find the value of x using sin cos tan pls!!

The measure of the angle obtained from the specified measure of the arc CD and the diameter of the circle CF are;

An arc of a circle is a part or portion of the circumference of the circle.

1. The angle at C, obtained from the measure of the arc CD is; (360 - (120 + 120))/2 = 60 (Angle at the center of a triangle theorem)

Therefore; m∠CAF = 90° - 60°/2 = 60°

m∠CAF = 90° - 60°/2 = 60°

2. m∠AFB = m∠FCB = 30°

3. m∠CEF = m∠CAF = 60°

4. m∠CFB = m∠CAF = 60° (Corresponding angles theorem)

5. m∠DCF = m∠BCF = 30° (Sum of angles at a point and angles formed by the diameter of a circle)

6. m∠BCD = m∠BCF + m∠DCF

Therefore; m∠BCD = 30° + 30° = 60°

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Answer:

∠1 + ∠2 = 135°

Step-by-step explanation:

From the text, it is given that the two unknows are adjacent angles.

∠2x + ∠2x + 7 = 135°

∠4x + 7 = 135°

∠4x = 128°

x = 32

Answer:

[tex]\angle 1 = 64[/tex]°

[tex]\angle 2 = 71[/tex]°

Step-by-step explanation:

If two adjacent angles form at a resulting angle, this means that both angles form the full resulting angle.

This means [tex]\angle1[/tex] and [tex]\angle2[/tex] have a sum of [tex]135[/tex]°. This can also be written as:

[tex]135 = 2x+2x+7[/tex] or [tex]135 = 4x+7[/tex]

This can be worked out using simple rearrangement:

[tex]135 = 4x+7\\=135-7 = 4x\\=128 = 4x\\\therefore x = 32[/tex]

Therefore we can simply substitute to get our angles:

[tex]\angle 1 = 2x = 32\times2 = 64\\\angle 2 = 2x+7 = 32\times2+7 = 71[/tex]

Hope this helps!!!

Answer:

The system is consistent.

Step-by-step explanation:

Answer:

  (b)  There is not enough information to know whether the system is consistent or inconsistent.

Step-by-step explanation:

Given a system of equations consists of two lines with the same slope, you want to know whether the system is consistent or inconsistent, whether the lines are perpendicular, or if there is enough information to tell.

Lines with the same slope are either parallel or coincident. If they are parallel, the system of equations is inconsistent. If they are coincident, the system of equations is consistent.

Parallel or coincident lines are not perpendicular. Perpendicular lines have opposite reciprocal slopes.

Since we cannot tell whether the lines are parallel or coincident from the given description, we have to say, "there is not enough information to know."

Answer:

Mean of given observations = Sum of given observations Total number of observations

∴11=x+(x+2)+(x+4)+(x+6)+(x+8)÷5

⇒55=5x+20

5x=55-20

5x=35

x=35/5

x=7

Hence, the value of x is 7.

Euler's theorem lets us draw the conclusion that a polyhedron cannot contain [tex]6[/tex] vertices or [tex]7[/tex] edges.

Four or even more plane face (all polygons) that meet in pairs along an edge and at least three edges that meet at a vertex make up a solid figure. Full solution, step-by-step Polyhedron: A three-dimensional object with only polygonal faces. There must be a minimum of different faces on a polyhedron.

A two-dimensional shape composed of line segments is known as a polygon. Square, triangle, hexagonal, etc. are a few examples. A polyhedron, on the other hand, is a three-dimensional object formed of polygons. For instance, a cube, a tetrahedron, etc.

[tex]V - E + F = 2[/tex]

In the case of a polyhedron with [tex]6[/tex] vertices and [tex]7[/tex] edges, we can plug in the values [tex]V=6[/tex] and [tex]E=7[/tex] to obtain:

[tex]6 - 7 + F = 2[/tex]

Simplifying this equation, we get:

[tex]F = 3[/tex]

Therefore, we can conclude that it is not possible for a polyhedron to have [tex]6[/tex] vertices and [tex]7[/tex] edges, based on Euler's theorem.

