2. [3 pts] Use the laws of logarithms to write the expression as a single logarithm (combine). 2 log, x-log, y+log, z

The domain of the expression is \( [-1,1] \).

To rewrite the quantity as an algebraic expression of \( x \), we need to use the definition of the cotangent function and the relationship between the sine and cosine functions. The cotangent function is defined as \[ \cot (\theta)=\frac{1}{\tan (\theta)}=\frac{\cos (\theta)}{\sin (\theta)} \]Using the relationship between the sine and cosine functions, \[ \cos^{2} (\theta)=1-\sin^{2} (\theta) \]we can rewrite the cotangent function in terms of the sine function as \[ \cot (\theta)=\frac{\sqrt{1-\sin^{2} (\theta)}}{\sin (\theta)} \]Substituting \( \arcsin (x) \) for \( \theta \) gives us \[ \cot (\arcsin (x))=\frac{\sqrt{1-\sin^{2} (\arcsin (x))}}{\sin (\arcsin (x))} \]Since \( \sin (\arcsin (x))=x \), we can simplify the expression to get \[ \cot (\arcsin (x))=\frac{\sqrt{1-x^{2}}}{x} \]This is the algebraic expression of the quantity in terms of \( x \).

The domain of the expression is the set of values of \( x \) for which the expression is defined. Since the expression involves a square root, we need to ensure that the radicand is non-negative. This gives us the inequality \[ 1-x^{2}\geq 0 \]Solving for \( x \) gives us the inequality \[ -1\leq x\leq 1 \]Therefore, the domain of the expression is \( [-1,1] \).

In conclusion, the quantity can be rewritten as an algebraic expression of \( x \) as \[ \cot (\arcsin (x))=\frac{\sqrt{1-x^{2}}}{x} \]and the domain on which the equivalence is valid is \( [-1,1] \).

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Answer:

squareroot(256)

16

Step-by-step explanation:

im genius

A dog eats soft food out of a 16oz packet. Every day the dog eats its meals split into three dishes breakfast, lunch, and dinner. If the dog needs to eat 11oz daily, each dish would have 3.67oz of food.

To find out  oz would be in each dish, we need to divide the total amount of food the dog needs to eat daily (11oz) by the number of dishes (3). This will give us the amount of food in each dish.

Here's the math:

11oz ÷ 3 dishes = 3.67oz per dish

So, each dish would have 3.67oz of food.

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The tοtal area οf the cοmpοsite figure is 358.38 mm² (rοunded tο twο decimal places).

Area is the measurement οf the size οf a surface οr a regiοn in a 2D plane, typically measured in square units. It is calculated by multiplying the length and width οf a surface οr regiοn fοr simple shapes like rectangles, οr by using fοrmulas specific tο each shape fοr mοre cοmplex shapes.

The area οf a semicircle with radius r is given by (π/2)r², and the area οf a trapezium with height h and parallel sides a and b is given by (h/2)(a+b).

Substituting the given values, we get

Area οf semicircle = (π/2)(9mm)² = 81π/2 mm²

Area οf trapezium = (13mm/2)(7mm+18mm) = 227.5 mm²

Therefοre, the tοtal area οf the semicircle and trapezium is:

81π/2 + 227.5 ≈ 358.38 mm²(rοunded tο twο decimal places).

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The difference in volumes between the total volume and initial volume is 40 milliliters.

Volume is a collection of two - dimensional points enclosed by a single dimensional line. Mathematically, we can write -

V = ∫∫∫ F(x, y, z) dx dy dz

Given is the volume flask as shown in the image.

Initial volume in the container {I} : 360 milliliters

Total volume of the container {T} : 400 milliliters

The difference in volumes between the total volume and initial volume -

{T} - {I}

400 - 360

40 milliliters

Therefore, the difference in volumes between the total volume and initial volume is 40 milliliters.

