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3 years ago

The coordinates of the vertices of ΔPQR are (–2, –2), (–6, –2), and (–6, –5).

Mathematics

1 answer:

melamori03 [73]3 years ago

6 0

<h3>Answer:</h3>

Yes, ΔPʹQʹRʹ is a reflection of ΔPQR over the x-axis

<h3>Explanation:</h3>

The problem statement tells you the transformation is ...

... (x, y) → (x, -y)

Consider the two points (0, 1) and (0, -1). These points are chosen for your consideration because their y-coordinates have opposite signs—just like the points of the transformation above. They are equidistant from the x-axis, one above, and one below. Each is a reflection of the other across the x-axis.

Along with translation and rotation, reflection is a transformation that does not change any distance or angle measures. (That is why these transformations are all called "rigid" transformations: the size and shape of the transformed object do not change.)

An object that has the same length and angle measures before and after transformation is congruent to its transformed self.

So, ... ∆P'Q'R' is a reflection of ∆PQR over the x-axis, and is congruent to ∆PQR.

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Answer:

$\sqrt{74}$

Step-by-step explanation:

Distance between two points

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

$\textsf{let}\:(x_1,y_1)=(2,-6)$

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$d=\textsf{length of segment AB}$

Substituting points into the distance formula and solving for d:

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Step-by-step explanation:

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3 years ago

Find a cubic function that has the roots 5 and 3-2i

Zolol [24]

Answer:

$P(x)=x^3-11x^2+43x-65$

Step-by-step explanation:

If the complex number $3-2i$ is a root of a cubic function, then the complex number $3+2i$ is a root too. Thus, the cubic function has three known roots $5,\ 3-2i,\ 3+2i$ and can be written as

$P(x)=(x-5)(x-(3-2i))(x-(3+2i)),\\ \\P(x)=(x-5)(x^2-x(3-2i+3+2i)+(3-2i)(3+2i)),\\ \\P(x)=(x-5)(x^2-6x+9-4i^2),\\ \\P(x)=(x-5)(x^2-6x+9+4),\\ \\P(x)=(x-5)(x^2-6x+13),\\ \\P(x)=x^3-11x^2+43x-65.$

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3 years ago

What is the coefficient of q in the sum of these two expressions?

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Answer:

23 and - 16 are the coefficients

Step-by-step explanation:

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3 years ago

Solve the system by using elementary row operations on the equations. Follow the systematic elimination procedure

Umnica [9.8K]

Answer:

The solution of the Given matrix

( x₁ , x ₂ ) = ( - 5 , 4 )

Step-by-step explanation:

Step(i):-

Given equations are x₁+4 x₂ = 11 ...(i)

2 x₁ + 7 x₂= 18 ...(ii)

The matrix form

A X = B

$\left[\begin{array}{ccc}1&4\\2&7\\\end{array}\right] \left[\begin{array}{ccc}x\\y\\\end{array}\right] = \left[\begin{array}{ccc}11\\8\\\end{array}\right]$

Step(ii):-

$\left[\begin{array}{ccc}1&4\\2&7\\\end{array}\right] \left[\begin{array}{ccc}x\\y\\\end{array}\right] = \left[\begin{array}{ccc}11\\8\\\end{array}\right]$

The Augmented Matrix form is

$[AB] = \left[\begin{array}{ccc}1&4&11\\2&7&18\\\end{array}\right]$

Apply Row operations, R₂ → R₂-2 R₁

$[AB] = \left[\begin{array}{ccc}1&4&11\\0&-1&-4\\\end{array}\right]$

The matrix form

$\left[\begin{array}{ccc}1&4\\0&-1\\\end{array}\right] \left[\begin{array}{ccc}x\\y\\\end{array}\right] = \left[\begin{array}{ccc}11\\-4\\\end{array}\right]$

The equations are

x₁ + 4 x₂ = 11 ...(a)

- x ₂ = - 4

x ₂ = 4

Substitute x ₂ = 4 in equation (a)

x₁ + 4 x₂ = 11

x₁ = 11 - 16

x₁ = -5

Final answer:-

The solution of the Given matrix

( x₁ , x ₂ ) = ( - 5 , 4 )

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3 years ago