How do I solve in trigonometry?

How Do I Solve In Trigonometry?

Answers

Answer 1

Given:-

A right angled triangle is given to us with hypotenuse= 42 and base= x .One of the angles is 64° .

To find:-

The value of x.

Answer :-

Here we will make use of trigonometric ratios . As we know that,

[tex]\sf \implies \cos\theta =\dfrac{base}{hypotenuse} \dots (1)\\[/tex]

And here,

hypotenuse= 42base = x [tex]\theta = 64^\circ [/tex]

So on substituting the respective values in (1) , we have;

[tex]\sf \implies \cos64^\circ =\dfrac{x}{42} \\[/tex]

And the value of

cos 64° = 0.438

[tex]\sf \implies 0.438 = \dfrac{x}{42} \\[/tex]

[tex]\sf \implies x = 42 \times 0.438 \\[/tex]

[tex]\sf \implies x = 18.396 \\[/tex]

[tex]\sf \implies \underline{\underline{ x \approx 18.4 }} \\[/tex]

and we are done!


Related Questions

Write an equation for the table.
Pls help!

Answers

Answer:

Step-by-step explanation:

its 3.02

Evaluate m³ +n if m= 1.2 and n = 13

Answers

Answer:

14.728

Step-by-step explanation:

m³ + n if m = 1.2 and n = 13

= (1.2)³ + 13

= 1.728 + 13

= 14.728

Select "Rational" or "Irrational" to classify each number.

2/3
π
400−−−
√36/2

Answers

The answer is:

2/3 - Rationalπ - Irrational400−−− - Rational√36/2 - Rational

Because it can be written as the ratio of two integers, 2/3 is a rational number (2 and 3).Since it has an unlimited number of non-repeating decimals after the decimal point and cannot be written as a finite or repeating decimal, is an irrational number.400 can be written as a ratio of two integers, making it a rational number (400 and 1).Because it reduces to 3, which is a ratio of two integers, 36/2 is a rational number (3 and 1). So, 36/2 makes sense.

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I need an answer quickkkk i am timed

Answers

The vertical asymptote is at x = -2

The horizontal asymptotes are at y =0.

How to get the asymptotes?

First, the vertical asymptote, it happens when the denominator becomes zero, then we need to solve:

-x - 2 = 0

x = -2

The vertical asymptote is at x = -2

For the horyzontal asymptotes we need to check the limit as x tends to ±∞, in both cases because x is only in the denominator, the function will tend to zero.

So we have two horizontal asymptotes at y = 0.

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what is the value of 10 ml in teaspoon?

Answers

10 ml is equal to 2 teaspoons. This is because 1 teaspoon is equal to 5 ml. To calculate the number of teaspoons in 10 ml, you must divide 10 ml by 5 ml. 10 ml divided by 5 ml equals 2 teaspoons.

To convert milliliters to teaspoons, you must use the conversion factor of 1 teaspoon = 5 ml. This means that for every 1 teaspoon, there are 5 milliliters. To figure out the number of teaspoons in 10 ml, you must take 10 ml and divide it by 5 ml. This will give you the number of teaspoons in 10 ml.When converting from milliliters to teaspoons, it is important to use the correct conversion factor. If you use the wrong conversion factor, you will end up with incorrect results. For example, if you use 1 teaspoon = 4 ml instead of 1 teaspoon = 5 ml, you will end up with an incorrect result.In addition to using the conversion factor, it is also important to keep in mind that a teaspoon is a measure of volume, not weight. This means that the amount of liquid in a teaspoon may vary depending on the density of the liquid. For example, a teaspoon of water will contain more liquid than a teaspoon of honey.

In conclusion, 10 ml is equal to 2 teaspoons. To convert milliliters to teaspoons, you must use the conversion factor of 1 teaspoon = 5 ml. It is important to remember that a teaspoon is a measure of volume, not weight, and the amount of liquid in a teaspoon may vary depending on the density of the liquid.

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What is 25 mcg to mg ?

Answers

25 mcg is equal to 0.025 mg. both are unit of measurement of weight.

The prefix "mcg" stands for microgram, which is a unit of measurement in the metric system that is one millionth of a gram (10⁻⁶ g). On the other hand, "mg" stands for milligram, which is one thousandth of a gram (10⁻³ g). Therefore, to convert from mcg to mg, you need to divide the value in mcg by 1000.

