Respuesta :

mhanifa

Answer:

  • Q9 - B) 8
  • Q10 - D) 4.5

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Question 9

We have a diagram and need to find the number of routes without repeat paths:

  • [tex]ABCA[/tex] or [tex]ACBA[/tex]

We can see that there is one route from A to B, two routes from B to C and two routes from C to A. This is same on reverse order.

This gives us the number of routes:

  • [tex]ABCA = 1*2*2 = 4[/tex]
  • [tex]ACBA = 2*2*1 = 4[/tex]

Total number is:

  • [tex]4 + 4 = 8[/tex]

The matching answer choice is B

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Question 10

From the given we can observe that:

ABC and DCE are similar triangles, since they have same angle at vertex E (vertical angles are equal) and both are right triangles.

From similarity we get same ratio of corresponding sides:

  • [tex]AE/DE = AB/CD = 3/9 = 1/3[/tex]

We can find areas of triangles ACD and ECD and subtract to get the area of triangle AEC:

  • [tex]S_{ACD} - S_{ECD} = S_{AEC}[/tex]

As per ratio of corresponding sides:

  • [tex]AE/DE = 1/3[/tex]

As per segment addition:

  • [tex]AE + DE = AD = 4[/tex]

From the two equations above we get:

  • [tex]DE = 3/4*AD = 3/4*4 = 3[/tex]

Now, the required area is:

  • [tex]S_{ACD} - S_{ECD} = 1/2(4*9) - 1/2(3*9) = 4.5[/tex]

This is matching the answer choice D

semsee45

Answer:

9)  B. 8

10)   D. 4.5

Step-by-step explanation:

Question 9

For ease of visualization, label the different legs of the journey on the diagram (see attachment).

The journey needs to start and end at point A, go through points B and C (in any order), and not travel any road twice.

The different routes are:

  • AB (u), BC (x), CA (w)
  • AB (u), BC (y), CA (w)
  • AB (u), BC (x), CA (z)
  • AB (u), BC (y), CA (z)
  • AC (w), CB (x), BA (u)
  • AC (z), CB (x), BA (u)
  • AC (w), CB (y), BA (u)
  • AC (z), CB (y), BA (u)

Therefore, there are 8 different routes.

Question 10

Triangles EDC and EAB are similar since they have congruent angles:

  • ∠EDC ≅ ∠EAB  (both right angles)
  • ∠DEC ≅ ∠AEB  (vertical angle theorem)

Therefore, their corresponding sides are in proportion.

⇒ CD : BA = ED : EA

⇒ 9 : 3 = ED : EA

⇒ 3 : 1 = ED : EA

Since we know that AD = 4:

⇒ ED = 3

⇒ EA = 1

Area of a triangle

[tex]\sf Area = \dfrac{1}{2} \times base \times height[/tex]

To find the area of triangle AEC, subtract the area of triangle EDC from the area of triangle ADC.

[tex]\begin{aligned}\textsf{Area of triangle AEC} & = \sf Area\:of\:\triangle ADC - Area\:of\:\triangle EDC\\& = \sf \dfrac{1}{2} \cdot CD \cdot AD-\dfrac{1}{2} \cdot CD \cdot ED\\& = \sf \dfrac{1}{2}(9)(4)-\dfrac{1}{2}(9)(3)\\& = \sf 18-13.4\\& = \sf 4.5\:\:units\:squared\end{aligned}[/tex]

Learn more about similar triangles here:

https://brainly.com/question/21427237

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