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riadik2000 [5.3K]
3 years ago
15

Consider the following triangle side lengths and determine if the triangle could exist. Justify your answer. Part A: 21,18,17 Pa

rt B: 3,12,8
Mathematics
1 answer:
Misha Larkins [42]3 years ago
7 0

Answer:

A yes, B no

Step-by-step explanation:

The triangle inequality states that the sum of any 2 sides of the triangle must be greater than the third side.

A Given 21, 18, 17 , then

21 + 18 = 39 > 17

21 + 17 = 38 > 18

18 + 17 = 35 > 21

Thus the triangle could exist

B Given 3, 12, 8 , then

3 + 12 = 9 > 8

3 + 8 = 11 < 12 ← fails the test

Thus the triangle does not exist

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Rotate angle ABC 90 degrees clockwise about the origin and then reflect over the x-axis
Lady_Fox [76]

Rotation and reflection are instances of transformation

See attachment for the new position of  \triangle ABC

From the question, we have:

A = (-1,1)

C = (-2,4)

The rule of 90 degrees clockwise rotation is:

(x,y) \to (y,-x)

Using the above transformation, the new points would be

A' = (1,1)

B' =(3,3)

C' = (4,2)

The next transformation is reflection over the x-axis

The rule of this transformation is:

(x,y) \to (x,-y)

So, the new points would be:

A" = (1,-1)

B" = (3,-3)

C" = (4,-2)

See attachment for the new points

Read more about transformation at:

brainly.com/question/11709244

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F(x) = x^2. What is g(x)
Alexeev081 [22]

Answer:

g(x) = - x² - 4 ⇒ A

Step-by-step explanation:

Let us revise the reflection and translation of a function

  • If the function f(x) reflected across the x-axis, then its image is g(x) = - f(x)
  • If the function f(x) reflected across the y-axis, then its image is g(x) = f(-x)
  • If the function f(x) translated horizontally to the right by h units, then its image is g(x) = f(x - h)  
  • If the function f(x) translated horizontally to the left by h units, then its image is g(x) = f(x + h)  
  • If the function f(x) translated vertically up by k units, then its image is g(x) = f(x) + k  
  • If the function f(x) translated vertically down by k units, then its image is g(x) = f(x) – k  

f(x) = x² is the blue curve

g(x) is its image is the red curve

∵ g(x) is the image of f(x)

∵ f(x) is opened upward

∵ g(x) is opened downward

→ That means the sign of y-coordinates of all points on the blue

   graph are opposite

∴ f(x) is reflected about the x-axis

∴ Its image is - f(x)

∵ The vertex of f(x) is (0, 0)

∵ The vertex of g(x) = (0, -4)

→ That means the function translated 4 units down

∴ - f(x) is translated 4 units down

∴ Its image is - f(x) - 4

∴ g(x) = - f(x) - 4

∵ f(x) = x²

∴ g(x) = - x² - 4

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Answer:

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Step-by-step explanation:

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