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PSYCHO15rus [73]
3 years ago
5

Show that the triangles are similar

Mathematics
1 answer:
ss7ja [257]3 years ago
6 0

Answer:

<ACB is supplementary to the < ECD by the definition of supplementary angles. Therefore the first part of your answer is <ACB = <ECD

We know that similar triangles have the same corresponding angle measurements for their angles and therefore one of the triangles is just a scaled up or down version of the original. Triangle EDC is a scaled down version of ABC. Therefore, the corresponding sides of triangle ECD have the same ratio to the corresponding sides of ABC. For example line segment EC and BC are corresponding line segment and lets find the ratio: 14/21 = 2/3

THe ratio of EC to BC is 2/3 and the ratio of CD to AC is also 2/3 (18 / 27=2/3)

Therefore, CE / BC is equal to DC / AC

Your full answer is

<ACB = <ECD, CE / BC = DC / AC

So triangle ABC ~ triangle CDE

Step-by-step explanation:

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What is the solution set of the equation?<br> <img src="https://tex.z-dn.net/?f=%5Csqrt%7Bx%7D%20-18%2B9x%3Dx" id="TexFormula1"
bagirrra123 [75]

9514 1404 393

Answer:

  x ∈ {2.07014981016}

Step-by-step explanation:

The equation can be rewritten as ...

  √x = 18-8x

  x = 324 -288x +64x²

  64x² -289x +324 = 0

  x = (289 ±√577)/128 ≈ {2.07015, 2.44548}

Since √x must be positive, we know that ...

  18 -8x ≥ 0

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The larger of the above solutions is extraneous, so the solution set is ...

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8 0
2 years ago
What is the HCF of 54
Gemiola [76]

The HCF is the Highest Common Factor of a number in this case 54. This is the highest number times another number which = 54. The HCF for 54 is 18.

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Step-by-step explanation:

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Read 2 more answers
Consider the angle. Which TWO statements are true?
svetoff [14.1K]

Answer:

C, E

Step-by-step explanation:

A. INCORRECT

A is wrong because a reflection across the x-axis DOES move the position of the figure (as it is flipped, so the position changes), but it DOES NOT change the angle (since a shift in position doesn't equal to a change in angle measure)

B. INCORRECT

Although a reflection across the x-axis does change the position of the angle, it DOES NOT change the measure of the angle.

C. CORRECT

A reflection across the x-axis does in fact move the position of the figure and does not change the angle measure. Reflections only deal with flipping a figure, not changing it's shape/distorting it so that the angle will change.

D. INCORRECT

A translation right will change the position of the figure but will not change the measure of the angle.

E. CORRECT

Yes, a translation right WILL change the position of the figure but will NOT change the measure of the angle. This is because a translation is simply moving a figure up and down; it has nothing to do with changing the shape of the figure/distorting it so that the angle is different.

8 0
3 years ago
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