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Answer:

0.9375

Step-by-step explanation:

In summary, 15/16 inches is the same as 0.9375 inches and 15/16 inches is also the same as 0.078125 feet.

The average adult have 02 liters of blood in the body.

The amount of blood circulating in a person depends on their height and weight, but the average adult has more than 5 liters. Blood volume is tightly regulated and linked to various organ systems. Additionally, it is closely related to sodium levels and hydration status. Maintenance of blood volume is essential for normal functioning as it is necessary for the continuous perfusion of body tissues.

According to the Question:

Given that:

The average adult has 1. 2 to 1. 5 gallons of blood in their body.

Now,

Based on the given conditions, formulate: 1.2 ×1.5

Calculate the product or quotient: 1.8

Round the number: 2 gallons.

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The value of a is obtained as 7, for the given expression, obtained using the scientific notations.

Numbers that are either too little or too huge to put in conventional decimal form can be expressed using scientific notation. Scientific notation is often known as standard index form simply scientific form among experts.

This notation is frequently used in the work of engineers, mathematicians, and scientists to make it considerably simpler to write large numbers. By using the "SCI" display option on the calculator, you can utilise scientific notation when using one.

The given number is:

63,000,000,000

Write the number in its scientific notation:

6.3 x 10¹⁰

Comparable number is 6.3 x 10³ which is 10ᵃ times larger than the 6.3 x 10¹⁰.

Dividing:

=  6.3 x 10¹⁰ / 6.3 x 10³

= 10⁷

Now, 10⁷ = 10ᵃ

As the base is same , thus the value of a = 7.

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The three orderer pairs in the form (x,y) that could be produced by the function y=12x+3x​ are (0,0), (1,15) and (-2,-30).

what is orderer pair?

The given function is:

y = 12x + 3x

Simplifying, we get:

y = 15x

To find ordered pairs in the form (x,y) that could be produced by this function, we can choose different values of x and substitute them into the equation to find the corresponding value of y. Here are three examples:

1. When x = 0:

y = 15x = 15(0) = 0

Therefore, the ordered pair is (0,0).

2. When x = 1:

y = 15x = 15(1) = 15

Therefore, the ordered pair is (1,15).

3. When x = -2:

y = 15x = 15(-2) = -30

Therefore, the ordered pair is (-2,-30).

In general, we can choose any value of x and find the corresponding value of y using the given function to obtain an ordered pair in the form (x,y).

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The nth term of the sequence 45, 40, 35, 30 is given by the formula a(n) = 50 - 5n.

To find the nth term of the sequence 45, 40, 35, 30, we need to first identify the pattern that governs the sequence. Here, we can see that each term is obtained by subtracting 5 from the previous term.

So, we can express the nth term of the sequence as:

a(n) = a(1) + (n-1)d

where a(1) is the first term of the sequence, d is the common difference between consecutive terms, and n is the index of the term we want to find.

In this case, a(1) = 45 and d = -5, since we are subtracting 5 from each term to get the next one. Substituting these values into the formula, we get:

a(n) = 45 + (n-1)(-5)

Simplifying, we have:

a(n) = 45 - 5(n-1)

Expanding the brackets, we get:

a(n) = 45 - 5n + 5

Simplifying further, we get:

a(n) = 50 - 5n

Therefore, the nth term of the sequence 45, 40, 35, 30 is given by the formula a(n) = 50 - 5n.

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The height of the building is about 364 feet.  

