Given: cos θ = 3/5 and θ is located in the fourth quadrant;
find cos2θ AND θ/2

To solve the question we must know about Logarithm.

A log function is a way to find how much a number must be raised in order to get the desired number.

\(a^c =b\)

can be written as

\(\rm{log_ab=c\)

where a is the base to which the power is to be raised,

b is the desired number that we want when power is to be raised,

c is the power that must be raised to a to get b.

For example, let's assume we need to raise the power for 10 to make it 1000 in this case log will help us to know that the power must be raised by 3.

\(\rm{log_{10}1000=3\)

The value of input can not be negative, the value of x is 8.

\(\rm{ log_2x+log_2(x-6)= 4\)

        \(\rm{ log_2x(x-6)= 4\)

        \( x(x-6)= 2^4\)

        \(x^2 -6x -16=0\\ x^2 -8x +2x-16=0\\ x(x-8)+2(x-8)=0\\ (x+2)(x-8) = 0\)

Equating factors against 0,

1.    \((x+2)=0\\ x=-2\)

2.     \((x-8)=0\\ x=8\)

As the value of input can not be negative, the value of x is 8.

Hence, the value of x is 8.

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Answer:

The answer is C

Step-by-step explanation:

C) x2 – 6x – 16 = 0

The car will travel 130.26 km in 1 hour 18 minutes if it maintains a constant speed of 1.67 km/min.

When we say that a car is traveling at a constant speed, it means that the car is moving at the same rate throughout the journey. In other words, the speed of the car does not change.

Now let's look at the problem. The car traveled 40km in 24 minutes, which means we need to find out how far it will go in 1 hour 18 minutes.

To solve this problem, we need to convert 1 hour 18 minutes into minutes.

1 hour = 60 minutes

Therefore, 1 hour 18 minutes = 60 + 18 = 78 minutes.

Now we know that the car traveled 40km in 24 minutes, and we want to find out how far it will go in 78 minutes.

We can use the formula:

distance = speed x time

Since we know the speed is constant, we can use it to find the distance.

To find the speed, we can use the formula:

speed = distance / time

Using the given information, we can calculate the speed:

speed = 40km / 24 minutes

speed = 1.67 km/min

Now we can use the speed to find the distance traveled in 78 minutes:

distance = speed x time

distance = 1.67 km/min x 78 minutes

distance = 130.26 km

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The highest score for the given distribution is 25.

This is because the distribution is divided into ranges, with the first range being 20-25, the second range being 15-19, the third range being 10-14, and the fourth range being 5-9.

The highest score in each range is the number on the right side of the dash.

Therefore, the highest score in the first range is 25, the highest score in the second range is 19, the highest score in the third range is 14, and the highest score in the fourth range is 9.

Since 25 is the highest score among all of the ranges, it is the highest score for the entire distribution.

The correct answer is c) 25.

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Based on the derivative, a function can cross the x-axis a certain number of times depending on the number of times the derivative changes sign.

A derivative is a mathematical tool that measures the rate of change of a function at a specific point. Specifically, it is the slope of the tangent line to the function at that point. The derivative can be used to determine where a function is increasing, decreasing, or reaching a maximum or minimum value.
When a function crosses the x-axis, it means that the y-value of the function is equal to zero. In order for a function to cross the x-axis, it must change sign from positive to negative or vice versa. This happens when the function passes through a maximum or minimum point.
If the derivative of the function is positive at a point, it means that the function is increasing at that point. If the derivative is negative, the function is decreasing. If the derivative is zero, it means that the function is neither increasing nor decreasing, and it could be at a maximum or minimum point.
Therefore, the number of times a function can cross the x-axis depends on the number of times the derivative changes sign. If the derivative changes sign twice, the function can cross the x-axis twice. However, if the derivative changes sign an odd number of times, the function can only cross the x-axis once.

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Pythagoras was an ancient Greek mathematician who founded the Pythagorean school of thought. The Pythagorean theorem is a fundamental concept in mathematics that is attributed to Pythagoras and his followers.

