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larisa86 [58]
2 years ago
5

What is the value of x? Enter your answer as a decimal to the nearest tenth in the box.

Mathematics
2 answers:
gogolik [260]2 years ago
7 0

ANSWER

23.6 feet

EXPLANATION

The given triangle is a right triangle.

The hypotenuse is 27 ft.

The given angle I s 29°

The unknown side x, is adjacent to the given angle.

We use the cosine ratio to get,

\cos(29 \degree)  =  \frac{adjacent}{hypotenuse}

\cos(29 \degree)  =  \frac{x}{27}

We multiply both sides by 27 to get;

x = 27\cos(29 \degree)

x = 23.6ft

to the nearest tenth.

k0ka [10]2 years ago
3 0

Answer:

x = 23.6

Step-by-step explanation:

<u>Points to remember</u>

<u>Trigonometric ratios </u>

Sin θ  = Opposite side/Hypotenuse

Cos θ = Adjacent side/Hypotenuse

Tan θ = Opposite side/Adjacent side

<u>To find the value of x</u>

From the figure we can see a right angled triangle, ABC

Cos 29 = Adjacent side/Hypotenuse

 = AB/AC

 = x/27

x = 27 * Cos 29

 = 27 * 0.87

 = 23.6

Therefore x = 23.6

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Answer:

1242 6th graders went on the trip.

Step-by-step explanation:

From the information given, you know that the theater has 2760 seats and that the students filled 45% of the seats, so to find the quantity of 6th graders that went on the trip, you have to calculate 45% of 2760:

2760*45%=1242

According to this, the answer is that 1242 6th graders went on the trip.

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1 year ago
A fabric store sells two types of ribbon. One customer buys 3 rolls of the lace ribbon and 2 rolls of the satin ribbon and has a
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<span>Let L be the number of yards on a roll of lace ribbon. Let S be the number of yards on a roll of satin ribbon. We can set up two equations. equation 1: 3L + 2S = 120 yards equation 2: 2L + 4S = 160 yards We can multiply (equation 1) by 2 and subtract (equation 2). equation 1: 6L + 4S = 240 yards equation 2: 2L + 4S = 160 yards 4L = 80 yards L = 20 yards equation 1: 3L + 2S = 120 yards 3(20 yards) + 2S = 120 yards 2S = 60 yards S = 30 yards There are 20 yards on a roll of lace ribbon. There are 30 yards on a roll of satin ribbon.</span>
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2 years ago
The tables represent two linear functions in a system.<br><br> What is the solution to this system?
Darya [45]

The solution to this system is (x, y) = (8, -22).

The y-values get closer together by 2 units for each 2-unit increase in x. The difference at x=2 is 6, so we expect the difference in y-values to be zero when we increase x by 6 (from 2 to 8).

You can extend each table after the same pattern.

In table 1, x-values increase by 2 and y-values decrease by 8.

In table 2, x-values increase by 2 and y-values decrease by 6.

The attachment shows the tables extended to x=10. We note that the y-values are the same (-22) for x=8 (as we predicted above). That means the solution is ...

... (x, y) = (8, -22)

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2 years ago
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We suspect that automobile insurance premiums (in dollars) may be steadily decreasing with the driver's driving experience (in y
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Answer:

D) a chi square test for independence.

Step-by-step explanation:

Given that we  suspect that automobile insurance premiums (in dollars) may be steadily decreasing with the driver's driving experience (in years), so we choose a random sample of drivers who have similar automobile insurance coverage and collect data about their ages and insurance premiums.

We are to check whether two variables insurance premiums and driving experience are associated.

Two categorical variables are compared for different ages and insurance premiums.

Hence a proper test would be

D) a chi square test for independence.

8 0
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​
Anna [14]

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

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- 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

6 0
2 years ago
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