In this case, 25 mcg divided by 1000 equals 0.025 mg. It's important to be mindful of the units when dealing with measurements, as confusion between different units of measurement can lead to incorrect calculations and dosing errors.

Overall, when converting from mcg to mg, you can easily make the conversion by dividing the value in mcg by 1000, as the prefix "milli" represents a factor of 1000 in the metric system.

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What is the value of 45 out of 50 percent?

Answers

Answer:

22.5%

Step-by-step explanation:

45×50/100 gives you the answer using BODMAS

1)
4 ft
5.4 ft
What is the area

Answers

Answer: 21.6

Step-by-step explanation:

length X height


4(5.4)=21.6

The probability of the union of two events occurring can never be more than the probability of the intersection of two events occurring.
a. True
b. False

Answers

The probability of the union of two events occurring can never be more than the probability of the intersection of two events occurring, this statement is false.

The union of two or more sets refers to the set with all the elements belonging to each set. An element is said to be in the union if it lies to at least one of the sets.

The intersection of two or more sets refers to the set of elements universal to each set. An element is in the intersection if it occurs in all of the sets.

The event that both A and B occur is the intersection of the events A occurs and B occurs. As such, it is a subset of each and cannot, therefore, have a larger probability than either one individually.

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Gina is making a square tablecloth. How much fabric does she need?

Answers

Answer:

Step-by-step explanation:

You need the area.

If this is a square - it is 54 × 54 = 2916 inches squared

I need help with this please and thank you.

Answers

The answer is (0,-1)

Answer: 6x^2-x-1

Step-by-step explanation:

(3x+1)(2x-1) = 6x^2 - 3x + 2x -1

6x^2-x-1

A cylinder is full at 471 cubic centimeters and has a radius of 5 centimeters. What is the height of the cylinder?

Use 3.14 for pi.

Dont forget to track your thinking on paper. You will need this answer for the next problem.

Question 7 options:

94.2 cm


18.84 cm


30 cm


6 cm

Answers

6 cmAnswer:

Step-by-step explanation:

Choose the situation that best fits the equation:
x - 6

Choose the situation that best fits the equation:
x - 6

a. Elena has fewer roses than Lin. Lin has 6 roses and Elena has x roses.


b. Elena has more roses than Lin. Lin has 6 roses and Elena has x roses.


c. Elena has half the roses Lin has. Lin has 6 roses and Elena has x roses.


d. Elena has twice as many roses as Lin. Lin has 6 roses and Elena has x roses.

Answers

Answer:

a. Elena has fewer roses than Lin. Lin has 6 roses and Elena has x roses.

Step-by-step explanation:

Please somebody help me

Answers

Using mathematical operators, the value of the expression is 23

What is simplification of expression

Simplification of an expression is the process of reducing a mathematical expression to its simplest form while retaining the same value. This is done by using various rules and techniques, such as combining like terms, using the distributive property, and applying the order of operations.

The goal of simplification is to make the expression easier to work with and understand. It also helps to avoid errors when solving problems or simplifying more complex expressions.

In this expression given;

3(x + 2y) - 2x + 10 = ?

x = 1, y = 2

3(1 + 2(2)) - 2(1) + 10 = 23

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sams monthly gross income is 6000$ if sams federal tax rate is 10.5% and his state tax rate is 4.25%
A)how much money does sam bring home annually
B)How much social security tax does Sam pay monthly
C)How much Medicare tax does Sam pay annually

Answers

A) To calculate how much money Sam brings home annually, we need to first find out how much he earns after taxes each month.

Federal tax = 10.5% of $6000 = $630
State tax = 4.25% of $6000 = $255

Total tax deductions = $630 + $255 = $885

Sam's take-home pay each month = $6,000 - $885 = $5,115

To find out how much he brings home annually, we can multiply his monthly take-home pay by 12:

Annual take-home pay = $5,115 x 12 = $61,380

B) Social security tax rate is 6.2%, and the maximum amount of income subject to social security tax in 2023 is $147,000.

So, Sam's monthly social security tax payment can be calculated as:

Social security tax = 6.2% of min($6000, $147,000) = 6.2% of $6000 = $372

Therefore, Sam pays $372 in social security tax each month.

