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laila [671]
3 years ago
7

Is there a dilation the Maps shape lll onto shape ll if so what is the scale factor and is it in enlargement or reduction?

Mathematics
1 answer:
DochEvi [55]3 years ago
6 0

Answer:

steps below

Step-by-step explanation:

Vertex of Shape I : (1,1) (2,1) (2,2) (1,2)   ---- (x,y)

Vertex of Shape II : (3,3) (6,3) (6,6) (3,6)   ---(x',y') : (x*3 , y*3)

Vertex of Shape III : (2,2) (4,2) (4,4) (2,4)  --- (x'',y'') -> (x' , y') : (x''*1.5 , y''*1.5)

Shape I dilate on to Shape II: Enlargement with scale factor of 3

dilation the Maps shape lll onto shape ll : Enlargement with scale factor of 1.5

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linear equation: y = -9x + 19
quadratic equation: y = x² - 6x + 9

Substitute the y in the quadratic equation by the its value in the linear equation.

-9x + 19 = x² - 6x + 9
      -  19               - 19    *subtract 19 to both sides
-9x         = x² - 6x -10
+9x              + 9x            *add 9x to both sides
0            = x² + 3x - 10
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Set each factor = 0 and solve
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x = -5         ;      x = 2

Find the corresponding value of y using the linear equation.
y = -9x + 19

x = -5                              x = 2
y = -9(-5) + 19               y = -9(2) + 19
y = 45 + 19                    y = -18 + 19
y = 64                            y = 1

(-5,64)                              (2,1)

Check each value on each equation.
y = x² - 6x + 9
(-5,64)                                                  (2,1)
64 = (-5)² - 6(-5) + 9                          1 = 2² - 6(2) + 9
64 = 25 + 30 + 9                                1 = 4 - 12 + 9
64 = 64                                               1 = 1

y = -9x + 19
64 = -9(-5) + 19                                  1 = -9(2) + 19
64 = 45 + 19                                      1 = -18 + 19
64 = 64                                              1 = 1

{(-5,64), (2,1)}

3 0
2 years ago
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