Mathematics College

determine the value of x using a trigonometric ratio.

Answers

Answer 1

Answer:

Step-by-step explanation:

Answer 2

The value of x in the triangle is given by trigonometric relations and the value is x = 8.86 units

What are trigonometric relations?

Trigonometry is the study of the relationships between the angles and the lengths of the sides of triangles

The six trigonometric functions are sin , cos , tan , cosec , sec and cot

Let the angle be θ , such that

sin θ = opposite / hypotenuse

cos θ = adjacent / hypotenuse

tan θ = opposite / adjacent

tan θ = sin θ / cos θ

cosec θ = 1/sin θ

sec θ = 1/cos θ

cot θ = 1/tan θ

Given data ,

Let the triangle be represented as ABC

Now , the height of the triangle is BC = 5.5 units

Let the angle be θ = 50°

Now ,

From the trigonometric relations ,

cos θ = adjacent / hypotenuse

Substituting the values in the equation , we get

cos θ = 5.5 / x

Multiply by x on both sides of the equation , we get

x ( cos θ ) = 5.5

Divide by cos θ on both sides of the equation , we get

x = 5.5 / cos θ

when θ = 50°

x = 5.5 / cos 50°

x = 5.5 / 0.642787

x = 8.556 units

Therefore , the value of x = 8.56 units

Hence , the value of x of triangle is x = 8.56 units

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Related Questions

rw/6+y=f And I have to solve for y so I’m confused on how to isolate it.

Answers

Answer:

The answer is

[tex]y = \frac{rw - 6f}{f} [/tex]

Step-by-step explanation:

[tex] \frac{rw}{6 + y} = f[/tex]

Cross multiply

We have

f(6 + y) = rw

6f + fy = rw

Move 6f to the right side of the equation to make fy stand alone

That's

fy = rw - 6f

Divide both sides by f to isolate y

That's

[tex] \frac{fy}{f} = \frac{rw - 6f}{f} [/tex]

We have the final answer as

[tex]y = \frac{rw - 6f}{f} [/tex]

Hope this helps you

A right triangle has vertices (−7,9),(3,9),(−7,−15). Find the perimeter of the triangle.

Answers

The perimeter of a triangle is 60 units if the right triangle has the vertices (-7, 9), (3, 9), (-7, -15).

What is meant by perimeter?

The perimeter calculation has various practical uses. A calculated perimeter is the length of fencing required to encircle a yard or garden. The circumference (perimeter) of a wheel/circle specifies how far it will roll in one revolution.

If the lengths of the triangle's sides are a, b, and c, the perimeter is the sum of their lengths:

P = a + b + c

The distance formula can be used to calculate any of the side lengths. However, because two of the sides are parallel to the axes, their lengths may be simply calculated by subtracting coordinates.

If the points are designated A, B, and C in that sequence, the two right-angle sides are as follows:

c = AB

= 3 -(-7)

= 10

b = AC

= 9 -(-15)

= 24

The Pythagorean theorem states that the third side of the relation can be found:

a² = b² +c²

a² = 10² +24² = 676

a=√676

a= 26

Now we can plug these numbers into the perimeter formula:

P = a + b + c = 26 + 24 + 10

P = 60

As a result, the perimeter of a triangle is 60 units.

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Find the a. MEAN and b. STANDARD DEVIATION for the data set. Round to two decimal places.
10) Country Number of Television Sets per 100 people
A 124
B 94
C 129
D 109
E 114
A) a. 115
b. 13.69
B)
a. 114
b. 13.69
C)
a. 114
b. 169
D) a. 113
b. 13.69
Provide an appropriate response.
11) If an adult male is told that his height is within 2 standard deviations of the mean of the normal distribution of heights of adult males, what can he assume?
A) His height measurement is in the same range as about 99.7% of the other adult males whose heights were measured.
B) His height measurement is in the same range as about 95% of the other adult males whose heights were measured.
C) He is taller than about 99.7% of the other men whose heights were measured.
D) He is taller than about 95% of the other men whose heights were measured. The scores on a driver's test are normally distributed with a mean of 100. Find the score that is:_____
12) Find the score that is 2 standard deviations below the mean, if the standard deviation is 26.
A) 126
B) 48
C) 152
D) 74
Suppose that prices of a certain model of new homes are normally distributed with a mean of $150,000. Use the 68-95-99.7 rule to find the percentage of buyers who paid:____
13) between $147,700 and $152,300 if the standard deviation is $2300.
A) 34%
B) 95%
C) 99.7%
D) 68%
14) more than $154,800 if the standard deviation is $2400.
A) 95%
B) 2.5%
C) 47.5%
D) 97.5%
A set of data items is normally distributed with a mean of 60. Convert the data item to a z-score, if the standard deviation is as given. 15) data item: 100; standard deviation:_____
a) 10
b) 40
c) 10
d) 4/3

Answers

Answer:

Explained below.