Let's use a proportion to solve the problem. We know that the height of the building and the length of its shadow are proportional to the height of the pole and the length of its shadow. That is:  

height of building/length of building shadow = height of pole/length pole shadow

We are given that the height of the pole is 10 feet, and its shadow is 5.5 feet long. We are also given that the length of the building shadow is 200 feet. We don't know the height of the building, so we'll use "h" to represent it. Substituting the given values into the proportion, we get:

h / 200 = 10 / 5.5

We can solve for "h" by cross-multiplying:

h = 200 * 10 / 5.5

h ≈ 363.6

Therefore, the height of the building is approximately 363.6 feet. Rounding to the nearest foot gives us the final answer:

The height of the building is about 364 feet.

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The subdivider has to get the deposit back to Max within 30 days.

A deposit is an amount of money paid to a vendor or a seller to secure goods or services. A deposit is a partial payment made to a business in advance of a larger purchase or delivery.

A subdivision is a housing development built on a portion of land that has been divided into multiple lots. The subdivider divides a large piece of land into smaller plots and sells each lot to individuals who are looking to build their own homes, thus creating a subdivision.

Max can get his deposit back within 30 days. This is because the subdivider has to refund the deposit within 30 days if the buyer cancels the reservation of the plot due to any reason, including the delay that the subdivider has experienced.

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Answer:

e. y = sin(x) + π

Step-by-step explanation:

We can see that the graph of y = sin(x) has been shifted vertically. This means that the added π should be outside the trigonometric function.

Therefore, e. y = sin(x) + π is the correct answer.

See the attached image for how a, b, c, and d values change the graphs of sine and cosine.

Answer:

The value of a+b+c is -2

Step-by-step explanation:

rewrite equation: a+b+c

substitute: (-1) + (2) + (-3)

simplify: -1 + 2 - 3

PEMDAS: 1 - 3

Which equals: -2

The time at which the population reaches 4,000 is t ≈ 2.51 hours after 12 pm or approximately 2:30 pm. A) The growth constant can be found using the formula for exponential growth:

$-N = N_0 e^{kt}$

where N₀ is the initial population, N is the final population, t is the time elapsed, and k is the growth constant.

Using the given information, we can set up two equations:

500 = N₀e^(0k)

1500 = N₀e^(2k)

Dividing the second equation by the first, we get:

3 = e^(2k)

Taking the natural logarithm of both sides, we get:

ln(3) = 2k

Therefore, the growth constant k is (ln(3))/2, approximately 0.549.

The population as a function of time can now be expressed as:

N(t) = 500e^(0.549t)

B) To find the population at 5 pm, we need to substitute t = 5 into the equation we found in part A:

N(5) = 500e^(0.549*5) ≈ 4,206

Therefore, the population at 5 pm is approximately 4,206 bacteria.

C) To find the time the population reaches 4,000, we need to solve the equation N(t) = 4,000 for t:

4,000 = 500e^(0.549t)

Dividing both sides by 500, we get:

8 = e^(0.549t)

Taking the natural logarithm of both sides, we get:

ln(8) = 0.549t

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Step-by-step explanation:

c = 2,8    and   d = 6,5

Use the distance formula  ( kind of a modified Pythagorean theorem)

s^2 = (x1-x2)^2  + (y1-y2)^2             ( s = distance)

s^2 = ( 2-6)^2 + ( 8-5)^2

s^2 = 25

s = 5 units

Answer: 11 1/3 gallons of lemonade

The range stays 48°.

To determine how the range changes when a value of 80.4° is added, we need to follow these steps:
Identify the minimum and maximum values in the original data set.
Calculate the original range by subtracting the minimum value from the maximum value.
Add the new value (80.4°) to the data set.
Identify the new minimum and maximum values.
Calculate the new range.
Compare the original and new ranges.

The minimum value is 57°, and the maximum value is 105°.
The original range is 105° - 57° = 48°.
Add the new value: [58, 61, 71, 77, 91, 100, 105, 102, 95, 82, 66, 57, 80.4].
The new minimum value is still 57°, and the new maximum value remains 105°.
The new range is still 105° - 57° = 48°.
Since the original range and the new range are both 48°, the range does not change.
The range stays 48°.