It states that in a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides. While this theorem is considered a cornerstone of mathematics today, it is important to understand that Pythagoras did not have access to the advanced mathematical tools and methods that we have today.

He had to rely on geometric constructions and reasoning to prove his theorem. Furthermore, Pythagoras believed that all numbers could be expressed as ratios of whole numbers, which is not always true in reality. Despite these limitations, the Pythagorean theorem has stood the test of time and continues to be a crucial tool in mathematics and other fields.

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c = pi/2, and the value of c > 1 such that the average value of f(x) on the interval [2, 20] is equal to c is c = pi/2.

The average value of a function f(x) on the interval [a, b] is given by:

Avg = 1/(b-a) * ∫[a, b] f(x) dx

We want to find a value of c > 1 such that the average value of the function \(f(x) = (9pi/x^2)cos(pi/x)\) on the interval [2, 20] is equal to c.

First, we find the integral of f(x) on the interval [2, 20]:

\(∫[2, 20] (9pi/x^2)cos(pi/x) dx\)

We can use u-substitution with u = pi/x, which gives us:

-9pi * ∫[pi/20, pi/2] cos(u) du

Evaluating this integral gives us:

\(-9pi * sin(u) |_pi/20^pi/2 = 9pi\)

Therefore, the average value of f(x) on the interval [2, 20] is:

\(Avg = 1/(20-2) * ∫[2, 20] (9pi/x^2)cos(pi/x) dx\)

= 1/18 * 9pi

= pi/2

Now we set c = pi/2 and solve for x:

Avg = c

\(pi/2 = 1/(20-2) * ∫[2, 20] (9pi/x^2)cos(pi/x) dx\)

pi/2 = 1/18 * 9pi

pi/2 = pi/2

Therefore, c = pi/2, and the value of c > 1 such that the average value of f(x) on the interval [2, 20] is equal to c is c = pi/2.

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Answer:

ribbon ata yan

Step-by-step explanation:

ssa

Answer:

$8.78

Step-by-step explanation:

cost = 3.28(0.7) + 1.4(4.63)

= 2.296 + 6.482

= 8.778

= $8.78

Answer:

\(8.11\)

Step-by-step explanation:

Rounded to nearest hundredth.

After Round to the nearest hundredth value of number is,

⇒ 8.11

We have to given that;

A number is,

⇒ 8.113

And, We an Round to the nearest hundredth.

Since, Rounding numbers refers to changing a number's digits such that it approximates a value.

Here, In number 8.113,

Digit in thousandth place is 3 which is less thn 5.

Hence, After Round to the nearest hundredth value of number is,

⇒ 8.11

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Answer:

5

Step-by-step explanation:

If you multiply each side by 5 to get 42:30 then subtract 42 by 30, 12 is leftover.

Answer:

The numbers should be 42 and 30

Step-by-step explanation:

Okay, so the equation should be:

7x - 5x = 12

2x = 12

x = 6

and find the numbers:

7 x 6 = 42

5 x 6 = 30

\(11m = 3n \\ \frac{11m}{11 \times n} = \frac{3n}{11 \times n} \\ \frac{m}{n} = \frac{3}{11} \)

ATTACHED IS THE SOLUTION

Answer: \(y^4\) + \(\frac{-73}{35}y^2\)- \(2\)

Step-by-step explanation:

Use FOIL:

\(y^4\) + \(\frac{-14}{5}y^2\) + \(\frac{5}{7}y^2\) + \(\frac{-70}{35}\)

Make  \(\frac{-14}{5}y^2\) and \(\frac{5}{7}y^2\) have the same numerator:

\(\frac{-14*7}{5*7}y^2 =\frac{-98}{35}y^2\)

\(\frac{5*5}{7*5} y^2=\frac{25}{35} y^2\)

Then add like terms and simplify:

\(y^4\) + \(\frac{-98}{35}y^2\) + \(\frac{25}{35} y^2\) + \(\frac{-70}{35}\)

\(y^4\) + \(\frac{-73}{35}y^2\)- \(2\)

\(\implies {\blue {\boxed {\boxed {\purple {\sf { {y}^{4} - \frac{73 }{ 35} y² - 2}}}}}}\)

\(\large\mathfrak{{\pmb{\underline{\orange{Step-by-step\:explanation}}{\orange{:}}}}}\)

\( = ( {y}^{2} + \frac{5}{7} )( {y}^{2} - \frac{14}{5} )\\\)

\( = {y}^{2} ( {y}^{2} - \frac{14}{5} ) + \frac{5}{7} ( {y}^{2} - \frac{14}{5} )\\\)

\(= {y}^{2 + 2} - ( \frac{14}{5} ) {y}^{2} + ( \frac{5}{7} ) {y}^{2} - \frac{5 \times 14}{7 \times 5}\\ \)

\(= {y}^{4} - \frac{14 \: {y}^{2} }{5} + \frac{5 \: {y}^{2} }{7} - 2\\\)

\( = {y}^{4} - \frac{14 \: {y}^{2} \times 7}{5 \times 7} + \frac{5 \: {y}^{2} \times 5}{7 \times 5} - 2\\\)

\( = {y}^{4} - \frac{ 98 \: {y}^{2} + 25 \: {y}^{2} }{35} - 2\\ \)

\( = {y}^{4} - \frac{73 }{ 35} y² - 2\\\)

By using the identity \((x + a)(x - b) = {x}^{2} + (a - b)x - ab\),

where \(x=y²\), \(a=\frac{5}{7} \) and \(b= \frac{14}{5}\)

\( = ( {y}^{2} + \frac{5}{7} )( {y}^{2} - \frac{14}{5} )\\\)

\( = ({ {y}^{2} })^{2} + ( \frac{5}{7} - \frac{14}{5} ) {y}^{2} - \frac{5}{7} \times \frac{14}{5}\\ \)

\( = {y}^{4} + (\frac{5 \times 5}{7 \times 5} - \frac{14 \times 7}{5 \times 7} ) {y}^{2} - 2\\\)

\( = {y}^{4} + ( \frac{25 - 98}{35} ) {y}^{2} - 2\\\)

\( = {y}^{4} - \frac{73}{35} {y}^{2} - 2\\ \)

\(\red{\large\qquad \qquad \underline{ \pmb{{ \mathbb{ \maltese \: \: Mystique35ヅ}}}}}\)

Answer:

Step-by-step explanation:

Let's assume the initial number of men at the exhibition is 10x, and the initial number of women is 3x.

After 110 men left, the number of men remaining is 10x - 110.

The total number of people remaining is (10x - 110) + (3x) = 13x - 110.

According to the given information, the number of men remaining (10x - 110) is 5/12 of the total number of people remaining (13x - 110). We can write this as an equation:

10x - 110 = (5/12)(13x - 110)

To solve this equation, we can start by simplifying both sides:

10x - 110 = (65/12)x - (55/6)

To get rid of the fractions, we can multiply both sides of the equation by 12:

12(10x - 110) = 65x - 110(2)

120x - 1320 = 65x - 220

Next, we can bring the x terms to one side and the constant terms to the other side:

120x - 65x = 1320 - 220

55x = 1100

Dividing both sides by 55, we find:

x = 20

Now, we can substitute the value of x back into the initial expressions to find the number of men and women:

Number of men = 10x = 10(20) = 200

Number of women = 3x = 3(20) = 60

Therefore, there were 60 women at the exhibition

Hope this answer your question

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a. The graph of the budget line would have hamburgers on the x-axis and bags of figs on the y-axis. b. the budget line equation represents Rachel's affordability based on her income and the prices of hamburgers and figs. Changes in prices, income, or additional resources can affect the slope, position, or rotation of the budget line on a graph.

a) Rachel's budget line equation can be written as follows:

Budget = (Price of Hamburger * Quantity of Hamburgers) + (Price of Figs * Quantity of Figs)

Since the price per hamburger is $3 and the price per bag of figs is $2, the equation becomes:

Budget = 3x + 2y

Where x represents the quantity of hamburgers and y represents the quantity of bags of figs. The graph of the budget line would have hamburgers on the x-axis and bags of figs on the y-axis.

b) If the price of figs increases to $3, the new budget line equation becomes:

Budget = 3x + 3y

The graph of the new budget line would show a steeper slope compared to the original budget line. This indicates that the relative price of figs has increased, making them relatively more expensive compared to hamburgers.

c) In this scenario, Rachel has an income of $50, the price per hamburger is $3, the price per bag of figs is $3, and she receives an additional $10 in cash from a friend. The new budget line equation can be written as:

Budget = (3x + 3y) + 10

The graph of the new budget line would shift upward parallel to the original budget line. The additional cash from Rachel's friend increases her purchasing power, allowing her to afford more hamburgers and/or bags of figs.

d) Now, Rachel's friend gives her a gift basket containing 3 free bags of figs. In this case, the budget line equation remains the same as in part c:

Budget = (3x + 3y) + 10

However, since Rachel receives 3 free bags of figs, she can allocate more of her budget towards purchasing hamburgers. This would cause the budget line to rotate outward from the y-intercept, resulting in a flatter slope. The new budget line would reflect Rachel's ability to purchase more hamburgers with the same income and price of figs.

In summary, the budget line equation represents Rachel's affordability based on her income and the prices of hamburgers and figs. Changes in prices, income, or additional resources can affect the slope, position, or rotation of the budget line on a graph.

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Answer: 18/9 if not it's something along that-

Step-by-step explanation:

7^2 = 49 so like 49-31 equals 18 and the denominator 3^2 = 9 , so if it's not 18/9 then it's like 1/2 or something bc 9 + 9 is 18 yk-

Answer: 0.4

Step-by-step explanation: Simplify the expression

The dimensions of the tank with minimum weight are approximately x ≈ 14.55 ft and h ≈ 34.34 ft.

To find the dimensions of the tank with minimum weight, we need to consider the relationship between the volume of the tank and the weight of the sheet steel.

Let's assume the side length of the square base of the tank is x, and the height of the tank is h.

The volume of the tank is given as 8788 ft³, so we have the equation x²h = 8788.

To determine the weight, we need to consider the surface area of the tank. Since the tank has an open top and a square base, the surface area consists of the base and four sides.

The base area is x², and the area of each side is xh. Therefore, the total surface area is 5x² + 4xh.

The weight of the sheet steel is directly proportional to the surface area. Thus, to minimize the weight, we need to minimize the surface area.

Using the equation for volume, we can express h in terms of x: h = 8788/x².

Substituting this expression for h into the surface area equation, we have A(x) = 5x² + 4x(8788/x²).

Simplifying the equation, we get A(x) = 5x² + 35152/x.

To find the dimensions of the tank with minimum weight, we need to minimize the surface area. This can be achieved by finding the value of x that minimizes the function A(x).

We can differentiate A(x) with respect to x and set it equal to zero to find the critical points:

A'(x) = 10x - 35152/x² = 0.

Solving this equation, we get x³ = 3515.2, which yields x ≈ 14.55.

Since the dimensions of the tank need to be positive, we discard the negative solution.

Therefore, the dimensions of the tank with minimum weight are approximately x ≈ 14.55 ft and h ≈ 8788/(14.55)² ≈ 34.34 ft.

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The value that is added on the left-hand side to make the equation equal is -1/100.

In mathematics, an expression is a group of numbers and operations. The components of a mathematical expression that perform an operation are as follows: multiplication, division, addition, and subtraction.

