Rewrite cos 4x I'm terms of cos x.

Answer:

x=2

Step-by-step explanation:

Answer:

x=2

Step-by-step explanation:

1. An equation for Lin is y = 1/3x + 8.

2. An equation for Diego is y = 2/3x + 6.

3. The intersection point of the solution is (6, 10).

Let there have total number of balloons are y.

Lin fills her balloons at a rate of 1/3 ounce per second.

So she filled 1/3 x balloons.

She has already filled balloons with 8 ounces of water.

So the required equation is;

y = 1/3x + 8.................(1)

Diego fills her balloons at a rate of 2/3 ounce per second.

So he filled 2/3 x balloons.

He has already filled balloons with 6 ounces of water.

So the required equation is;

y = 2/3x + 6.................(2)

To determine the intersecting point we solve the both equation.

Subtract equation 1 and 2, we get

1/3x + 8 - 2/3x - 6 = 0

-1/3x + 2 = 0

Subtract 2 on both side, we get

-1/3x = -2

Multiply by -3 on both side, we get

x = 6

Now put the value of x in equation 1

y = 1/3 × 6 + 8

y = 10

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As per the given triangle, the length of AB rounded to 3 significant figures is 10.7 units.

We are given a triangle ABC with a right angle at A, i.e., CAB = 90°. Let AC be the side opposite to the right angle, and let AB be the hypotenuse. We are also given that ABC = 57° and AC = 9.2.

Using the trigonometric function, we can relate the angles and sides of a right-angled triangle. In particular, we can use the sine function to relate the angle opposite to a side and the hypotenuse. Thus, we have:

sin(ABC) = AC/AB

Substituting the given values, we get:

sin(57°) = 9.2/AB

Now, we can solve for AB by multiplying both sides by AB and dividing by sin(57°):

AB = 9.2/sin(57°)

Using a calculator, we get:

AB ≈ 10.692

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Answer:

a,c,d

Step-by-step explanation:

We can see here that the equivalent expressions are:

B. [tex](\frac{st}{x} )^{3} (\frac{xt^{2} }{s} )[/tex]

C. [tex](\frac{st^{4} x}{x^{7}t^{-2} } ) (\frac{sx^{7} }{tx^{3} } )[/tex]

An expression is a combination of values, variables, operators, and function calls that are evaluated to produce a result. Expressions can be simple or complex, and they can be used in various parts of a program to perform calculations, comparisons, assignments, and other operations.

We see here that the selected expressions are actually equivalent to [tex]\frac{s^{2}t^{5} }{x^{2} }[/tex].

Thus,  [tex](\frac{st}{x} )^{3} (\frac{xt^{2} }{s} )[/tex] =  [tex]\frac{s^{2}t^{5} }{x^{2} }[/tex]

and  [tex](\frac{st^{4} x}{x^{7}t^{-2} } ) (\frac{sx^{7} }{tx^{3} } )[/tex] =  [tex]\frac{s^{2}t^{5} }{x^{2} }[/tex]

When the selected expressions are simplified and broken down they actually give us the given expression.

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Answer:

3c(d^2+4d+4)

Step-by-step explanation:

common factor is 3 and c

Answer:

Step-by-step explanation:

If the value of the house has increased by 63%, it is still worth 100% of the $349,634 it was originally, but now we are adding 63% to that 100% to find the new value. Thus, 349634(1.63) = $569,903.42.  The 1.63 is 163% as a decimal, just in case.

Answer: $100,000

Step-by-step explanation:

$100,000. This is because the balance in the account varies jointly with principal, the annual interest rate, and time measured in years with a constant of proportionality of 1. Therefore, the balance in the account at the end of 50 years is 10,000 × 1 × (1 + 0.05)50, which is equal to $100,000.

Answer:

$35000

Step-by-step explanation:

account worth = deposit + simple interest

/ 100

 intrest = deposit x year x simple interest

10000×50×5/100=25000

account worth = deposit + simple interest

 = 10000 + 25000

 = $ 35000

Yes, the triangles ∆AOR and ∆EOD are similar. By Angle-Angle similarity rule, triangle AOR is similar to triangle EOD.

