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guapka [62]
3 years ago
10

The vertices of polygon ABCD are at A(1, 1), B(2, 3), C(3, 2), and D(2, 1). ABCD is reflected across the x-axis and translated 2

units up to form polygon A′B′C′D′. Match each vertex of polygon A′B′C′D′ to its coordinates.
Mathematics
2 answers:
OLEGan [10]3 years ago
8 0
A'= (1, 1)

B'=(2, -1)

C'=(3, 0)

D'=(2,1)



good luck
shepuryov [24]3 years ago
3 0

Answer:

The vertices of image are A'(1,1), B'(2,-1), C'(3,0) and D'(2,1).

Step-by-step explanation:

Given information: The vertices of polygon ABCD are A(1, 1), B(2, 3), C(3, 2), and D(2, 1).

If a figure reflected across the x-axis, then

(x,y)\rightarrow (x,-y)

The vertices of polygon after reflection are

A(1,1)\rightarrow A_1(1,-1)

B(2,3)\rightarrow B_1(2,-3)

C(3,2)\rightarrow C_1(3,-2)

D(2,1)\rightarrow D_1(2,-1)

If a figure translated 2 units up, then

(x,y)\rightarrow (x,y+2)

The vertices of polygon after reflection and translation are

A_1(1,-1)\rightarrow A'(1,1)

B_1(2,-3)\rightarrow B'(2,-1)

C_1(3,-2)\rightarrow C'(3,0)

D_1(2,-1)\rightarrow D'(2,1)

ABCD is reflected across the x-axis and translated 2 units up to form polygon A′B′C′D′.

Therefore the vertices of image are A'(1,1), B'(2,-1), C'(3,0) and D'(2,1).

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Select all the factors roots of x^3 +2x^2-16x-32
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Factor by grouping. Group up the terms into pairs, factor each pair, then factor out the overall GCF.

x^3 + 2x^2 - 16x - 32

(x^3 + 2x^2) + (-16x-32) ... pair up terms

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x^2(x + 2) - 16(x + 2) ... factor -16 from the second group

(x^2 - 16)(x + 2) .... factor out (x+2)

(x - 4)(x + 4)(x + 2) .... Use the difference of squares to factor x^2-16

---------------------------

The original expression completely factors to (x - 4)(x + 4)(x + 2)

The three factors are x - 4  and  x + 4   and   x + 2

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A rectangle has a width of (4g) and a length of (28 - 3). The perimeter of the rectangle is 54 units. What is the
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Step-by-step explanation:

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The graph of the quadratic function y=-x^2-2x+3 is shown below
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Answer:

The axis of symmetry is at x=-1

The graph has an x-intercept at (1,0)

The graph has a vertex at (-1,4)

Step-by-step explanation:

we have

y=-x^{2}-2x+3

Statements

case 1) The graph has root at 3 and 1

The statement is False

Because, the roots of the quadratic equation are the values of x when the value of y is equal to zero (x-intercepts)

Observing the graph, the roots are at -3 and 1

case 2) The axis of symmetry is at x=-1

The statement is True

Observing the graph, the vertex is the point (-1,4)

The axis of symmetry in a vertical parabola is equal to the x-coordinate of the vertex

so

the equation of the axis of symmetry is x=-1

case 3) The graph has an x-intercept at (1,0)

The statement is True

see procedure case 1)

case 4)  The graph has an y-intercept at (-3,0)

The statement is False

Because, the y-intercept is the value of y when the value of x is equal to zero

Observing the graph, the y-intercept is the point (0,3)

case 5) The graph has a relative minimum at (-1,4)

The statement is False

Because, is a vertical parabola open downward, therefore the vertex is a maximum

The point (-1,4) represent the vertex of the parabola, so is a maximum

case 6) The graph has a vertex at (-1,4)

The statement is True

see the procedure case 5)

see the attached figure to better understand the problem

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