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Katena32 [7]
3 years ago
7

Identify the transformation that maps the regular hexagon with a center (-7, 3.5) onto itself

Mathematics
2 answers:
Doss [256]3 years ago
8 0
The answer is D , because you rotate 120 degrees  clockwise 
mote1985 [20]3 years ago
4 0

Answer:

Option D - rotate 120° clockwise about (-7, 3.5) and reflect across the line x=-7              

Step-by-step explanation:

To identify : The transformation that maps the regular hexagon with a center (-7, 3.5) onto itself

Solution :

A regular hexagon which has 6 axes of symmetry.

So, the angle of rotational symmetry is given by 360 divides by number of sides.

\frac{360}{60}=60^\circ is the angle of rotational symmetry.

Since 90° is not a multiple of 60°, we will eliminate choices A and B.

120° is a multiple of 60°

So, it rotate clockwise 120°

Reflection across the line :

When you reflect a point across the line y = x, the x-coordinate and y-coordinate change places.

Which implies that the reflection across the line is x=-7

Therefore, Option D is correct that the transformation of a regular hexagon is

rotate 120° clockwise about (-7, 3.5) and reflect across the line x=-7

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Graph each piecewise function. Then identify the properties.
Alexxx [7]

Answer:

Domain: (-∞, -2) U [-2, 1] U (1, ∞)

Range: (-∞, 2) U [-3, -∞)

Step-by-step explanation:

This function is composed of three polynomial functions, a positive slope line m = \frac{1}{2}, whose domain is all real numbers, a horizontal line, and a negative slope line m = -1 whose domain is all real numbers.

Observe in the attached graph that the function has a discontinuity in x = -2, it has a jump.

When x approaches -2 by the left hand, y tends to 2. But when x approaches -2 from the right y tends to -3.

In addition, the function comes from -∞, then has a maximum value at y = 2 and finally derece up to -∞

Then we can conclude that for this piecewise function:

Domain: (-∞, -2) U [-2, 1] U (1, ∞) All Real Numbers

Range: (-∞, 2) U [-3, -∞)

4 0
3 years ago
The equation x^2+ (k - 3)x + (3 - 2k) = 0, where k is a constant, has two distinct real roots.
Lisa [10]

Step-by-step explanation:

For quadratic equation ax^2 + bx + c = 0 to have two distinct real roots,

b^2 - 4ac must be positive.

b^2 - 4ac > 0

(k - 3)^2 - 4(3 - 2k) > 0

k^2 - 6k + 9 - 12 + 8k > 0

k^2 + 2k - 3 > 0

4 0
2 years ago
Please help!!!
Leto [7]

Answer:

 - The scientist can use these two measurements to calculate the distance between the Sun and the shooting star by applying one of the trigonometric functions: Cosine of an angle.

- The scientist can substitute these measurements into cos\alpha=\frac{adjacent}{hypotenuse} and solve for the distance between the Sun and the shooting star (which would be the hypotenuse of the righ triangle).

Step-by-step explanation:

 You can observe in the figure attached that  "AC" is the distance between the Sun and the shooting star.

Knowing the distance between the Earth and the Sun "y" and the angle x°,  the scientist can use only these two measurements to calculate the distance between the Sun and the shooting star by applying one of the trigonometric functions: Cosine of an angle.

 This is:

cos\alpha=\frac{adjacent}{hypotenuse}

In this case:

\alpha=x\°\\\\adjacent=BC=y\\\\hypotenuse=AC

Therefore, the scientist can substitute these measurements into cos\alpha=\frac{adjacent}{hypotenuse} , and solve for the distance between the Sun and the shooting star "AC":

cos(x\°)=\frac{y}{AC}

AC=\frac{y}{cos(x\°)}

3 0
3 years ago
Read 2 more answers
Determine how triangles WVX and YZX can be shown to be similar.
NeX [460]

Answer:

D

Step-by-step explanation:

7 0
2 years ago
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Please help me i beg you I really need
SCORPION-xisa [38]
The correct answer is B, sorry if it wasn't correct.
3 0
3 years ago
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