See the above figure, it consists two triangles say ∆AOR and ∆EOD. Now, we check whether both of triangles are similar or not. Similar triangles are are the triangles that have corresponding sides in ratio to each other and corresponding angles equal to each other. It's time to check the similarity property in ∆AOR and ∆EOD.

In ∆AOR, measure of angle R = 105°

In ∆EOD, measure of angle D = 35°

measure of angle DOE = 40°

Sum of interior angles of triangle = 180°

so, measure of angle E = 180° - 35° - 40°

= 105°

Now, in ∆AOR and ∆EOD,

Measure of angle R = measure of angle E = 105° ( since equal angles)

Measure of angle AOR = measure of angle EOD ( corresponding angles)

Thus, two angles of triangle EOD are congruent or equal to the corresponding angles of another triangle, AOR. So, by Angle-Angle ( AA) congruence rule, ∆AOR is similar to the ∆EOD.

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Complete question:

See the above figure, Are the triangles similar? If yes, write a similarity statement and explain how you know they are similar.

We have ,

Cost of jacket , (F) = $48.10 

Saving per day, (A)  = $1.85 

We have to find the no. of days(n) of saving to have the sufficient amount for jacket. 
We know , 

A × n = F 

=> n = F/A 

=> n = $48.10/$1.85 

=> n = 26  

It will take 26 days for Caden to have enough money for the jacket. 

The scale factor of the dilation of the vertices of the cone when dilated is 4.5

The area of a circle is proportional to the square of its radius. Since the base of the cone is a circle

The ratio of the areas of the base of the dilated cone to the original cone is equal to the square of the scale factor.

Let the scale factor be k. Then, we have:

(area of dilated cone's base) / (area of original cone's base) = k²

(729π) / (36π) = k²

k² = 20.25

Taking the positive square root of both sides we get:

k = 4.5

Therefore, the scale factor of the dilation is 4.5.

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The rectangle is formed by connecting the points (-4, 4), (5, 4), (-4, -4), and (5, -4).

The length of the rectangle is the distance between the points (-4, 4) and (5, 4), which is 5 - (-4) = 9 units.

The width of the rectangle is the distance between the points (-4, 4) and (-4, -4), which is 4 - (-4) = 8 units.

Therefore, the area of the rectangle is:

Area = Length x Width = 9 x 8 = 72 square units.

So, the area of the rectangle shown is 72 square units. Therefore, the answer is 72 square units.

Answer:

-27V + 4

Step-by-step explanation:

i think

the tax estimated to be collected by the government during the financial year 2020/21 is 666.9 billion rands.

why it is and what is a financial year?

The tax estimated to be collected by the government during the financial year 2020/21 is not explicitly given in the table. However, the total revenue collected by the government during the financial year 2020/21 is given, which is:

666.9 billion rands

Therefore, the tax estimated to be collected by the government during the financial year 2020/21 is 666.9 billion rands.

A financial year (also known as fiscal year) is a period of 12 months that a company or government uses for financial reporting and accounting purposes. It does not necessarily correspond to the calendar year, which is a period of 12 months starting on January 1st and ending on December 31st.

The financial year is important because it helps organizations to keep track of their financial performance over a consistent period of time, which facilitates comparison of financial results from year to year. The financial year is often chosen to align with a company's operational cycle, which may be seasonal or have other considerations that affect the timing of revenues and expenses.

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The 99% confidence interval for the average length (in inches) of all six-month-old boys is 27.74 in. to 27.98 in. The correct answer is E

This is calculated using the average length (27.6 in.) and standard deviation (0.28 in.) recorded by the pediatrician. To calculate the confidence interval, you need to calculate the margin of error. The margin of error is found using the following formula:

ME = (Critical Value) x (Standard Deviation/√Sample Size)

For a 99% confidence interval, the critical value is 2.58. Therefore, the margin of error for this sample is (2.58) x (0.28/√50) = 0.24 in. This means that the 99% confidence interval for the average length of all six-month-old boys is 27.6 in. ± 0.24 in., or 27.74 in. to 27.98 in. The correct answer is E

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C(g) = 10 + 15g

C'(g) = 80

The monthly charges of Company C for using 2 Gigabyte of data usage.

