.3K]
2 years ago
13

Which of the following statements best describes the location of −(−1) on a number line? (5 points)

Mathematics
1 answer:
Tanzania [10]2 years ago
6 0

Answer:

It is 1 unit to the right of 0.

Step-by-step explanation:

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3 years ago
Solve the system of linear equations for x and y.(cos θ)x + (sin θ)y=1(−sin θ)x + (cos θ)y = 0x=y=
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Answer:

\bold{x =cos\theta}\\\bold{y=sin\theta}

Step-by-step explanation:

The given system of linear equations is:

(cos\theta)x+(sin\theta)y=1\\(-sin\theta)x+(cos\theta)y=0

We have to solve the equations for the values of x, y.

Let us use elimination method in which we eliminate one of the variables from the two variables.

For this, let us multiply the first equation by sin\theta and second equation by cos\theta

Now, the equations become:

(cos\theta.sin\theta)x+(sin\theta.sin\theta)y=sin\theta\\\Rightarrow (cos\theta.sin\theta)x+(sin^2\theta)y=sin\theta ....... (1)\\\\(-sin\theta.cos\theta)x+(cos\theta.cos\theta)y=0\\\Rightarrow (-sin\theta.cos\theta)x+(cos^2\theta)y=0 ..... (2)

Now, let us add (1) and (2):

(sin^2\theta)y+(cos^2\theta)y=sin\theta\\\Rightarrow (sin^2\theta+cos^2\theta)y=sin\theta\\\Rightarrow (1)y=sin\theta\\\Rightarrow y = sin\theta

Using the equation:

(-sin\theta)x+(cos\theta)y=0

Putting value of y:

\Rightarrow (-sin\theta)x+(cos\theta)sin\theta=0\\\Rightarrow (sin\theta)x=(cos\theta)sin\theta\\\Rightarrow x = cos\theta

So, the answer to the system of linear equations is:

\bold{x =cos\theta}\\\bold{y=sin\theta}

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