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4 years ago

What is the area of a triangle whose sides have length $\sqrt{70},$ $\sqrt{70},$ and $\sqrt{28}$?

Mathematics

1 answer:

Mars2501 [29]4 years ago

6 0

Answer:

360.92

I hope that is right, but I am not entirely sure. Depends on what you round to.

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Which rule describes a composition of transformations that maps pre-image PQRS to image P"Q"R"S"?

FinnZ [79.3K]

The correct option is Option D $\boxed{{r_{y-axis}}o{R_{0,270^\circ }}\left({x,y}\right)}$ .

Further explanation:

A translation is a transformation that transforms the figure with a fixed distance in the same direction.

A rotation is the transformation that rotates the figure with given angles.

Given:

It is given that the two transformations that maps pre-image PQRS to image ${\text{P''Q''R''S''}}$ .

Step by step explanation:

Step 1:

It can be seen from the given figure that that the pre image is in the first quadrant and the image is the third quadrant.

The coordinates in the second quadrant represents as $\left({-x,y}\right)$ and in the third quadrant represents as $\left({-x,-y}\right)$ if $x,y$ are positive.

Therefore, the rotation is in the counter clockwise direction of $270^\circ$ .

Step 2:

The rotation of $270^\circ$ in the counter clockwise direction represents the coordinates as,

$\left({x,y}\right)\to\left({y,-x}\right)$

It can be seen that the coordinate of ${\text{PQRS}}$ are as follows,

$\begin{aligned}P=\left({1,1}\right)\hfill\\Q=\left(1,5}\right)\hfill\\R=\left({3,5}\right)\hfill\\S=\left({3,1}\right)\hfill\\\end{aligned}$

Then after rotation of $270^\circ$ counterclockwise on ${\text{PQRS}}$ $\left( {x,y}\right)\to\left({y,-x}\right)$ as,

$\begin{gathered}P\left({1,1}\right)\to\left({1,-1}\right)\hfill\\Q\left({1,5}\right)\to\left({5,1}\right)\hfill\\R\left({3,5}\right)\to\left({5,-3}\right)\hfill\\S\left({3,1}\right)\to\left({1,-3}\right)\hfill\\\end{gathered}$

Step 3:

Now apply the rule of $y$ axis of reflection ${R_{y-axis}}\left({x,y}\right)\to\left({-x,y}\right)$ on the above transformation as,

$\begin{gathered}\left({1,-1}\right)\to\left({-1,1}\right)=P''\hfill\\\left({5,1}\right)\to\left({-5,-1}\right)=Q''\hfill\\\left({5,-3}\right)\to\left({-5,-3}\right)=R''\hfill\\\left({1,-3}\right)\to\left({-1,-3}\right)=S''\hfill\\\end{gathered}$

Therefore, the given transformation is the rotation of $270^\circ$ counterclockwise followed by $y$ axis of reflection.

Therefore, this is the composition of transformation.

The composition of the given transformation can be written as,

${r_{y-axis}}o{R_{0,270^\circ}}\left({x,y}\right)$

Therefore, option D ${r_{y-axis}}o{R_{0,270^\circ}}\left({x,y}\right)$ is correct.

Learn more:

Learn more about what is the final transformation in the composition of transformations that maps pre-image abcd to image a"b'c"d"? a translation down and to the right a translation up and to the right a 270° rotation about point b' a 180° rotation about point b' brainly.com/question/2480946

Learn more about the transformation of function brainly.com/question/7297858

Learn more about midpoint of the segment brainly.com/question/3269852

Answer details:

Grade: High school

Subject: Mathematics

Chapter: Transformations

Keywords: transformations, dilation, translation, rotation, counterclockwise, angle, clockwise, coordinates, mapping, rigid transformation, right side, left side, quadrant, composition.

3 0

3 years ago

Read 2 more answers

What are the x-intercepts of the quadratic function?

Vaselesa [24]

X=-2 and x=5 solve it in factoring form by finding what multiplies to give you -10 and adds to give you -3 using 1 and -10

7 0

3 years ago

A student is trying to solve the set of two equations given below:

Brrunno [24]

To eliminate z multiply equation A by 7 and subtract both equations or divide equation B by 7 and subtract. (in this case, multiplying Equation A by 7 would be easier)

7 0

3 years ago

Suppose that you see a flock of birds at an angle of elevation of 32 degrees if the birds are at an altitude of 12,000 feet and

Firlakuza [10]

We know that

tan 32°=opposite side/adjacent side
[adjacent side]=[opposite side]/tan 32°

in this problem

opposite side-----> will be the altitude of the flock of birds minus your eye level above the ground
(12000-6)-----> 11994 ft

adjacent side------->will be the horizontal distance between you and the birds
32°------> an angle of elevation

[adjacent side]=[11994]/tan 32°-------> 19194.41 ft

the answer is
The horizontal distance from the birds is 19194.41 ft

7 0

3 years ago

A large industrial firm allows a discount on any invoice that is paid within 30 days. of all invoices, 10% receive the discount.

Daniel [21]

This situation has two outcomes: either an invoice is discounted or not. This two outcomes satisfy what we call a binomial distribution (note "bi" in binomial).

The binomial distribution tells us the probability that a randomly selected sample will have the outcome of success. In this case, we consider receiving the discount as the "success" outcome while not receiving it means "failure". The distribution takes the form:

$P(X=x)= _{n}C_{x} p^{x} q^{n-x}$
where n is the total number of samples, x is the number of samples you'll expect to have a success outcome, p is the probability of success, q is the probability of failure, and nCx is the combination of n samples taken x at a time.

You have an inconsistency regarding the total number of samples by the way, but I will take the first mentioned sample of 15 as I answer (you can just follow through the same process for another value).

For the next step, let's digest the problem to get the needed variables.

The total number of samples, n, is equal to 15. The probability of success (receiving a discount), p, is 10% or 0.1, and the probability of failure (not receiving a discount) is 90% or 0.9.

For P(X=x), we need to find the probability that less than two of the samples have success outcomes therefore we need to find the probability that NO invoice will receive the discount plus the probability that ONE invoice will receive the discount. This is equivalent to saying
$P(X\ \textless \ 2)=P(X=0)+P(X=1)$

Calculating these probabilities we'll get:
$P(X=0)= _{15}C_{0} (0.1)^{0} (0.9)^{15}=0.206$
$P(X=1)= _{15}C_{1} (0.1)^{1} (0.9)^{14}=0.343$
$P(X\ \textless \ 2)=P(X=0)+P(X=1)=0.206+0.343=0.549$

ANSWER: The probability that fewer than 2 sampled invoices will receive the discount is 0.549 or 54.9%.

6 0

3 years ago