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VMariaS [17]
3 years ago
13

The electrician arrives at Laura's house to fix her broken furnace. The electrician charges 90 dollars for the first hour and 60

dollars for each additional hour. If the total bill comes to 330 dollars how long will the electrician at Laura's house?
Mathematics
1 answer:
tamaranim1 [39]3 years ago
7 0

Answer:

5 hours

Step-by-step explanation:

Electrician got 90 for the first hour from the total bill, thus we can say:

330 - 90 = 240 remaining for remaining hours

$60 per hour, so $240 for how many hours?? We divide:

240/60 = 4 hours

So, electrician works 4 hours for 60 per hour = 2 * 6 = 240

and 1 hour for 90 (first hour) = 1 * 90 = 90

Total Bill is 240 + 90 = 330 {exactly what we have}

So we have checked and back-worked our problem to get electrician's total hours of work:

1 + 4 = 5 hours

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zhenek [66]

<u>Solving Q1: Given BE = ED and AE = EC.</u>

Considering triangles ΔAED and ΔCEB;

1. AE = EC (given)

2. ∠AED = ∠CEB (vertical angles)

3. ED = EB (given)

ΔAED ≡ ΔCEB (Side-Angle-Side congruency of triangles)

∠DAE = ∠BCE and AD = BC (using CPCTC)

⇒ AD║BC (Converse of Alternate Interior angles theorem)


Similarly consider triangles ΔABE and ΔCDE;

1. AE = CE (given)

2. ∠BEA = ∠DEC (vertical angles)

3. BE = DE (given)

ΔABE ≡ ΔCDE (Side-Angle-Side congruency of triangles)

∠ABE = ∠CDE and AB = CD (using CPCTC)

⇒ AB║CD (Converse of Alternate Interior angles theorem)


Since we have AB║CD, AB = CD and AD║BC, AD = BC.

Therefore, quadrilateral ABCD is a parallelogram.

****************************************************************************************************

<u>Solving Q2: The parallelogram has the angle measures shown in the diagram.</u>

It is clearly visible that both the triangles are Isosceles triangles, so opposite sides in each triangle are equal.

Consider two triangles given in the problem, we have two sets of congruent angles and one included side is common in both triangles.

Using Angle-Side-Angle congruence of triangles, both the triangles would be congruent too.

Using CPCTC, we can say opposite sides of quadrilateral would be congruent.

Therefore, all sides in given quadrilateral are equal.

Hence, Given quadrilateral is a Rhombus.

7 0
2 years ago
11 halves divided by 7
Tamiku [17]

Answer:

\large\boxed{\dfrac{11}{14}}

Step-by-step explanation:

\dfrac{\frac{11}{2}}{7}=\dfrac{11}{2}\div7=\dfrac{11}{2}\div\dfrac{7}{1}=\dfrac{11}{2}\cdot\dfrac{1}{7}=\dfrac{(11)(1)}{(2)(7)}=\dfrac{11}{14}

4 0
3 years ago
Read 2 more answers
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ivann1987 [24]

Answer:

x = -7

Step-by-step explanation:

−30=5(x+1)

Divide each side by 5

-30/5=5/5(x+1)

-6 =x+1

Subtract 1 from each side

-6-1 = x+1-1

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8 0
3 years ago
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Andru [333]
The answer is a, 2^2 * 3

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3 years ago
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stellarik [79]

Answer:

The answer would be 11.51

Step-by-step explanation:

π is rougroughly 3.14

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3.14 + 8.37 = 11.51

8 0
1 year ago
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