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x<4 is the solution of the inequality 5 x < 20

A number system is defined as a system of writing to express numbers.

The given inequality is  5 x < 20

We have to solve for x

Divide both sides by 5

x<20/5

Divide numerator and denominator by 5

x<4

The graph of x<4 is given in the attachment.

Hence, x<4 is the solution of the inequality 5 x < 20

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The solution of the equation Bx =     1       2       3   is    x =        2      6      4.

To find the solution of the equation Bx =
1
2
3
, we can multiply both sides of the equation by the inverse of B, B^-1. This will give us:

B^-1 Bx = B^-1
1
2
3


Since the product of a matrix and its inverse is the identity matrix, I, we can simplify the left side of the equation to:

Ix = B^-1
1
2
3


And since the product of the identity matrix and any vector is just the vector itself, we can simplify further to:

x = B^-1
1
2
3


Now, we can plug in the given values for B^-1 and the right side of the equation to find the solution for x:

x =
-1 0 1
2 2 0
1 0 1
*
1
2
3


Multiplying the matrices gives us:

x =
(-1)(1) + (0)(2) + (1)(3)
(2)(1) + (2)(2) + (0)(3)
(1)(1) + (0)(2) + (1)(3)


Simplifying further gives us:

x =
2
6
4


So, the solution of the equation Bx =     1       2       3   is    x =        2      6      4

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The linear inequality answer using interval notation are [10/63, ∞]

To solve the linear inequality 3x+(1)/(3)>=(3)/(2)x+(4)/(7), we need to isolate the variable on one side of the inequality.

Here are the steps to do so:

1. Subtract (3)/(2)x from both sides of the inequality: 3x-(3)/(2)x+(1)/(3)>=(4)/(7)

2. Combine like terms on the left side of the inequality: (3/2)x+(1)/(3)>=(4)/(7)

3. Subtract (1)/(3) from both sides of the inequality: (3/2)x>=(4)/(7)-(1)/(3)

4. Find a common denominator and combine the fractions on the right side of the inequality: (3/2)x>=(12-7)/(21)

5. Simplify the fraction on the right side of the inequality: (3/2)x>=(5)/(21)

6. Multiply both sides of the inequality by the reciprocal of (3/2) to isolate the variable: x>=(5)/(21)*(2)/(3)

7. Simplify the fraction on the right side of the inequality: x>=(10)/(63)

The solution to the inequality is x>=(10)/(63). In interval notation, this is expressed as [10/63, infinity).

So the answer is [10/63, infinity]

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a.   It will take you 2 seconds to catch up to your friend.

b.  You will be 60 feet ahead of your friend when you cross the finish line.

a. This is because you are skating at a rate of 12 feet per second and your friend has a head start of 20 feet, so you must cover 20 feet in 2 seconds (20 feet/12 feet per second).

b. You will be 60 feet ahead of your friend when you cross the finish line.

This is because your friend is skating at a rate of 10 feet per second, and you are skating at a rate of 12 feet per second, so you will gain an additional 2 feet per second.

Therefore, in the 180-foot race, you will have gained an additional 60 feet over your friend (180 feet/2 feet per second).

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Answer:

Mate show the full picture please..half of the question is not shown.

Step-by-step explanation:

Answer:

16.1 is the closest asnwer

Step-by-step explanation:

if you didn't understand feel free to send me a message bro

Answer: 11 weekends

Step-by-step explanation: I did 470.80 divided by 37.50 and got 12 with a decimal, so then I multiplied 37.50 by 11 and got 412.5, then added the 58.30 .

Answer:

Step-by-step explanation:

So first you have to subtract the total that the computer costs by how much zach already has. Then you get 411.7. Then you have to divide 411.7 by 37.50 to get how many weeks it takes to get the computer. Which is 10.96 or 11. 11 weeks is the answer! You can check this by multiplying 37.50 by 11 and add 58 because he already has that money, you will get 470! which is close so there you go!

