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Morgarella [4.7K]

3 years ago

15

a board 35 feet long is cut into two pieces such that the length of one piece is two-thirds of the length of the other piece. Fi

nd the length of the shorter piece of board.

1 answer:

Ghella [55]3 years ago

5 0

9514 1404 393

Answer:

14 ft

Step-by-step explanation:

The ratio of lengths is ...

shortest : longest = (2/3) : 1 = 2 : 3

Then the ratio of the shortest to the total is ...

shortest : (shortest +longest) = 2 : (2 +3) = 2/5

The shortest piece length is ...

(2/5)×(35 ft) = 14 ft

The shorter piece of the board is 14 ft long.

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I need help really bad

Stella [2.4K]

The answer is 18. You add 5 to both sides of the equation. the 5 cancels out. You are left with 2/3x=12. Then you divide 12 by 2/3 to get x. 12 divided by 2/3 is 18

5 0

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.

3 0

2 years ago

Read 2 more answers

A box of 8 marbles has 4 red, 2 green, and 2 blue marbles. If you select one marble, what is the probability that it is a red or

Yakvenalex [24]

Answer:

3/4

Step-by-step explanation:

add the no. of red marbles and blue marbles

2+4 = 6

Probability so divide 6/8 simplified to 3/4

4 0

3 years ago

Factor. Explain.<br> 24x³y²-4x²y+84x^4

Elan Coil [88]

Answer:

$\boxed{\bold{4x^2\left(6xy^2-y+21x^2\right)}}$

Step By Step Explanation:

Apply Exponent Rule $\bold{\:a^{b+c}=a^ba^c}$

$\bold{x^4=x^2x^2,\:x^3y^2=x^2x}$

$\bold{24x^2x-4x^2y+84x^2x^2}$

Rewrite 84: $\bold{21\cdot \:4}$

Rewrite 24: $\bold{6\cdot \:4}$

$\bold{6\cdot \:4x^2x-4x^2y+21\cdot \:4x^2x^2}$

Factor Out Common Term $\bold{4x^2}$

$\bold{4x^2\left(6xy^2-y+21x^2\right)}$

➤ $\boxed{\bold{Mordancy}}$

6 0

2 years ago

Benny has saved three thousand nine hundred cents over four days from selling lemonade.How many dollars does Benny have?

saw5 [17]

30 Dollars.

Hope this helps please mark this as Brainliest answer,

6 0

3 years ago