Step-by-step explanation:

(10)

The data set is:

S = {124, 94, 129, 109, 114}

The mean and standard deviation are:

[tex]\bar x=\frac{1}{n}\sum x=\frac{1}{5}\times [124+94+...+114]=114\\\\s=\sqrt{\frac{1}{n-1}\sum ( x-\bar x)^{2}}[/tex]

[tex]=\sqrt{\frac{1}{5-1}\times [(124-114)^{2}+(94-114)^{2}+...+(114-114)^{2}]}\\=\sqrt{\frac{750}{4}}\\=13.6931\\\approx 13.69[/tex]

The correct option is B.

(11)

According to the Empirical 95% of the data for a Normal distribution are within 2 standard deviations of the mean.

So, the adult male's height is in the same range as about 95% of the other adult males whose heights were measured.

The correct option is B.

(12)

Let the score be X.

Given:

μ = 100

σ = 26

[tex]X=\mu-2\sigma[/tex]

[tex]=100-(2\times 26)\\=100-52\\=48[/tex]

The correct option is B.

(13)

Let X be the prices of a certain model of new homes.

Given: [tex]X\sim N(150000, 2300^{2})[/tex]

Compute the percentage of buyers who paid between $147,700 and $152,300 as follows:

[tex]P(147700<X<152300)=P(\frac{147700-150000}{2300}<\frac{X-\mu}{\sigma}<\frac{152300-150000}{2300})[/tex]

[tex]=P(-1<Z<1)\\=0.68\\[/tex]

According to the 68-95-99.7, 68% of the data for a Normal distribution are within 1 standard deviations of the mean.

The correct option is D.

(14)

Compute the percentage of buyers who paid more than $154,800 as follows:

[tex]P(X>154800)=P(\frac{X-\mu}{\sigma}>\frac{154800-150000}{2400})[/tex]

[tex]=P(Z>2)\\=0.975\\[/tex]

According to the 68-95-99.7, 95% of the data for a Normal distribution are within 2 standard deviations of the mean. Then the percentage of data above 2 standard deviations of the mean will be 97.5% and below 2 standard deviations of the mean will be 2.5%.

The correct option is D.

(15)

The z-score is given as follows:

[tex]z=\frac{x-\mu}{\sigma}[/tex]

Luke is 5 years younger than 3 times Sydney's age, s. In this situation, what does 3s represent?
0 Luke's age
O Sydney's age
o three times Luke's age
O three times Sydney's age

Answers

Answer:

Step-by-step explanation:

'3s' represents 'three times Sydney's age.'

Answer:

three times Sydney's age

Step-by-step explanation:

i took a test on this

If you roll a 6-sided die 4 times, what is the probability of one roll being a multiple of 3? A)2/3 B)16/81 C)145/1296 D)65/81 E)625/1296 (I really need help! Pls answer fast!)

Answers

Answer:

671/1296

The probability of rolling at least one six is therefore 1 − 625/1296 = 671/1296 ≈ . 517.

Step-by-step explanation:

Answer:

671/1296

Step-by-step explanation:

What is value of
X+8
Enter your answer in the box
2x-5
B
10
14
Plz help

Answers

Answer:

not 100% but i think x may be 23.5

Step-by-step explanation:

The values of (x+8) and (2x-5) are 35 and 49 respectively.

What is a triangle?

A triangle is defined as a two-dimensional shape with three sides, three interior angles, and three vertices.

Given a triangle, ABC

We have,

(x+8)/10 = (2x-5)/14

7x+56 = 10x-25

3x = 81

x = 27

X+8 = 35

2x-5 = 49

Hence, The values of (x+8) and (2x-5) are 35 and 49 respectively.

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pt 2 6-7 Pleaseee Helpp

Answers

Answer:

w = 15

Step-by-step explanation:

x ___w___ = 3 x 5

w = 15

Hi there! Hopefully this helps!

----------------------------------------------------------------------------------------------------

Answer: w = 15~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

[tex]\frac{w}{5} = 3[/tex]

Multiply both sides by 5.

[tex]w = 3 \times 5[/tex]

Multiply 3 and 5 to get, you guessed it, 15!

100 megatons+234 help please

Answers

Answer:

we know,

1 megaton=1000kg

100 megaton=100000

now,

total weight=100000+234

=100234.

a kayak travels in a lake at an average speed of 35m/min. if the perimeter of a lake was 8400 m how many hours does it take for the kayak to travel around the whole lake

Answers

Answer:

I think Its 4hrs

Step-by-step explanation:

8400m÷ 35m = 240mins

240mins= 4hrs

A line slope of 2 passes through the point (4,8). What is the equation in slope-intercept form?

Answers

The equation would be Y=2x

Please help. Will select brainliest.