Step-by-step explanation:

The cell phone plan from Company C costs $10 per month, plus $15 per gigabyte for data used. The plan from Company D costs $80 per month, with unlimited data.

Now, the monthly cost in Company C for using g gigabyte of data will be  

C(g) = 10 + 15g ........ (1)

Again, the monthly cost in Company D for using g gigabyte of data will be  

C'(g) = 80 ......... (2)

Now, from equation (1), the statement C(2) = 10 + 15 × 2 = 40, means that monthly charges of Company C for using 2 Gigabyte of data usage. (Answer)

Answer:

Step-by-step explanation:

Write the formula for the nth term of the sequence as a function: f(n)=n(n+7).

So now our goal is to compute f(11). To do that, we substitute x=11 in our function, meaning that the 11th term of the sequence = 11*18, which equals 198.

The area is covered with 1.4 gallons of water per square foot, approximately 5388.9 gallons of water were used.

We use the formula for the area of a circle: A = πr².

The radius can be determined by dividing the diameter, which is 70 feet, by 2. Therefore, r = 35 feet.

To find the area of the circle, substitute the value of r into the formula for the area of a circle: A = πr².
A = πr²
A = π(35)²
A = 3.14 × 1225
A = 3842.5 square feet
We know that this area is covered with 1.4 gallons of water per square foot, so we can multiply the area of the circle by 1.4 to get the total gallons of water used:

Total gallons of water used = A * 1.4
1.4 × 3842.5 ⇒ 5,379.5 gallons.

Therefore, the total gallons of water used is 5,379.5 gallons.

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Answer: In a parallelogram, opposite angles are equal, so we can set up the following equation:

3x + 10 = 180 - (4x + 10)

Simplifying and solving for x, we get:

3x + 10 = 170 - 4x

7x = 160

x = 20

Now we can substitute x = 20 into the expressions for the angles to find their values:

3x + 10 = 70 degrees

4x + 10 = 90 degrees

Since opposite angles in a parallelogram are equal, the other two angles must also be equal to these values. Therefore, the internal angles of the parallelogram are:

70 degrees, 70 degrees, 110 degrees, 110 degrees

Step-by-step explanation:

Robert is currently 10 years old. Given that five years ago Sharon was twice as old as Robert was then, we can set up the following equation: y + 5 = 2(y)

We are given the information that Sharon is five years older than Robert, and five years ago Sharon was twice as old as Robert was then. This means we can create a system of equations to solve for Robert's age.

Let x = Robert's current age

Let y = Robert's age five years ago

Given that Sharon is five years older than Robert, we can set up the following equation:

x + 5 = Sharon's current age

Given that five years ago Sharon was twice as old as Robert was then, we can set up the following equation:

y + 5 = 2(y)

Solving the first equation for x, we get x = Sharon's current age - 5. Substituting this into the second equation, we get:

y + 5 = 2(Sharon's current age - 5)

Solving this equation for y, we get y = (Sharon's current age - 5)/2.

Since Sharon is five years older than Robert, Sharon's current age is x + 5. Substituting this into our equation for y, we get:

y = (x + 5 - 5)/2

Simplifying this equation, we get y = x/2. This means that Robert's age five years ago was half of his current age.

Since we know that Robert is currently 10 years old, Robert's age five years ago was 5. Therefore, Robert is currently 10 years old.

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The answer of the given question based on the interest rate the answer is  the premium paid for each subsequent year would be ¢840

A premium rate is price per unit of insurance coverage for specific risk that an insurer charges its policyholders. It is typically expressed as  percentage of  total insured value of  policy.

To calculate the premium paid for subsequent years, we need to know what the premium rate is for those years. The premium rate may change from year to year depending on various factors such as the age of the car, the driver's record, etc.