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The three students who are correct in their approach to solving the problem are Nico, Aditi, Sandra.

Algebra is a branch of mathematics that deals with mathematical symbols and the rules for manipulating these symbols to solve equations and solve problems. It involves using letters, symbols, and numbers to represent variables and unknowns in mathematical expressions, equations, and functions.

In algebra, variables represent quantities that can vary, such as the height of a building, the speed of a car, or the price of a product. Algebraic expressions and equations involve combining these variables, symbols, and numbers using operations such as addition, subtraction, multiplication, and division.

Algebra includes various topics such as linear algebra, quadratic equations, polynomials, matrices, and functions. It also includes the use of graphs and charts to represent mathematical relationships and solve problems.

The three students who are correct in their approach to solving the problem are:

Nico: Two-fifths (5 + x) = 8. (Five-halves)

Aditi: Two-fifths (5 + x) = 8. Five-halves (5) + five-halves x = (five-halves) 8

Sandra: Two-fifths (5 + x) = 8. two-fifths (5) + two-fifths x = 8

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a) The amount deducted from Marika Perez's paycheck for social security taxes is $171.62

b) The amount deducted for Medicare taxes is $40.10.

To calculate the amount of social security taxes deducted from Marika Perez's biweekly pay, we need to multiply her gross pay by the social security tax rate of 6.2%. Similarly, to calculate the amount of Medicare taxes deducted, we need to multiply her gross pay by the Medicare tax rate of 1.45%.

The calculations are as follows

Social Security tax deduction = gross biweekly pay x social security tax rate

= $2,768 x 0.062

= $171.62

Medicare tax deduction = gross biweekly pay x Medicare tax rate

= $2,768 x 0.0145

= $40.10

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Answer: If Sydney needs to make exactly 8 dozen items for a bake sale, that means she needs to make a total of 8 x 12 = 96 items

The measure of the missing angle is 43 degrees.

What is triangle?

A triangle is a geometric shape with three sides and three angles. It is a closed, two-dimensional figure with straight sides. The sum of the angles in a triangle always adds up to 180 degrees.

To find the measure of the missing angles, we need to use the fact that the sum of the angles in a triangle is 180 degrees. Therefore, we can find the measure of the missing angle by subtracting the sum of the other two angles from 180 degrees.

Let's call the missing angle x. Then we have:

105° + 32° + x = 180°

Simplifying, we get:

x = 180° - 105° - 32°

x = 43°

Therefore, the measure of the missing angle is 43 degrees.

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The length of the bow of the circle is 9π/ 2 = 4.5 *3.14 = 14.13.  

The  bow time of a circle can be determined with the compass

and significant point of view exercising the bow time frame strategy.

 ⇒ angle =   arc/ radius  

⇒ 135 ° =   bow/ 6

 ⇒  arc =  135 ° * 6  

⇒  bow =  135 ° * π/ 180 ° * 6  

⇒  bow =  9π/ 2  

⇒ 9π/ 2 = 4.5 *3.14   ⇒14.13

  In calculation, a bow is characterized as a piece of the limit of a circle or a bend. It can likewise be indicated as an open bend. The limit of a circle is the border or the distance around a circle,  else called the circuit.

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Answer:

$110.2

Step-by-step explanation:

$76 × 45%

$34.2

$76 + $34.2

$110.2

Compounded Principal Interest Rate per Compounding Period Number of Compounding Periods Final Amount

Annually $9,200 6% / year 1 $20,101.83

Semi-Annually $9,200 3% / 6 months 30 $20,480.73

Quarterly $9,200 1.5% / 3 months 60 $20,740.64

Monthly $9,200 0.5% / month 180 $21,027.54

Weekly $9,200 0.12% / week 780 $21,118.33

Daily $9,200 0.016% / day 5,475 $21,183.05

What is compound interest ?

