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3 years ago

Trapezoid W′X′Y′Z′ is the image of trapezoid WXYZ under a dilation through point C.

Mathematics

2 answers:

dem82 [27]3 years ago

8 0

Answer:

Option C.

Step-by-step explanation:

Given information: WX=8m and W'X'=6m

It is given that Trapezoid W′X′Y′Z′ is the image of trapezoid WXYZ under a dilation through point C.

Scale factor is the ratio of corresponding sides of image and preimage.

$\text{Scale factor}=\frac{Corresponding side of image}{Corresponding side of preimage}$

For the given figure,

$\text{Scale factor}=\frac{W'X'}{WX}$

$\text{Scale factor}=\frac{6}{8}$

$\text{Scale factor}=\frac{3}{4}$

Since image and preimage lie on the same side of the center of dilation. So, the scale factor is positive number.

Therefore, the correct option is C.

Luda [366]3 years ago

4 0

The answer is 3 over 4

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From a thin piece of cardboard 30 in. by 30 in., square corners are cut out so that the sides can be folded up to make a box. Wh

Brilliant_brown [7]

Answer:

Dimensions 5in x 10in x 10in will yeild a box with a max. volume of 500 cubic inches

Step-by-step explanation:

Volume = height x length x width

considering 'x' as the length of the square corners that has been cut out from the cardboard and also, that is height of the cardboard box.

square corners are cut out so that the sides can be folded up to make a box, cardboard sides would reduce by 2x

therefore,

V = x (30-2x) (30-2x) ---> eq(1)

V=( 30x - 2x²) (30-2x)

V= 900x- 60x² - 60x² + 4x³

V= 4x³ - 120 x²+ 900x

Taking derivative w.r.t 'x'

dV/dx = 12x² - 240 x +900

dV/dx = 4 (3x² - 60x +225)

For maximum dV/dx, make it equal zero

dV/dx = 0

so, 4 (3x² - 60x +225)=0

3x² - 60x+225=0 (taking 3 common)

x² - 20x + 75 =0

Solving this quadratic equation

x² - 15x -5x + 75 =0

x(x-15) - 5(x-15) =0

Either (x-15)=0

x=15

Or x-5=0

x = 5

if we substitute x=15 in eq(1), volume becomes zero.

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When x= 5

eq(1)=>V = 5 (30-2(5)) (30-2(5))

V= 5 (10) (10)

V= 500 cubic inches,

Therefore, Dimensions 5in x 10in x 10in will yeild a box with a max. volume of 500 cubic inches

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4 years ago

Which property is illustrated by the following statement if ABC=DEF and DEF=XYZ then ABC=XYZ

Harlamova29_29 [7]

Answer:

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Step-by-step explanation:

Let A be any non empty set and R is any subset of the Cartesian product A × A. Then, R is a relation on A.

The relation R is said to be a transitive relation if (a, b) ∈ R, (b, c) ∈ R, then (a, c) ∈ R.

It is given that ABC = DEF and DEF = XYZ, then ABC = XYZ.

This shows the transitive property of equality.

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3 years ago

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Answer:

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3 years ago

Trapezoid W′X′Y′Z′ ​ is the image of trapezoid WXYZ under a dilation through point C.

Trapezoid W′X′Y′Z′ is the image of trapezoid WXYZ under a dilation through point C.