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3 years ago

Which inequality is equivalent to -r >13?

Mathematics

1 answer:

Alinara [238K]3 years ago

4 0

Answer:

$r \: < \: - 13$

Step-by-step explanation:

The given inequality is

$- r \: > \: 13$

We need to simplify this inequality.

We multiply both sides by -1 and reverse the inequality sign.

This implies that:

$r \: < \: - 13$

This can also be written as:

$- 13 \: > r$

All these are equivalent to the given inequality.

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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

A bag has 6 RED marbles and 9 Blue marbles in it. What is the ratio probability of pulling a Red marble out of the bag ?

finlep [7]

Answer:

6:9

Step-by-step explanation:

5 0

4 years ago

Read 2 more answers

A, B, C, or D? I need help with this

dmitriy555 [2]

The answer is C. Have a good day!

4 0

3 years ago

To win trivia game ,Nevan must score 90 points.each correct answers is worth 1 3/4 points, and each incorrect answer is worth -1

Phantasy [73]

Answer:

Nevan wins with 96 points.

Step-by-step explanation:

58*1.75=101.5 and 22*(-0.25)=-5.5. 101.5+(-5.5)=101.5-5.5=96>90

8 0

3 years ago

What is 0.70 simplest form

Arturiano [62]

7/10 because there is two places after the decimal point making it 100 so move the decimal point two places to the right which makes it 70 and 70/100 in simplest form is 7/10

3 0

3 years ago