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3 years ago

Find the values of x and y.

Mathematics

1 answer:

malfutka [58]3 years ago

4 0

Answer:

y=57, x=77

Step-by-step explanation:

The line that creates x-3 is parrelell to the line that makes 74 degrees

You know that x-3=74

When you simplify you get x=77

Now that you know that x-3=74 you can add all the angles to 180 because they are a supplementary angle

74+41+(y+8)=180, then simplify

115+y+8=180, simplify more

123+y=180

y=57

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Find the equation of the axis of symmetry of the following parabola algebraically.

mr Goodwill [35]

Answer:

the equation of the axis of symmetry is $x=8$

Step-by-step explanation:

Recall that the equation of the axis of symmetry for a parabola with vertical branches like this one, is an equation of a vertical line that passes through the very vertex of the parabola and divides it into its two symmetric branches. Such vertical line would have therefore an expression of the form: $x=constant$ , being that constant the very x-coordinate of the vertex.

So we use for that the fact that the x position of the vertex of a parabola of the general form: $y=ax^2+bx+c$ , is given by:

$x_{vertex}=\frac{-b}{2\,a}$

which in our case becomes:

$x_{vertex}=\frac{-b}{2\,a} \\x_{vertex}=\frac{48}{2\,(3)} \\x_{vertex}=\frac{48}{6} \\x_{vertex}=8$

Then, the equation of the axis of symmetry for this parabola is:

$x=8$

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