Solve the following system of equations.

Find the measure of angle x in the figure below A.35° B.47° C.51° D.62°

Dafna11 [192]

First of all, we know that a line is 180°. This means if we add the angles of 61°, 57°, and angle y, we should get 180°.

$\sf 61\textdegree +57\textdegree+y=180\textdegree$

Simplify:

$\sf 118\textdegree +y=180\textdegree$

Subtract 118° to both sides:

$\sf y=62\textdegree$

We also know that all three angles of a triangle add up to 180°. So we have:

$\sf 67\textdegree+62\textdegree +x=180\textdegree$

Simplify:

$\sf 129\textdegree +x=180\textdegree$

Subtract 129° to both sides:

$\sf x=\boxed{\sf 51\textdegree}$

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3 years ago

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Base: z(x)=cosx Period:180 Maximum:5 Minimum: -4 What are the transformation? Domain and Range? Graph?

garik1379 [7]

Answer:

The transformations needed to obtain the new function are horizontal scaling, vertical scaling and vertical translation. The resultant function is $z'(x) = \frac{1}{2} + \frac{9}{2} \cdot \cos \left(\frac{\pi\cdot x}{90^{\circ}} \right)$ .

The domain of the function is all real numbers and its range is between -4 and 5.

The graph is enclosed below as attachment.

Step-by-step explanation:

Let be $z (x) = \cos x$ the base formula, where $x$ is measured in sexagesimal degrees. This expression must be transformed by using the following data:

$T = 180^{\circ}$ (Period)

$z_{min} = -4$ (Minimum)

$z_{max} = 5$ (Maximum)

The cosine function is a periodic bounded function that lies between -1 and 1, that is, twice the unit amplitude, and periodicity of $2\pi$ radians. In addition, the following considerations must be taken into account for transformations: