All categories

2 years ago

What is the length of line segment EF if DE is 6ft and DF is 11ft and angle FDE is 40 degrees

Mathematics

1 answer:

Anna [14]2 years ago

6 0

Answer:

The length of EF = 7.48 feet

Step-by-step explanation:

* Lets consider these tree segment formed triangle DEF

- We have the length of two sides and the measure of the

including angle between these two sides

* So we can use the cos Rule to find the length of the third side

- The cos rule ⇒ a² = b² + c² - 2bc cosA

# a is the side opposite to angle A

# b is the side opposite to angle B

# c is the side opposite to angle C

# Angle A is the including angle between b and c

* In the problem

∵ DE = 6 feet

∵ DF = 11 feet

∵ m∠FDE = 40° ⇒ including angle between DE and DF

and opposite to EF

- By using cos Rule

∴ (EF)² = (DE)² + (DF)² - 2(DE)(DF) cos∠FDE

∴ (EF)² = (6)² + (11)² - 2(6)(11) cos(40)

∴ (EF)² = 55.882133 ⇒ take square root for both sides

∴ EF = 7.47543 ≅ 7.48 feet

* The length of EF = 7.48 feet

You might be interested in

Barbara sells iced tea for $1.49 per bottle and water for $1.25 per bottle. She wrote an equation to find the number of drinks s

Oksana_A [137]

The way she put it implies that she will sell many water bottles and only one iced tea. the correct equation would be 1.25x+1.49y=100, as she may sell different amounts of each.

4 0

1 year ago

The table and the graph show the relationship between the edge length, x, of a cube and its surface area, y. Is the relation a f

d1i1m1o1n [39]

Answer:

Yes, the relationship between x and y is a non-linear function.

Step-by-step explanation:

Given the table

Edge Length, x Surface Area, y

1 6

2 24

3 54

4 96

The table values clearly represent a function, because each input value has one and only one output value. i.e. there is no repetition of x values.

Also from the table values and the graph, it is clear that the function is not a linear function, because the graph is not a straight line. Also, In a cubic function, the highest power over the x variable(s) is 3. So, it is not a linear function.

Hence, we conclude that Yes, the relationship between x and y is a non-linear function.

Therefore, the 'last option' is correct.

4 0

2 years ago

It costs 20 cents to receive a photo and 30 cents to send a photo from a cellphone. C is the cost of one photo (either sent or r

ddd [48]

Answer:

(a) PC(C)= $\left \{ {{0.6 \ \ \ \ x=20} \atop 0.4 \ \ \ \ {x=30}} \right. \\\ 0 \ \ \ \ \ \ \ else$

(b) E[C] = 24 cents

Step-by-step explanation:

Given:

Cost to receive a photo = 20 cents

Cost to send a photo = 30 cents

Probability of receiving a photo = 0.6

Probability of sending a photo = 0.4

We need to find

(a) PC(c)

(b) E[C]

Solution:

(a)

PC(C)= $\left \{ {{0.6 \ \ \ \ c=20} \atop 0.4 \ \ \ \ {c=30}} \right. \\\ 0 \ \ \ \ \ \ \ else$

(b)

Expected value can be calculated by multiplying probability with cost.

E[C] = Probability × cost

E[C] = $0.6\times20 +0.4 \times 30 = 12 + 12 = 24\ cents$

3 0

2 years ago

The graph shows the distance Kendrick walks in different lengths of time.

Vlad1618 [11]

Answer:

1) 5

2) 0.2

Step-by-step explanation:

The complete question is attached below.

The x-axis represents the time in hours and y-axis represents the distance in kilometers.

The first question asks how many kilometers, does Kendrick walk per hour. The straight line represents the distance traveled at various amounts of time.

The point marked on the graph is against time = 1 hour and Distance = 5 km. So this shows:

Kendrick walks 5 kilometers in 1 hour.

In next part, we have to find how much time Kendrick takes to walk 1 kilometer.

Since, we know that:

Kendrick walks 5 kilometers in time = 1 hour

Dividing both sides by 5, we can write:

Kendrick walks 1 kilometer in time = 1/5 hour = 0.2 hour

So, Kendrick takes 0.2 hours to walk 1 kilometer.

7 0

2 years ago

Read 2 more answers

Joey is buying plants for his garden. He wants to have at least twice as many flowering plants as nonflowering plants and a mini

vodomira [7]

(24, 12) and (36, 0). The least amount of flowering plants occurs when x=2y, and the largest amount occurs when y=0. These two points satisfy both conditions and both sum to 36.

7 0

2 years ago

Read 2 more answers

What is the length of line segment EF if DE is 6ft and DF is 11ft and angle FDE is 40 degrees​

What is the length of line segment EF if DE is 6ft and DF is 11ft and angle FDE is 40 degrees