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Naily [24]
3 years ago
13

#4 find the value of x round answer to the nearest tenth

Mathematics
2 answers:
mel-nik [20]3 years ago
8 0

Answer:

x= 8.9

Step-by-step explanation:

Using our knowledge of trig functions

tan theta = opp/ adjacent

tan 25 = x /19

Multiply each side by 19

19 tan 25 = x

8.859845504944973263770117701191629574910197156776 =x

Rounding to the nearest tenth

8.9

AnnyKZ [126]3 years ago
6 0

Answer:

Step-by-step explanation:

Since this is a right angled triangle:

tan(∅) = opposite side/adjacent side

In this triangle:

tan(25°) = x/19

x = 8. 86 ≅ 8.9

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Answer:

Common denominator is 15

Step-by-step explanation:

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3 years ago
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' <u>brainly.com/question/2480946</u>
  • Learn more about the transformation of function <u>brainly.com/question/7297858 </u>
  • Learn more about midpoint of the segment <u>brainly.com/question/3269852</u>

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.

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