C) Medicare tax rate is 1.45% of all earnings, with no maximum income limit.

So, Sam's annual Medicare tax payment can be calculated as:

Medicare tax = 1.45% of $6000 x 12 = $1,044

Therefore, Sam pays $1,044 in Medicare tax annually

Preview
-116. Solve the following systems of equations using any method (graphing, elimination, substitution). Check each
solution, if possible.
a. - 2x + 3y = 1
2x+6y= 2
c. 3x - y = 7
y = 3x - 2
b. y = x + 4
x = -3y
d. x + 2y = 1
3x + 5y = 8

Answers

The equations are solved using graphing, elimination, substitution methods.

What is system of equation?

A system of equations are the set of equations where the solution for these equations are the intersecting point between the equations.

The systems of equations are given below are given below,

(a) -2x + 3y = 1(using elimination method)

     2x+6y= 2

     eliminating x term we get,

     9y = 3

     ⇒y=3.

(b)  y = x + 4 ---(1)(using substitution method)

     x = -3y---(2)

     Substitute (2) in (1) we get,

     y = -3y+4

     ⇒4y=4 ⇒y=1

(c)   3x - y = 7 (using graphing method)

      y = 3x - 2

     This system has no intersection point

     So this system has no solution.

    ( The graph is attached below.)

(d)   x + 2y = 1-----(1) (using elimination method)

      3x + 5y = 8-----(2)

     For eliminating x we have to the multiply equation(1) by 3,

      we get 3x+6y=3

      eliminating 3x we get, y=-5/3 substitute y in (1) we get x=49 /3

Hence, the equations are solved using graphing, elimination, substitution methods.

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A rectangular prism is 8.8 centimeters long and 4.4 centimeters high. Its volume is 271.04 cubic centimeters. What is the width of the rectangular prism?

Answers

The height of the cylindrical concrete pillar is approximately 153.2 centimeters.

How to find the volume of a right rectangular prism?

Suppose that the right rectangular prism in consideration be having its dimensions as 'a' units, 'b' units, and 'c' units, then its volume is given as:

[tex]V = a\times b \times c \: \: unit^3[/tex]

We are given that;

Length of prism=8.8cm

Height=4.4cm

Volume=271.04 cubic centimeters.

Now,

We can use the formula for the volume of a cylinder to find the height of the pillar. The formula for the volume of a cylinder is:

V = πr^2h

where V is the volume, r is the radius, and h is the height.

First, we need to find the radius of the pillar. The diameter of the pillar is given as 10 centimeters, so the radius is half of that:

r = 10/2 = 5 centimeters

Now we can substitute the given volume and radius into the formula and solve for the height:

12,042 = π(5)^2h

Divide both sides by π(5)^2:

h = 12,042 / (π(5)^2)

h ≈ 153.2 centimeters (rounded to one decimal place)

Therefore, by the given volume the answer will be 153.2 centimeters.

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hi guys can u guys answer this question​

Answers

Answer:

a= 77, b= 77, c= 103.

Step-by-step explanation:

a= 77 (vertically opposite)

b= a= 77 (corresponding angles)

c= 180-77

 = 103 (angles on a straight line)

what is 18% of 45 help please

Answers

Answer:

8.1

Step-by-step explanation:

100%= 45

1%= 45÷100

= 0.45

18%= 0.45×18

= 8.1

Pythagorean Theorem. I have to turn this in by Friday

Answers

Answer:

1. b = [tex]\sqrt{20}[/tex]

2. c = [tex]\sqrt{2[/tex]

3. b = [tex]\sqrt{105}[/tex]

4. c = [tex]\sqrt{113}[/tex]

5. c = [tex]\sqrt{52}[/tex]

6. b = [tex]\sqrt{80}[/tex]

7. b = [tex]\sqrt{130}[/tex]

8. a = [tex]\sqrt{48}[/tex]

9. c = [tex]\sqrt{149[/tex]

10. c = [tex]\sqrt{5}[/tex]

Example:

[tex]a^{2}[/tex] + [tex]b^{2}[/tex] = [tex]c^{2}[/tex]

[tex]8^{2}[/tex] + [tex]b^{2}[/tex] = [tex]12^{2}[/tex]

64 + [tex]b^{2}[/tex] = 144

64 + [tex]b^{2}[/tex] = 144 - 64

[tex]b^{2}[/tex] = 80

[tex]\sqrt{b}[/tex] = [tex]\sqrt{80}[/tex]

please fill out the steps

Answers

The simplified form of a rational equation [x + 1 / (x - 2)] / [x² / (x - 2) + 1] is equivalent to (x - 1) / (x + 2).