Assuming the premium rate remains constant at 8% of the insured value for all subsequent years, we can calculate the premium paid for each year as follows:

First year: 8% of ¢10,500 = ¢840

Second year: 8% of ¢10,500 = ¢840

Third year: 8% of ¢10,500 = ¢840

And so on...

So the premium paid for each subsequent year would be ¢840 if the premium rate remains constant at 8% of the insured value.

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If the distance between the tracks is 5m , then the train ride on track 2 is 15.7 m farther than track 1.

Let the distance traveled on Track 1 be = "d₁" and

Let the distance traveled on Track 2 be = "d₂",

We know that the distance from Track 1 to the center is 30 m,

So, the radius of Track 1 is 30 m.

Therefore, the distance traveled on Track 1 is the circumference of a circle with radius 30 m, which is:

⇒ d₁ = 2×π×r1 = 2×π×30 = 60π ,

The distance between the track1 and track2 is 5m ,

So, the radius of Track 2 is = 30 + 5 = 35 m,

So, the distance traveled on Track 2 beyond Track 1 is the difference between the circumference of the two circle with radius 35 m and the circumference of a circle with radius 30 m, which is:

⇒ 35π - 30π = 5π

The distance traveled on Track 2 beyond Track 1 plus the distance traveled on Track 1 gives the total distance traveled on Track 2:

⇒ d₂ = d₁ + 5π = 60π + 5π = 65π

So, the train ride on Track 2 is farther than Track 1 by:

⇒ d₂ - d₁ = 65π - 60π = 5π

⇒ 5π = 5×3.14 = 15.7m .

Therefore, the train ride on Track 2 is 15.7 meters farther than Track 1.

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Therefore, 150 is the largest integer that is a factor of both 1450 and 2400.

Prime factorization is the process of breaking down a positive integer into its prime factors, which are prime numbers that can divide the integer without a remainder. Every positive integer can be written as a product of prime numbers in a unique way, called its prime factorization.  Prime factorization is important in many mathematical applications, such as finding the greatest common divisor and least common multiple of two or more integers, simplifying fractions, and solving problems related to divisibility, prime numbers, and modular arithmetic.

Here,

To find the largest integer that is a factor of both 1450 and 2400, we need to first express both numbers in terms of their common prime factors and then find the product of the common prime factors raised to their lowest exponent.

The prime factorization of 1450 is 2 × 5² × 29.

The prime factorization of 2400 is 2⁴ × 3 × 5².

To find the common factors of these two numbers, we need to look for the prime factors that appear in both factorizations. These common prime factors are 2, 5², and 3.

To find the largest integer that is a factor of both 1450 and 2400, we need to multiply these common prime factors raised to their lowest exponent:

2 × 5² × 3 = 150

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To create a function from these points, we need to find an equation that passes through all four points. There are several ways to do this, but one common method is to use linear regression to fit a line to the data.

Here's a mathematical approach to creating a function using four ordered pairs, finding its inverse, and ensuring that the inverse is also a function: Let's assume we have four ordered pairs: (a, b), (c, d), (e, f), and (g, h). We can use the formula for a line, y = mx + b, where m is the slope and b is the y-intercept, to create the function. To find m and b, we can use the following formulas: m = (nΣ(xy) - ΣxΣy) / (nΣ(x^2) - (Σx)^2)

b = (Σy - mΣx) / n where n is the number of points, Σ denotes the sum of the values, and x and y represent the coordinates of the points. Substituting the coordinates of the four points into these formulas, we can find the equation of the line that passes through them. Once we have the equation, we can define our function as f(x) = mx + b. To find the inverse of the function, we can solve for x in terms of y. Starting with the equation y = mx + b, we can isolate x on one side: y - b = mx

x = (y - b) / m

Now we have an expression for x in terms of y, which defines the inverse of the function. We can define the inverse function as g(y) = (y - b) / m. To ensure that the inverse is also a function, we need to check that for each y in the range of the function, there is only one corresponding x value. In other words, we need to check that the function is one-to-one.

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The number of ways by using the generating functions and Binomial theorem is

There are various methods to solve the given question. Here's one way to solve it. To distribute 12 identical cookies to 4 distinct children such that all cookies are distributed and each child may receive 0, 1, 2, 3, or 4 cookies, we can use generating functions.