Therefore , the solution of the given problem of angles comes out to be  Lines I and m can be inferred to be parallel by the Corresponding Angles Converse .

An angle is a shape in Euclidean geometry consisting of two rays, or sides of a circular, that split at the angle's apex and the angle's apex, which is in the middle. Where they are located, two rays can join to form an angle. Angle is another outcome of two entities interacting. They are known as dihedral angles.

Here,

The Corresponding Angles Converse states that if two parallels are intersected by a transversal such that a set of corresponding angles are congruent, then perhaps the two lines are parallel.

This can be used to demonstrate that lines I and m are parallel.

We can infer that 1 and 2 are corresponding angles because 1 2.

We can infer that they have the same measure because they are congruent.

Let's now think about the transversal line t. Lines I and m can be inferred to be parallel by the Corresponding Angles Converse because 1 and 2 are corresponding angles and t crosses both I and m.

We have thus demonstrated that I / m.

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The given statement " If A is an m x n matrix and B is an n x n matrix, then A × B is an m x n matrix" is True.  Correct answer of (a) is T.

This statement is definately true because, it helps to consider the dimensions of a matrix. The dimensions of a matrix refer to the number of rows and columns it contains. In the case of an m x n matrix (A) and an n x n matrix (B), the dimensions of A are m rows and n columns, while the dimensions of B are n rows and n columns.

When A is multiplied by B, the result is an m x n matrix, meaning it contains m rows and n columns. This is due to the fact that the number of columns of the first matrix (A) must equal the number of rows of the second matrix (B) in order for the matrices to be compatible for multiplication.

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Answer:

x = 1

Step-by-step explanation:

17.25x+3.89=21.14
17.25x=17.25
x = 1

Answer:

The solution to the equation is x = 1

Step-by-step explanation:

Hi,

We need to isolate the term that contains the variable "x", so we will subtract 3.89.

17.25x + 3.89 - 3.89 = 21.14 - 3.89

We obtain:

17.25x = 17.25

Dividing both sides by 17.25:

x = 1

Therefore, the solution to the equation is x = 1.

Good luck!

Answer:

No

Step-by-step explanation:

6x-2

Factor out -1

( - -6x + -2)

- ( -6x +2)

- ( 2 -6x)

This is not equal to (2+6x) because of the negative sign out front.

To graph a quadratic function, follow the steps explained to obtain the smooth curve of the quadratic function.

Graphing quadratic functions involves plotting the points on a coordinate plane that satisfy the equation of the function. Quadratic functions are typically written in the form:

f(x) = ax^2 + bx + c

where;

To graph a quadratic function, you can follow these steps:

x = -b / 2a

y = f(x)

You can find the x-coordinate of the vertex by using the formula above, and then substitute it into the function to find the corresponding y-coordinate.

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Answer:

- 75.00

Step-by-step explanation:

400 - 475 = - 75

Helping in the name of Jesus.

Answer:

She's in debt $75

Step-by-step explanation:

475-400=-75

Answer:

30%

Step-by-step explanation:

First, I added up the number of minutes in 2 1/2 hours. 2 hours is 120 minutes, and 1/2 hour is 30 minutes. 120 + 30 = 150.

Next, divide 45 (which is the number out of 150 we are determining the percentage for) by 150 (which is the total number of minutes). Multiply that number by 100 to get 30. The answer is 30%.

The percentage of those standing is 60%

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

Using the above as a guide, we have the following:

Seated : Standing = 1 : 2

Standing : VIP = 6 : 1

Multiply Seated : Standing = 1 : 2 by 3

Seated : Standing = 3 : 6

Standing : VIP = 6 : 1

Combine the ratios

Seated : Standing : VIP = 3 : 6 : 1

So, we have

Standing = 6/(3 + 6 + 1) * 100%

Evaluate

Standing = 60%

Hence, the percentage is 60%

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The correct statement is (a) Regression coefficients estimated using least squares are always BLUE.

