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podryga [215]
4 years ago
5

A triangle has vertices at A (1, 3), B (4, 2), and C (3, 8). Which transformation would produce an image with vertices A¢(-1, 3)

, B¢(-4, 2), C ¢(-3, 8)?
Mathematics
1 answer:
olya-2409 [2.1K]4 years ago
5 0

Answer:

Reflection across the Y axis

Step-by-step explanation:

If you plot each point of the triangle in its before and after positions you are able to see that the triangle's original shape was reflected across the Y axis to reach its end form.

Think about a rubik's cube rolling if you are struggling with reflections.

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During a certain period of time, about 70 northern sea otters had an annual growth of 18%. Use an exponential function to find t
Alenkinab [10]

Answer:

135.71 sea otters

Step-by-step explanation:

y = 70(1.18)^4

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6 0
3 years ago
. Find the area of the regular dodecagon inscribed in a circle if one vertex is at (3, 0).
devlian [24]

Answer:

Area of the regular dodecagon inscribed in a circle will be 27 square units.

Step-by-step explanation:

A regular dodecagon is the structure has twelve sides and 12 isosceles triangles inscribed in a circle as shown in the figure attached.

Since angle formed at the center by a polygon = \frac{360}{n}

Therefore, angle at the center of a dodecagon = \frac{360}{12} = 30°

Since one of it's vertex is (3, 0) therefore, one side of the triangle formed or radius of the circle = 3 units

Now area of a small triangle = \frac{1}{2}.(a).(b).sin\theta

where a and b are the sides of the triangle and θ is the angle between them.

Now area of the small triangle = \frac{1}{2}.(3).(3).sin30

= \frac{9}{4}

Area of dodecagon = 12×area of the small triangle

= 12×\frac{9}{4}

= 27 unit²

Therefore, area of the regular octagon is 27 square unit.

4 0
3 years ago
The length of a rectangle is 5ft longer than twice the width if the perimeter is 58 ft find the length and width of the rectangl
Travka [436]
----------------------------------
Define x :
----------------------------------
Let the width be x.
Width = x
Length = 2x + 5                // Length is 5ft longer than twice the width

----------------------------------
Formula for Perimeter :
----------------------------------
Perimeter = 2 (Length + Width)

----------------------------------
Find Width :
----------------------------------
58 = 2 ( 2x + 5 + x)         // Substitute Length and Width into formula
58 = 2 (3x + 5)                // Combine like terms
58 = 6x + 10                    // Apply distributive property
48 = 6x                            // Take away 10 from both sides
6x = 48                            // Switch sides. Make x the subject
x = 8                                // Divide by 6 on both sides

----------------------------------
Find Length and Width :
----------------------------------
Width = x = 8 ft
Length = 2x + 5 = 2(8) + 5 = 21 ft

--------------------------------------------------------------------
Answer: The length is 21 ft and the width is 8 ft.
--------------------------------------------------------------------

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