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icang [17]
2 years ago
9

Triangles DEF and D'E'F' are shown on the coordinate plane below: . . Triangle DEF and triangle D prime E prime F prime with ord

ered pairs at D negative 1, 6, at E 1, 3, at F 6, 3, at D prime 1, negative 6, at E prime negative 1, negative 3, at F prime negative 6, negative 3. . . What rotation was applied to triangle DEF to create triangle D'E'F'?. . A.90° clockwise. . B.180°. . C.None of the above. . D.90° counterclockwise
Mathematics
2 answers:
Brilliant_brown [7]2 years ago
4 0
<span><u><em>The correct answer is:</em></u>
180</span>°<span> rotation.

<u><em>Explanation: </em></u>
<span>Comparing the points D, E and F to D', E' and F', we see that the x- and y-coordinates of each <u>have been negated</u>, but they are still <u>in the same position in the ordered pair. </u>

 <u>A 90</u></span></span><u>°</u><span><span><u> rotation counterclockwise</u> will take coordinates (x, y) and map them to (-y, x), negating the y-coordinate and swapping the x- and y-coordinates.

<u> A 90</u></span></span><u>°</u><span><span><u> rotation clockwise</u> will map coordinates (x, y) to (y, -x), negating the x-coordinate and swapping the x- and y-coordinates.

Performing either of these would leave our image with a coordinate that needs negated, as well as needing to swap the coordinates back around. 

This means we would have to perform <u>the same rotation again</u>; if we began with 90</span></span>°<span><span> clockwise, we would rotate 90 degrees clockwise again; if we began with 90</span></span>°<span><span> counter-clockwise, we would rotate 90 degrees counterclockwise again. Either way this rotates the figure a total of 180</span></span>°<span><span> and gives us the desired coordinates.</span></span>
aleksley [76]2 years ago
4 0

The Real answer is 90 degrees clockwise not 180 degrees, i tried the approved answer above and got it wrong. If you examine the picture it makes more sense than just rotating it 180 degrees, plus the question doesn't specify if it is 180 degrees clockwise, or counterclockwise, so it makes sense for the answer to be: <u><em>90 degrees clockwise!</em></u>

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Answer:

x = 117

Step-by-step explanation:

Given

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2 years ago
What is the ratio of 14 days to 3 weeks in simplest form? user: express 3x3x3x5x5 using exponents
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7 0
3 years ago
Jade used candle molds, as shown, to make candles that were perfect cylinders and spheres:
Fittoniya [83]

Answer:

The difference in the amount of wax needed is 84.78 in³ (84.78 cubic inches)

Step-by-step explanation:

Given

<em>Cylinder</em>

Radius = 3 inches

Height = 7 inches

<em>Sphere</em>

Radius = 3 inches

Required

The difference in the amount of wax needed to make a candle from each of these molds

The quantity or amount required to make a wax of candle from each molds can be calculated by getting the volume of both molds

The volume of a cylinder is calculated using

<em>V₁ = πr²h</em>

where r and h are the radius and the height of the cylinder, respectively.

r = 3 in and h = 7 in

The volume of a sphere is calculated using

V_{2} = \frac{4}{3}\pi r^3

where r is the radius of the sphere

r = 3 in

Calculating V₁

V₁ = πr²h

V₁ = π * 3² * 7

V₁ = π * 9 * 7

V₁ = π * 63

V₁ = 63π

Calculating V₂

V_{2} = \frac{4}{3}\pi r^3

V_{2} = \frac{4}{3} * \pi * 3^3

V_{2} = \frac{4}{3} * \pi * 27

V_{2} = \frac{108}{3} * \pi

V₂ = 36π

Having calculated the volume of each molds, the difference in the amount of wax needed can then be calculated.

Difference = V₁ - V₂

Substituting 63π for V₁ and 36π for V₂

Difference = 63π - 36π

Difference = 27π

<em>(Taking π = 3.14)</em>

Difference = 27 * 3.14

Difference = 84.78

Hence, difference in the amount of wax needed is 84.78 in³

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