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irakobra [83]
2 years ago
12

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

he height of the pre-image is 5. 8 m. What is the height of the image? Enter your answer as a decimal in the box. M.
Mathematics
2 answers:
UkoKoshka [18]2 years ago
5 0

17.4 m - I took the test on k-12 and I got it wrong because I thought it was 52.2m. I reviewed the test and the correct answer said "17.4m"
Westkost [7]2 years ago
4 0

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:

<u><em>L = k × M</em></u>

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 <u><em>k²</em></u><em> </em>to get each other corresponding quantity from their similar figures' quantities.

<u><em>So </em></u><u><em>area </em></u><u><em>of </em></u><u><em>first figure </em></u><u><em>= k² × area of second figure</em></u>

Similarly,

<u><em>Volume </em></u><u><em>of first figure = k³ × volume of second figure.</em></u>

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:

<u><em>So area of pre-image = k² × area of dilated image</em></u>

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

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Answer in factored form x^2+11x+7
KATRIN_1 [288]
X² <span>+ 11x + 7

because 7 is a prime number, this doesn't factor prettily. you'll want to use the quadratic formula; if you aren't familiar with it, i'd either research it or look it up in your textbook, because it's clunky and not easily understood in this format:

(-b </span>± √((b)² - 4ac))/(2a)

in your equation x² + 11x + 7 ... a = 1, b = 11, and c = 7. what you do is you take the coefficients of every term, then plug it into your equation:
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not pretty, i know. but, regardless, you can simplify it:
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and you can't simplify it further. -11 isn't divisible by 2, and 93 doesn't have a perfect square that you can take out from beneath the radical. the ± plus/minus symbol indicates that you have 2 answers, so you can write them out separately:

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they look confusing, but those are your two factors. they can be simplified just slightly by changing the signs in the middle due to the -11:

(x + (11 + √93)/2) (x - (11 - √93)/2)

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7 0
3 years ago
PLEASE HELP ASAP!!
natita [175]

We can infer and logically deduce that the arc intersected by these chords are not congruent.

<h3>What is a circle?</h3>

A circle can be defined as a closed, two-dimensional curved geometric shape with no edges or corners. Also, a circle refers to the set of all points in a plane that are located at a fixed distance (radius) from a fixed point (central axis).

In Geometry, a circle is generally considered to be a conic section which is formed by a plane intersecting a double-napped cone that is perpendicular to a fixed point (central axis) because it forms an angle of 90° with the central axis.

<h3>What is an arc?</h3>

In Geometry, an arc can be defined as a trajectory that is generally formed when the distance from a given point has a fixed numerical value.

Let the radii of the two (2) different circles with center O and O' be r₁ and r₂ respectively. Also, two (2) isosceles triangles AOB and COD would be formed and as such we have:

AO = OB = r₁.

CO = O'D = r₂.

By critically observing the diagram (see attachment) of these circles, we can logically deduce that the arc intersected by chord AB is greater than the arc intersected by the chord CD.

This ultimately implies that, the arcs intersected by these chords are not congruent.

Read more on arcs here: brainly.com/question/11126174

#SPJ1

<u>Complete Question:</u>

Two circles with different radii have chords AB and CD, such that AB is congruent to CD. Are the arcs intersected by these chords also congruent? Explain.

Hint: It would be helpful to draw two circles and label them according to the given information, then evaluate possible arc measures.

Consider the type of triangle that may be drawn by connecting the endpoints of a chord to the center of a circle. Compare the triangles made by two circles with different radii.

3 0
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pashok25 [27]

Answer: c)She should have multiplied 15 by 3 instead of dividing.


Step-by-step explanation:

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which means if Ruby makes more than 3 quilts, the time will be more than 1 month.

To find the number of months to make 15 quilts, she need to divide 15 by 3

Thus, the number of months to make 15 quilts=5

Her answer was 1/5 which was absolutely wrong as if she is making 3 quilt in 1 month then in 1/5  month she would make fewer than 3 quilts.

She divides 3 by 15 instead of 15 by 3, thus but the unit is quilts not months.

Thus the only wrong option is c)She should have multiplied 15 by 3 instead of dividing.


4 0
3 years ago
Read 2 more answers
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