Given [1/-2  - 3/4  of -8/15],

to add a number so the sum equals the product of -7/50 and 11/14

let the number be x

according to the question,

[1/-2  - 3/4  of -8/15] + x = -7/50*11/14

taking LHS

[1/-2  - 3/4  of -8/15] = -1/2 - (3(-8)/60)

[1/-2  - 3/4  of -8/15] = -1/2 + 24/60

[1/-2  - 3/4  of -8/15] = (-30 + 24)/60

[1/-2  - 3/4  of -8/15] =-6/60 = -1/10

RHS

-7/50*11/14 = -77/700 = -11/100

substitute the values

[1/-2  - 3/4  of -8/15] + x = -7/50*11/14

-1/10 + x = -11/100

x = -11/100 + 1/10

x = (-11 + 10)/100

x = -1/100

Hence -1/100 is added to make the equation equal.

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Answer:

Decimal Form:  5.29150262

Step-by-step explanation:

Brainliest?

15 more than the sum of 5 and a number a, when translated into a mathematical expression will become b. (5 + n) + 15.

An algebraic expression is a mathematical expression that can contain numbers, variables, and operations.

An algebraic expression can represent a specific value for a given value of the variable, and can be used to describe mathematical relationships and solve equations.

Algebraic expressions can be simplified, added, subtracted, multiplied and divided.

Algebraic expressions can also be represented in different forms, such as polynomials, rational expressions, exponential expressions and logarithmic expressions.

"15 more than the sum of 5 and a number a" can be represented algebraically as:

15 + (5 + a)

or

(5 + a) + 15

which can also be simplified as

a + 20

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Answer: k = 6

Step-by-step explanation: only one solution

Answer:

your answer will be 12

Step-by-step explanation:

\(4x-6=42\\\\4x=42+6\\\\4x=48\\\\x=12\)

have a nice day ^_^

Answer:

\(x=12\)

Step-by-step explanation:

∠B=∠E

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

∠A=∠D

⭒☆━━━━━━━☆⭒

hope it helps...

have a great day!!

Answer:

\(\frac{2}{21}\) i think

Step-by-step explanation:

Answer:

2/21

Step-by-step explanation:

Answer:

0.6 is equivalent

Answer:

60/100=6/10=4/5

0.6

Step-by-step explanation:

these are all equivalent

Answer:

\(f'(x)= \frac{13}{(2x+3)^2}\\\)

Step-by-step explanation:

\(f(x)= \frac{3x-2}{2x+3} \\\)

\(f'(x)=\frac{dy}{dx} = \frac{d}{dx}(\frac{3x-2}{2x+3})\\ f'(x)= \frac{(2x+3)\frac{d}{dx}(3x-2)-(3x-2)\frac{d}{dx}(2x+3) }{(2x+3)^{2} } \\f'(x)= \frac{(2x+3)(3)-(3x-2)(2)}{(2x+3)^{2} } \\\)

\(f'(x)= \frac{6x+9-6x+4}{(2x+3)^{2} }\\ f'(x)= \frac{13}{(2x+3)^2}\\\)

if the distribution of arrival delays is skewed, a larger sample size may be required to obtain accurate estimates of the population parameters compared to a normal distribution.

The distribution of a variable can affect the sample size required to obtain accurate estimates of the population parameters. When the distribution of the variable of interest is skewed, the sample size required to obtain accurate estimates may be larger than when the distribution is normal.

Skewed distributions have tails that extend further in one direction than the other, which means that the data are not evenly spread out around the mean. In such cases, the sample mean may be less representative of the population mean, and the sample size required to obtain a precise estimate of the population mean may be larger.

Furthermore, the standard deviation, which is a measure of the variability of the data, may also be affected by the skewness of the distribution. Skewed distributions tend to have a larger standard deviation than normal distributions, which means that a larger sample size may be needed to obtain a more accurate estimate of the population standard deviation.

In summary, if the distribution of arrival delays is skewed, a larger sample size may be required to obtain accurate estimates of the population parameters compared to a normal distribution.

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