Compound interest is a method of calculating interest where interest is added to the principal amount, and the interest is also calculated on the accumulated interest. This results in the growth of the principal amount over time. Compound interest is often used in investments, loans, and savings accounts. The formula for calculating compound interest is [tex]A = P (1 + r/n)^{nt}[/tex], where A is the final amount, P is the principal amount, r is the interest rate, n is the number of times the interest is compounded per year, and t is the time in years.

According to the question:
Compound Interest Formula: [tex]A = P(1 + r/n)^{nt}[/tex]

where A is the final amount, P is the principal invested, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years the money is invested.

Compounded Principal Interest Rate per Compounding Period Number of Compounding Periods Final Amount

Annually $9,200 6% / year 1 $20,101.83

Semi-Annually $9,200 3% / 6 months 30 $20,480.73

Quarterly $9,200 1.5% / 3 months 60 $20,740.64

Monthly $9,200 0.5% / month 180 $21,027.54

Weekly $9,200 0.12% / week 780 $21,118.33

Daily $9,200 0.016% / day 5,475 $21,183.05

Note: The final amounts have been rounded to the nearest cent.

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The equation of the straight line is y = -2x - 4, the value of x₁ is -1 and the value of y₁ is -2.

To find the equation of a straight line given its slope and one point, we use the point-slope form of the equation:

−y − y₁​ = m(x−x₁ )

where m is the slope of the line, and (x₁, y₁) is the given point.

In this case, m = -2 and the point is (-1, -2). So we have:

x₁ = -1

y₁ = -2

m = -2

Substituting these values into the point-slope form, we get:

y−(−2)=−2(x−(−1))

Simplifying and rearranging terms, we get the equation of the line:

y + 2 = -2x - 2

y = -2x - 4

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Answer:

z = 66

y = 120

Step-by-step explanation:

First, we can solve for z because it is supplementary to 114°.

114° + z° = 180°

-114°         -114°

z° = 66°

z = 66

Now, we can solve for y using the fact that the interior angles of a quadrilateral add to 360° (think about a rectangle: 4 x 90°).

We have to use the z value that we solved for earlier.

81° + 93° + y° + z° = 360°

↓ substituting in z-value

81° + 93° + y° + 66° = 360°

↓ combining like terms

240° + y° = 360°

-240°         -240°

y° = 120°

y = 120

We have that, the probability of hitting the coin toss at least 6 out of 7 times is approximately 0.0625. Which corresponds to option d. 0.0625.

1. Determine the probability of success and failure.

Since the coin is fair, the probability of success (flipping it correctly) is 0.5, and the probability of failure (flipping it incorrectly) is also 0.5.

2. Calculate the probability of flipping the coin correctly exactly 6 times.

Using the binomial probability formula

[tex]P(X = 6) = C(7, 6) * (0.5)^6 * (0.5)^1\\P(X = 6) = 7 * (0.5)^6 * (0.5)^1\\P(X = 6) \approx 0.0547\\[/tex]

3. Calculate the probability of performing the toss correctly all 7 times.

Using the binomial probability formula.

[tex]P(X = 7) = C(7, 7) * (0.5)^7 * (0.5)^0\\P(X = 7) = 1 * (0.5)^7 * 1\\P(X = 7) \approx 0.0078\\[/tex]

4. Calculate the probability of calling the flip correctly at least 6 times.

[tex]P(X \geq  6) = P(X = 6) + P(X = 7)\\P(X \geq  6) \approx 0.0547 + 0.0078\\P(X \geq  6) \approx 0.0625\\[/tex]

Thus, the probability of hitting the coin toss at least 6 out of 7 times is approximately 0.0625, which corresponds to option d. 0.0625.

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1. Battling the stereotypes architects face.

2. Arguing for good design over cheap construction.

3. Making time for hand sketching

4. Finding great materials to match great designs.

5. Bridging the generation gap (making a design appealing to different generations)