How to simplify a rational equation

In this problem we need to determine the simplified form of a rational equation, whose form is:

R(x) = P(x) / Q(x)

Where:

P(x) - Polynomic numerator.Q(x) - Polynomic denominator.

The simplification process can be done by means of algebra properties. First, write the rational equation:

[x + 1 / (x - 2)] / [x² / (x - 2) + 1]

Second, expand the numerator and the denominator:

[(x² - 2 · x + 1) / (x - 2)] / [(x² + x - 2) / (x - 2)]

Third, simplify the fraction by algebra properties:

[(x² - 2 · x + 1) · (x - 2)] / [(x² + x - 2) · (x - 2)]

(x - 1)² / [(x + 2) · (x - 1)]

(x - 1) / (x + 2)

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an object has a mass of 8.1kg what is its weight

Answers

The weight of the object is 79.461 newtons.

How to determine the weight

The standard value for the acceleration due to gravity is approximately 9.81 m/s^2 near the Earth's surface.

To find the weight of an object with a mass of 8.1 kg, we can use the formula:

Weight = mass x acceleration due to gravity

So, the weight of the object is:

Weight = 8.1 kg x 9.81 m/s^2

Weight = 79.461 N (newtons)

Hence, the weight is 79.461 newtons.

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Use the distributive property to write an equivalent expresión for the perimeter of the triangle

Answers

The equivalent perimeter expression is 3 * 3

How to detemrine the perimeter

From the question, we have the following parameters that can be used in our computation:

Side lengths = 3m, 3m and 3m

The perimeter of the triangle is the sum of the side lentths

So, we have

perimeter = 3 + 3 + 3

Using the distributive property, we have

Perimeter = 3 * 3

Hence, the perimeter expression is 3 * 3

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Complete question

The lengths of the sides of a triangle are represented by 3m, 3m and 3m.

Find the coordinates of the centroid of the triangle with the vertices s(2, 5), t(6, 5), and r(10, 0).

Answers

The centroid of this triangle is located at the point (6, 3).

The centroid of a triangle is the point where the three medians of a triangle intersect. Medians are the line segments that connect each vertex of the triangle to the midpoint of the opposite side.

The centroid is the "center of mass" or the "balance point" of the triangle. In other words, if the triangle were made of a solid material and suspended by a string attached to the centroid, it would balance.

To find the coordinates of the centroid of a triangle, we will use the following formula:

G = (x1 + x2 + x3)/3, (y1 + y2 + y3)/3

Where G is the centroid, and (x1, y1), (x2, y2), and (x3, y3) are the coordinates of the triangle's vertices.

So for the triangle with the vertices s(2, 5), t(6, 5), and r(10, 0), we have:

G = (2 + 6 + 10)/3, (5 + 5 + 0)/3

G = (18/3, 10/3)

G = (6, 3.333...), which we can round to (6, 3)

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2) The school that Imani goes to is selling tickets to the annual dance competition. On the first day
of ticket sales the school sold 12 senior citizen tickets and 6 student tickets for a total of $252.
The school took in $98 on the second day by selling 6 senior citizen tickets and 1 student ticket.
What is the price each of one senior citizen ticket and one student ticket?

Answers

The price of each ticket is given as follows:

Senior: $14.Student: $14.

How to obtain the prices?

The prices for each type of ticket are obtained via a system of equations, for which the variables are given as follows:

Variable x: price of a senior ticket.Variable y: price of a student ticket.

On the first day of ticket sales the school sold 12 senior citizen tickets and 6 student tickets for a total of $252, hence:

12x + 6y = 252

2x + y = 42 (simplifying by 6).

y = 42 - 2x.

The school took in $98 on the second day by selling 6 senior citizen tickets and 1 student ticket, hence:

6x + y = 98

y = 98 - 6x.

Equaling the two equations, the value of x is obtained as follows:

42 - 2x = 98 - 6x

4x = 56

x = 56/4

x = 14.

