Please help me find all the missing angles

Mathematics

1 answer:

diamong [38]3 years ago

3 0

Answer:

Look at image I attached below.

Step-by-step explanation:

Important points to memorize when finding missing angles like these:

Two angles directly across from each other, not next to, are equal.
All angles that are on one side of a straight line add up to 180°, because a straight line has an angle measure of 180°.
A full spin-around equals 360°.
All angles in any triangle add up to 180°.

When you know all these important rules, the rest is just a matter of adding and subtracting.

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Using the Addition Method, solve for x in the following system of linear equations.

Anna71 [15]

Answer:

x = 0

Step-by-step explanation:

if 2y + x = 4

we can assume that y = 2
if y - 3x = 2

it means 2 - 0 = 2

therefore x = 0

4 0

2 years ago

Is x+y+1=0 a tangent of both y^2=4x and x^2=4y parabolas?

Lubov Fominskaja [6]

Answer:

yes

Step-by-step explanation:

The line intersects each parabola in one point, so is tangent to both.

For the first parabola, the point of intersection is ...

y^2 = 4(-y-1)

y^2 +4y +4 = 0

(y+2)^2 = 0

y = -2 . . . . . . . . one solution only

x = -(-2)-1 = 1

The point of intersection is (1, -2).

For the second parabola, the equation is the same, but with x and y interchanged:

x^2 = 4(-x-1)

(x +2)^2 = 0

x = -2, y = 1 . . . . . one point of intersection only

___

If the line is not parallel to the axis of symmetry, it is tangent if there is only one point of intersection. Here the line x+y+1=0 is tangent to both y^2=4x and x^2=4y.

_____

Another way to consider this is to look at the two parabolas as mirror images of each other across the line y=x. The given line is perpendicular to that line of reflection, so if it is tangent to one parabola, it is tangent to both.