Answers

Answer:

Heptagon: D

Spetagon: D

Nonagon: B

5. Evaluate
a) (-3)²/(-9/4)²

Answers

Answer:

16/9

Step-by-step explanation:

Order of Operations: BPEMDAS

Step 1: Exponents

(-3)² = 9

(-9/4)² = 81/16

9/81/16

Step 2: KCF (Keep Change Flip)

9(16/81)

144/81

Step 3: Simplify

144/9 = 16

81/9 = 9

16/9

A password contains three digits, such as 175. How many different passwords can be formed?

Answers

Answer: There are 1000 different passwords.

Step-by-step explanation:

Given: A password contains three digits.

Number of digits from 0 to 9 = 10

Using fundamental principle of counting,

The number of different passwords = (Number of choices for digits) x (Number of choices for digits) x (Number of choices for digits)

= (10) x (10)x (10)

=1000

Hence, there are 1000 different passwords.

add or subtract as indicated and write the result in standard form 3i+(-6-i)

A:6-4i
B:-6+2i
C:6-2i
D:-6+4i

Answers

Answer:

B: -6+2i

Step-by-step explanation:

3i + (-6 - i) = ⇒ open parenthesis3i - 6 - i = ⇒ simplify-6 + 2i ⇒ answer in standard form of a+bi

At the end of the day of teaching the skill of cutting and sewing to make capes, Ms. Ironperson and Mr. Thoro decided to go to the Shawarma Mediterranean Grill. Ms. Ironperson ordered 3 chicken shawarma wraps and 2 orders of spiced potatoes for a total bill of $42.95. Mr. Thoro ordered 5 chicken shawarma wraps and 4 orders of spiced potatoes for a total bill of $74.91. What is the cost of a chicken shawarma wrap? What is the cost of one order of spiced potatoes? If x denotes the cost of a chicken shawarma wrap and y denotes the cost of an order of spiced potatoes, what are the equations needed to solve this problem?

Answers

Answer:

The cost of a chicken shawarma wrap is $10.99 and the cost of one order of spiced potatoes is $4.99.

Step-by-step explanation:

X denotes the cost of a chicken shawarma wrap and Y denotes the cost of an order of spiced potatoes.

From the provided information we can form two equations for the total price paid by Ms. Ironperson and Mr. Thoro.

[tex]3x+2y=42.95...(i)\\5x+4y=74.91...(ii)[/tex]

Multiply (i) by 4 and (ii) by 2 and subtract the two resulting equations:

[tex]3x+2y=42.95\ \ \ ]\times 4\\5x+4y=74.91\ \ \ ]\times2\\\\\Rightarrow\\\\12x+8y=171.80\\10x+8y=149.82\\\\\text{subtract}\\\\2x=21.98\\\\x=10.99[/tex]

Substitute x = 10.99 in (i) and solve for y as follows:

[tex]3x+2y=42.95\\\\(3\times 10.99)+2y=42.95\\\\2y=9.98\\\\y=4.99[/tex]

Thus, the cost of a chicken shawarma wrap is $10.99 and the cost of one order of spiced potatoes is $4.99.

A(n) ___
is a numerical summary of a population.

Answers

Answer:

parameter

Step-by-step explanation:

Find the recursive formula for this general term formula. [tex]t_{n} = n!/9^{-(n-1)}, n\geq 3[/tex]

Answers

Please give me a couple of minutes, I’ll answer in the comment section

What is the distance between point (6, -1) and point (5, 3) rounded to the nearest tenth?

Answers

Answer:

The answer is

4.1 units

Step-by-step explanation:

The distance between two points can be found using the formula

[tex] \sqrt{ ({x1 - x2})^{2} + ({y1 - y2})^{2} } [/tex]

where

( x1 , y1) and ( x2 , y2) are the points

From the question

The points are (6, -1) and (5, 3)

The distance between the points is

[tex] \sqrt{( {6 - 5})^{2} + ({ - 3 - 1})^{2} } [/tex][tex] = \sqrt{ {1}^{2} + ( { - 4})^{2} } [/tex][tex] = \sqrt{1 + 16} [/tex][tex] = \sqrt{17} [/tex]

= 4.123105

We have the final answer as

4.1 units

Hope this helps you

determine whether y = 4x+5 and y= 1/4x-2 are perpendicular

Answers

Answer:

No, they are not perpendicular

Step-by-step explanation:

Perpendicular lines will have opposite reciprocal slopes, meaning that the slopes will have opposite signs and be the reciprocals of each other.

We can see that the slopes of the lines are not opposite reciprocals.

4 and 1/4 are not opposite reciprocals because they do not have opposite signs.

2. What is the sum of the three solutions (find the values for x, y, and z, then add the answers)?
2x + 3y − z = 5 x
− 3y + 2z = −6
3x + y − 4z = −8
please show steps

Answers

Answer:

x = 30/7 , y = 46/7 , z = 48/7

Step-by-step explanation:

Solve the following system:

{2 x + 3 y - z = 5 x | (equation 1)

2 z - 3 y = -6 | (equation 2)

3 x + y - 4 z = -8 | (equation 3)

Express the system in standard form: