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3 years ago

Triangle CAT is transformed to produce triangle DOG.

Mathematics

1 answer:

PilotLPTM [1.2K]3 years ago

3 0

Using transformations and congruency concepts, it is found that with these following transformations, the triangles will be congruent.

A reflection, then a translation.
A rotation, then a reflection.

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Two triangles are congruent if they have the same lengths of the sides and the same angles.

In a reflection, there is a rule that changes the coordinates (x,y), but does not change the lengths of the sides of the triangles, thus they will still be congruent.
A reflection is also a special case of rotation, thus, in a rotation, the triangles are also congruent.
A translation is also similar to a reflection, using rules to shift the triangle up, down, left or right according to it's coordinates, not changing the sides or angles, thus congruent.
In a dilation, the lengths of the sides are changed, thus, the triangles will not be congruent.

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Thus, from the bullet points above, the correct options are:

A reflection, then a translation.
A rotation, then a reflection.

A similar problem is given at brainly.com/question/24267298

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2 years ago

A ball is thrown into the air and its position is given by h ( t ) = − 6.3 t 2 + 53 t + 24 where h is the height of the ball in

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$h'(t) = -12.6 t +53$

Now we can set up the derivate equal to 0 and we have:

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And solving for t we got:

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So then we can conclude that t = 4.206 is a maximum for the function.

And the corresponding height would be:

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Step-by-step explanation:

For this case we have the following function:

$h(t) = -6.3t^2 +53 t+24$

In order to maximize this function we need to take the first derivate respect the time and we have:

$h'(t) = -12.6 t +53$

Now we can set up the derivate equal to 0 and we have:

$-12.6 t +53 = 0$

And solving for t we got:

$t = \frac{53}{12.6}= 4.206$

For the second derivate respect the time we got:

$h''(t) = -12.6$

So then we can conclude that t = 4.206 is a maximum for the function.

And the corresponding height would be:

$h(t=4.206) = -6.3(4.206)^2 +53*4.206+24= 135.468 ft$

So the maximum occurs at t = 4.206 s and with a height of 135.468 m

8 0

3 years ago

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maksim [4K]

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54/96, 55/95, 60/89, 66/88, 69/83, 72/82, 73/75, 74/75.
Since we ended with 74 and 75, pick the decimal number that's in between those two numbers, 74.5.
74.5 is your median.
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Range is the difference of the highest number and the lowest number.
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The range is 42.

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3 years ago