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4 years ago

Triangles ABD and ACE are similar right triangles. which ratio best explains why the slope of AB is the same as the slope of AC

Mathematics

2 answers:

sertanlavr [38]4 years ago

4 0

B. AC/EA = AB/DA because theyre equal slopes just different sizes

DochEvi [55]4 years ago

3 0

Answer:

The correct option is d.

Step-by-step explanation:

The slope of a line is

$Slope=\frac{Rise}{Run}$

Slope of line AB is

$m_{AB}=\frac{BD}{DA}$

Slope of line AC is

$m_{AC}=\frac{CE}{EA}$

Triangles ABD and ACE are similar right triangles, therefore the corresponding sides are proportional.

$\frac{AB}{AC}=\frac{BD}{CE}=\frac{AD}{AE}$

Using last two ratios, we get

$\frac{BD}{CE}=\frac{AD}{AE}$

The required ratio is

$\frac{BD}{DA}=\frac{CE}{EA}$

Therefore the correct option is d.

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A gym initially has 5000 members. Each year, the gym loses 10% of its current members and gains 100 new members. Which recursive

Elis [28]

Answer:

An = A0 + 100 * n - (An-1) * 0.10

Step-by-step explanation:

Tenemos una regla recursiva para una secuencia es una fórmula que nos dice cómo avanzar de un término a otro en una secuencia. Por lo tanto debemos buscar a An.

Hay un valor inicial que es 5000, una ganancia y una perdida de clientes, que podemos representar así:

An = 5000 + Ganancia - Perdida

Inicial = A0 = 5000

Ganancia = 100, pero cómo sucede cada año, sería: 100 * n

Perdida = 10% de los miembros actuales, si al principio son 5000 por lo tanto A0 * 0.10, pero en este primer caso es que es A0, pero en general serían An-1

reemplazando:

An = A0 + 100 * n - (An-1) * 0.10

7 0

4 years ago

Benny the Barber (see Question 1) is considering the addition of a second chair. Customers would be selected for a haircut on a

Artyom0805 [142]

According to the information presented, Benny should decide not to add a second chair because the average number of clients waiting is 1 (very low), the average waiting time for a client is 10 minutes (very low), and the average time a customer is in the store is 20 minutes (very low).

According to the information, an average of 2 clients arrive at the hairdresser for every hour (60 min) and each cut takes a maximum of 20 minutes. Therefore, the hairdresser would have an average of 40 minutes busy and 20 minutes free for each hour.

Additionally, customers who must wait do not have to spend a long time waiting in the store because the maximum waiting time is 10 minutes (in the case that both customers arrive at the same time).

Below is a graph where the information of both cases is compared (with an additional chair and without an additional chair) and it is inferred that an additional chair is not necessary because the number of clients waiting and the waiting time is not high.

Learn more in: brainly.com/question/25400126

3 0

3 years ago

Can someone help me with this worksheet please!!!!

Marat540 [252]

(1) The missing term in the sequence, a₁₂ = 0.8.

(2) The missing term in the sequence, a₈ = 102.5.

(3) The missing term in the sequence, a₈ = 111.

(4) The missing term in the sequence, a₁₂ = -19.

(5) The missing term in the sequence, a₁₂ = 94.

(6) The missing term in the sequence, a₆ = 40.

(7) The missing term in the sequence, a₃₆ = -52.

(8) The missing term in the sequence, a₂₁ = -58.

<h3>Missing term of the sequence</h3>

The missing term in the sequence is determined as follows;

Tₙ = a + (n - 1)d

T₄ = a + 3d

18.4 = a + 3d ---(1)

T₅ = a + 4d

16.2 = a + 4d ---(2)

subtract (1) from (2)

-2.2 = d

18.4 = a + 3(-2.2)

a = 25

a₁₂ = a + 11d

a₁₂ = 25 + 11(-2.2)

a₁₂ = 0.8

a₂ = a + d

57.5 = a + d -- (1)

a₅ = a + 4d

80 = a + 4d --- (2)

solve (1) and (2)

d = 7.5

a = 50

a₈ = a + 7d

a₈ = 50 + 7(7.5)

a₈ = 102.5

a₁₀ = a + 9d

141 = a + 9d --- (1)

a₁₃ = a + 12d

186 = a + 12d --- (2)

Subtract (1) from (2)

d = 15

a = 6

a₈ = a + 7d

a₈ = 6 + 7(15)

a₈ = 111

a₂₂ = a + 21d

-49 = a + 21d ---- (1)

a₂₅ = a + 24d

-58 = a + 24d --- (2)

subtract (1) from (2)

d = -3

a = 14

a₁₂ = a + 11d

a₁₂ = 14 + 11(-3)

a₁₂ = -19

a₄ = a + 3d

-2 = a + 3d --- (1)

a₈ = a + 7d

46 = a + 7d ---- (2)

Subtract (1) from (2)

d = 12

a = -38

a₁₂ = a + 11d

a₁₂ = -38 + 11(12)

a₁₂ = 94

a₉ = a + 8d

64 = a + 8d --- (1)

a₁₂ = a + 11d

88 = a + 11d --- (2)

Subtract (1) from (2)

d = 8

a = 0

a₆ = a + 5d

a₆ = 0 + 5(8)

a₆ = 40

a₂₀ = a + 19d

-4 = a + 19d ---- (1)

a₂₃ = a + 22d

-13 = a + 22d --- (2)

Subtract (1) from (2)

d = -3

a = 53

a₃₆ = a + 35d

a₃₆ = 53 + 35(-3)

a₃₆ = -52

a₂₈ = a + 27d

5 = a + 27d ---- (1)

a₃₃ = a + 32d

50 = a + 32d --- (2)

Subtract (1) from (2)

d = 9

a = -238

a₂₁ = a + 20d

a₂₁ = -238 + 20(9)

a₂₁ = -58

Learn more about arithmetic progression here: brainly.com/question/6561461

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5 0

3 years ago

Identify the part, whole and percent in the following statement: Find 15% of 750

erma4kov [3.2K]

You have to multiply 750*100 and then divide 75,000 with 15, which gives you 5,000

8 0

3 years ago

What is 45.833 rounded to the nearest hundredths

aliya0001 [1]

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8 0

3 years ago

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