Let's assume that the generating function for the number of ways of distributing the 12 identical cookies to the 4 distinct children is given by:

(1 + x + x₂ + x₃ + x₄)⁴

We need to find the coefficient of x12 in the above equation. Using the Binomial theorem, the above equation can be expanded as:

(1 + x + x₂ + x₃ + x₄)⁴ ⇒ (1 + x + x₂ + x₃ + x₄)(1 + x + x₂  + x₃ + x₄)(1 + x + x₂ + x₃ + x₄)(1 + x + x₂  + x₃ + x₄)

After multiplying the above equation, we need to find the coefficient of x₁₂. The answer to the given question is as follows:

The coefficient of x₁₂ ⇒ 715 ways

Therefore, there are 715 ways to distribute the 12 identical cookies to 4 distinct children such that all cookies are distributed and each child may receive 0, 1, 2, 3, or 4 cookies.

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Answer: The diameter of the drawing of the planet= 14 mm

Step-by-step explanation:

Given: In a drawing of the solar system the scale is 1 mm = 500 km

which means [tex]1 \ km=\frac{1}{500}mm[/tex] on the drawing.

The diameter of planet =7000 kilometers.

Then the diameter of the drawing of the planet [tex]=\frac{7000}{500}=14[/tex]

Therefore, the diameter of the drawing of the planet= 14 mm.

The measure of angle K in the inscribed quadrilateral DUCKDUCKD is equal to the central angle of the circle OOO. This central angle is 360 degrees divided by the number of sides of the quadrilateral, which is 4, so the measure of angle K is 90 degrees.

The measure of angle K in the inscribed quadrilateral DUCKDUCKD is equal to the central angle of the circle OOO. The central angle is the angle formed by two radii inside the circle. When a shape is inscribed in a circle, each of the angles of the shape has the same measure as the central angle of the circle. In this case, the quadrilateral has four sides, so the measure of the central angle is 360 degrees divided by the number of sides of the quadrilateral, which is 4. Therefore, the measure of angle K is 90 degrees. This is true for all inscribed shapes; the measure of each angle is equal to the measure of the central angle of the circle. This is because when a shape is inscribed in a circle, each of its angles touches two radii of the circle. Therefore, the measure of each angle is equal to the measure of the central angle of the circle.

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complete question

Quadrilateral DUCKDUCKD, U, C, K is inscribed in circle OOO. What is the measure of angle K∠Kangle, K? ^circ ∘ degrees

The equation of the line that is perpendicular to line m and passes through the point (3, 2) is y = (2/5)x + 4/5.

To find the equation of a line that is perpendicular to line m, we need to know the slope of line m.

The slope of line m can be found using the two given points on the line, (0, -3) and (-2, 2):

slope of line m = (change in y) / (change in x) = (2 - (-3)) / (-2 - 0) = 5 / (-2) = -5/2

A line perpendicular to m will have a slope that is the negative reciprocal of -5/2. The negative reciprocal is obtained by flipping the fraction and changing its sign.

slope of line perpendicular to m = -1 / (-5/2) = 2/5

Now we have the slope of the line perpendicular to m and a point that it passes through, (3, 2). We can use the point-slope form of the equation of a line to find its equation:

y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope.

Substituting in the values we have:

y - 2 = (2/5)(x - 3)

Simplifying:

y - 2 = (2/5)x - (6/5)

y = (2/5)x - (6/5) + 2

y = (2/5)x + 4/5

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The job will take 5 hours time for a crew of 5 people.

Inverse variation means that as one value increases, the other decreases. In this example, as the number of people on the crew increases, the amount of time it takes to complete the job decreases. To solve this problem, we must first find the rate of change. We can do this by dividing 8 hours (the amount of time it took the crew of 3 people) by 3 people, which gives us a rate of 2.67 hours per person. Then, to find the time for the crew of 5 people, we can multiply the rate of change (2.67 hours per person) by the number of people on the crew (5). This gives us a total of 13.35 hours, which can be rounded to 5 hours time.

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