Which expression represents 76 decreased by an unknown number?

A trapezoidal prism undergoes a dilation. The surface area of the pre-image is 35 m². The surface area of the image is 315 m². T

Westkost [7]

The original object is called pre-image, and its dilated version is called image. The height of the image for the considered case is 17.4 m

<h3>How does dilation affect length, area, and volume of an object?</h3>

Suppose a figure (pre image) is dilated (dilated image) by scale factor of k.

So, if a side of the figure is of length L units, and that of its similar figure is of M units, then:

L = k × M

where 'k' will be called as scale factor.

The linear things grow linearly like length, height etc.

The quantities which are squares or multiple of linear things twice grow by square of scale factor. Thus, we need to multiply or divide by k² to get each other corresponding quantity from their similar figures' quantities.

So area of first figure = k² × area of second figure

Similarly,

Volume of first figure = k³ × volume of second figure.

It is because we will need to multiply 3 linear quantities to get volume, which results in k getting multiplied 3 times, thus, cubed.

For this case, we're given that;

Surface area of pre-image = 35 m²
Surface area of dilated image = 315 m²
Height of pre-image = 5.8 m
Height of dilated image.

Let the scale fator of dilation be k.

Then:

So area of pre-image = k² × area of dilated image

Thus, we get:

$35 = k^2 \times 315\\\\k = \sqrt{\dfrac{35}{315}} = 1/3$

(took positive root as scaling is done by non-negative factors as only magnitude matters mostly)

Thus, we get:

Height of pre-image = (1/3) × Height of dilated image (say h)

$5.8 = (1/3) \times h\\h = 3 \times 5.8 = 17.4 \rm \: m$

Thus, the original object is called pre-image, and its dilated version is called image. The height of the image for the considered case is 17.4 m

Learn more about dilation here:

brainly.com/question/3266920

4 0

2 years ago

Read 2 more answers

x-y=5 what is the slope intercept form of the equation of the line what is the slope intercept form of the equation of the line

dimaraw [331]

X - y = 5 in slope intercept form is y = x - 5

3 0

3 years ago

Knowing that this number, the Golden Ratio, is present not just in mathematics, but may also be present within your own brain an

pychu [463]

The Golden Ratio is a mathematical relationship that exists in art, shapes, nature and the human body. The golden ratio can be present in your body, from the length of your arms and legs when compared to your torso. Fingers is another example because the length of our fingers, each section from the tip of the base to the wrist is larger than the preceding.

The measurement of the human navel to the floor and to the top of the head to the navel is also the Golden ratio. Plastic surgeons and dental surgeons use it to reconstruct the human face. It also appears in everything around us like in the nature and science. It appears on in flower petals because it is believed that each petal is placed to so that each petal gets the best exposure to sunlight. Dolphins, starfish, sea urchins and honeybees also exhibit the proportion like humans. DNA molecules measures 34 angstroms by 21 angstroms at each full cycle of the double helix spiral, these two number are successive numbers. I think that the Golden Ratio is just a freak coincidence that happened.

5 0

3 years ago

2(3x – 1) = –6x – 2 can someone help

Gnom [1K]

Let's solve your equation step-by-step.

2(3x−1)=−6x−2

Step 1: Simplify both sides of the equation.

2(3x−1)=−6x−2

(2)(3x)+(2)(−1)=−6x+−2(Distribute)

6x+−2=−6x+−2

6x−2=−6x−2

Step 2: Add 6x to both sides.

6x−2+6x=−6x−2+6x

12x−2=−2

Step 3: Add 2 to both sides.

12x−2+2=−2+2

12x=0

Step 4: Divide both sides by 12.

12x/12= 0/12

x=0

Answer:

x=0

HOPE THIS HELPS!!! :)

5 0

3 years ago

NO LINKS OR FILES!!!!!!! How many millimeters is this line segment?

34kurt

Answer:

remember this line it will help you

<h3>Milli centi deci meter dega hecto kilometer</h3>

Step-by-step explanation:

<h2>milli to centi takes 10 points difference so option c. 40 millimeters is the correct answer</h2>

7 0

2 years ago