Then the value of y is of:

y = 98 - 6(14)

y = 14.

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How does a number line help to show that 3 divided by 1/4 is equal to 3x4

Answers

Answer:

To show that 3 divided by 1/4 is equal to 3x4 on a number line:

1. Draw a number line starting from 0 and mark every 1/4 division.

2. Label 3 divisions with the corresponding value '3'.

3. Move 4 divisions in the same direction as that of 3 divisions.

4. Mark the point at 4 divisions and label it as ’12’.

5. From the starting point to the point labelled ‘12’, there are 7 divisions.

6. Since each division represents a quantity of 1/4, dividing 3 by 1/4 (or multiplying by 4) will result in a total of 12, or 3x4.

Do anybody know the answer?

Answers

The solution of the equation y = - 7x + 1 are,

⇒ (6, - 41) and (- 8, 57)

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The equation is,

⇒ y = - 7x + 1

Hence, Substitute the given points into equation and check the solution as;

Put (x, y) = (- 6, - 35)

⇒ y = - 7x + 1

⇒ - 35 = - 7 × - 6 + 1

⇒ - 35 ≠ 43

Thus, It is not the solution.

Put (x, y) = (4, 27)

⇒ y = - 7x + 1

⇒ 27 = - 7 × 4 + 1

⇒ 27 ≠ - 27

Thus, It is not the solution.

Put (x, y) = (6, - 41)

⇒ y = - 7x + 1

⇒ - 41 = - 7 × 6 + 1

⇒ - 41 = - 41

Thus, It is the solution.

Put (x, y) = (- 8, 57)

⇒ y = - 7x + 1

⇒ 57 = - 7 × - 8 + 1

⇒ 57 = 57

Thus, It is the solution.

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.
Roselle has 2 cups of popcorn and 7 oz of soda for a total of 212 calories. Carmel has 1
cup of popcorn and 11 oz of soda for a total of 226 calories. Determine the number of
calories per cup of popcorn and per ounce of soda.

Answers

There are 50 calories per cup of popcorn and 16 per ounce of soda.

What is the solution to the equation?

A solution to an equation is a number that can be substituted for the variable to provide a true number statement.

Let's represent x be the number of calories per cup of popcorn

And let's represent y be the number of calories per ounce of soda.

The two equations are based on the given details:

2x + 7y = 212 ....(i)

1x + 11y = 226 ....(ii)

From equation (ii), we have

x + 11y = 226

x = 226 - 11y

Substitute the value of x = 226 - 11y in equation (i), and solve for y:

y = 16

Substitute the value of y = 16 in equation (ii), and we get

x = 50

Thus, the number of calories per cup of popcorn is 50 and the number of calories per ounce of soda is 16.

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What is 1 Litre equal to in cm3?

Answers

There are 1000 cubic centimetres in a litre (cm3). This is so because one cubic centimetre (cc) equals one millilitre (ml), and one litre (l) equals 1000 ml.

1000 ml make up 1 litre (L).

ml (millilitres) = cm3

1000 ml = 1000 cm3

1 L = 1000 cm3

One litre is equal to one thousand cubic centimetres (cm3). This is because one cubic centimetre is equivalent to one millilitre (ml), and one litre is equal to 1000 millilitres (ml). The subsequent actions can be conducted in order to calculate this. Initially, one litre (L) equals one thousand millilitres (ml). Second, one cubic centimetre is equivalent to one millilitre (cm3). Thus, one millilitre is equivalent to one hundred cubic centimetres. Last but not least, one litre equals one thousand cubic centimetres, or 1 L = 1000 cm3. Anybody wishing to translate between the two different volume measures will find this information valuable. For instance, if a recipe calls for a certain amount of an ingredient in litres, it is simple to convert that amount to cubic centimetres if necessary.

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Word problem with multiple decimal operations
Maria sells beaded necklaces. Each large necklace sells for $4.50 and each small necklace sells for $3.90. How much will she
earn from selling 1 large necklace and 4 small necklaces?

Answers

Answer: $20.10

Step-by-step explanation: If you multiply 3.90 by 4 and add 4.50 you get 20.10

Answer:

!20.1

Step-by-step explanation:

I got here by multiplying $3.90 by four and adding $4.50. This equals $20.1

Hence the answer is: She will earn $20.1

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