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liq [111]
2 years ago
14

Figure

Mathematics
1 answer:
ludmilkaskok [199]2 years ago
5 0

Answer:

  • a rotation, followed by a translation
  • a translation, followed by two reflections

Step-by-step explanation:

The rigid motions are the transformations that produce congruent images.

There are three main kinds of rigid motions  :

  • Reflections : Flips a figure across a line of reflection.
  • Rotations : Rotates a figure about some degrees around a center point.
  • Translations : Moves figure on a plane about some distance in a certain direction.

But dilation is not a rigid transformation because it may change the size of the image. It is usually used to shrink or enlarge a shape.

So, the options having dilation and term "stretch" cannot produce congruent figures.

Hence, the correct options are :

  • a rotation, followed by a translation
  • a translation, followed by two reflections
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Given: Triangle ABC : triangle ADB. AB =24, AD =16 <br> Find: AC
RoseWind [281]

Answer:

<h2>AC = 36.01</h2>

Step-by-step explanation:

Given ΔABC and ΔADB, since both triangles are right angled triangles then the following are true.

From ΔADB, AB² = AD²+BD²

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BD² = 576-256

BD² = 320

BD = \sqrt{320}

BD = 17.9

from ΔABC, AC² = AB²+BC²

SInce AC = AD+DC and BC² = BD² + DC² (from ΔBDC )we will have;

(AD+DC)² = AB²+ (BD² + DC²)

Given AD = 16, AB = 24 and BD = 17.9, on substituting

(16+DC)² = 24²+17.9²+ DC²

256+32DC+DC² =  24²+17.9²+ DC²

256+32DC = 24²+17.9²

32DC = 24²+17.9² - 256

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DC = \frac{640.41}{32}

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6 0
2 years ago
How much of 30% HCI and 45% HCI would be needed to mix and produce 50 liters of 35% HCI
VladimirAG [237]

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  0.15x = 0.05(50) . . . . . simplify, subtract 0.30(50)

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33  1/3 liters of 30% and 16 2/3 liters of 45% HCl are needed.

_____

<em>Comment on the solution</em>

You may notice that the general solution to a mixture problem of this sort is that the fraction of the mix that is the highest contributor is ...

  (mix % - low %) / (high % - low %) = (.35 -.30) / (.45 -.30) = .05/.15 = 1/3

5 0
3 years ago
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