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3 years ago

6

Anyone know the answer to this ?

1 answer:

olga55 [171]3 years ago

7 0

A. 6, 6, 24, 36
B. 5, 1, 12, 5
C. 8, 4, 24, 32
D. 8, 2, 20, 16
E. 8, 6, 28, 48
F. 7, 3, 20, 21

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Step-by-step explanation:

1st of all we should let the ration of boys to girls be 2x and 3x.

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3 years ago

Select the correct answer from each drop-down menu. Quadrilateral PQRS, with vertex P(-5, -3), undergoes a transformation to for

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i) A. 180º rotation about the origin, ii) $Q' = (4, 5)$ .

Step-by-step explanation:

i) In this case, we understand that vertex $P = (-5,-3)$ changed to $P' = (5,3)$ after doing an operation. At first we must calculate the distance of each point regarding origin by Pythagorean Theorem:

Point P:

$OP = \sqrt{(x_{P}-x_{O})^{2}+(y_{P}-y_{O})^{2}}$

If we know that $x_{P} = -5$ , $y_{P} = -3$ , $x_{O} = 0$ and $y_{O} = 0$ , the distance $OP$ is:

$OP = \sqrt{(-5-0)^{2}+(-3-0)^{2}}$

$OP \approx 5.831$

Point P':

$OP' = \sqrt{(x_{P'}-x_{O})^{2}+(y_{P'}-y_{O})^{2}}$

If we know that $x_{P'} = 5$ , $y_{P'} = 3$ , $x_{O} = 0$ and $y_{O} = 0$ , the distance $OP'$ is:

$OP' = \sqrt{(5-0)^{2}+(3-0)^{2}}$

$OP' \approx 5.831$

As $OP = OP'$ , origin is the center of rotation.

Besides, $P'$ is a multiple of $P$ , that is:

1) $(-5, -3)$ Given

2) $((-1)\cdot 5, (-1)\cdot 3)$ $(-a)\cdot b = -a\cdot b$

3) $(-1)\cdot (5, 3)$ Scalar multiplication of a vector/Result.

The value of the scalar proves that P experimented a 180º rotation about the origin. Hence, the correct answer is A.

ii) If $Q = (-4, -5)$ and the same operation described in item i) is used, then, the location of $Q'$ is:

$Q' = (-1)\cdot Q$

$Q' = (-1) \cdot (-4,-5)$

$Q' = ((-1)\cdot (-4), (-1)\cdot (-5))$

$Q' = (4, 5)$

Which corresponds to option C.

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3 years ago