Therefore, statement (a) is true. The other statements are not correct. Statement (b) is incorrect because the omitted variable bias can be positive or negative, depending on the direction of the correlation between the omitted variable and the other explanatory variables. Statement (c) is incorrect because R2 j is obtained from the regression of the jth explanatory variable on the rest of the explanatory variables, not the dependent variable. Statement (d) is incorrect because statement (a) is true.

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Two comparations can be done:

I understand that we want to compare the numbers:

√144 and 12.9329...

Notice that the second number has infinite decimals after the decimal point (and there is no a clear pattern), so it is an irrational number.

For the first one, we know that:

12*12 = 144

So 144 is a perfect square, then when we apply the square root we will get:

√144 = 12

Then the two comparations are:

√144 is rational and 12.9329... is irrational.

And:

12.9329...> √144

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The first equation describing the given conditions is x - y = 2, as the difference between the two outputs of a firm is 2. The second equation is 8x = 10y, as eight times the larger quantity is 10 times the smaller quantity. The system of equations can be written as:

x - y = 2
8x = 10y

To solve the system, we can use the substitution method. First, we can solve for x in the first equation:

x = y + 2

Then, we can substitute this expression for x into the second equation:

8(y + 2) = 10y

Distributing the 8 gives:

8y + 16 = 10y

Subtracting 8y from both sides gives:

16 = 2y

Dividing by 2 gives:

y = 8

Finally, we can substitute this value of y back into the first equation to find x:

x = 8 + 2 = 10

So the two output levels are x = 10 and y = 8.

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The formula:

[tex]\huge\begin{array}{ccc}C=2\pi r\end{array}[/tex]

[tex]r[/tex] - radius

We have:

[tex]r=6.5m[/tex]

Substitute:

[tex]C=2\cdot6.5m\cdot\pi=13\pi m[/tex]

Use: [tex]\pi\approx3.14[/tex]

[tex]C\approx13m\cdot3.14=40.82m[/tex]

Answer:40.82 meters

The circumference of the circle.

The formula:

- radius

SOLUTION:

We have:

Substitute:

Use:

Step-by-step explanation:

Give bro above me the good stuff

The answer is sin(2x) = 0.8824.

If cot(x) = 5/3, we can use the identity cot(x) = 1/tan(x) to find the value of tan(x). Therefore, tan(x) = 1/(5/3) = 3/5.

Now, we can use the identity sin(2x) = 2sin(x)cos(x) to find the value of sin(2x). First, we need to find the values of sin(x) and cos(x).

Since tan(x) = 3/5, we can use the Pythagorean identity 1 = sin^2(x) + cos^2(x) to find the values of sin(x) and cos(x).

Let's assume sin(x) = 3/a and cos(x) = 5/a. Then, we can plug these values into the Pythagorean identity and solve for a:

1 = (3/a)^2 + (5/a)^2

1 = 9/a^2 + 25/a^2

1 = 34/a^2

a^2 = 34

a = √34

Therefore, sin(x) = 3/√34 and cos(x) = 5/√34.

Now, we can plug these values into the identity sin(2x) = 2sin(x)cos(x) to find the value of sin(2x):

sin(2x) = 2(3/√34)(5/√34)

sin(2x) = 30/34

sin(2x) = 0.8823529411764706

To 4 decimal places, sin(2x) = 0.8824.

the answer is sin(2x) = 0.8824.

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According to the Pythagorean theorem, |AC| = 10 * sqrt(5/3)

The Pythagorean Theorem states that the square on the tangent line (the side across from the right angle) of a right triangle, or, in standard algebraic form, a2 + b2, are equal to a square just on legs.

The following are some significant applications of the Pythagoras theorem in daily life: used in architecture and building. used to determine the shortest distance in two-dimensional navigation.

Since the diagonals of a rectangle are identical, the Pythagorean theorem states that AB = CD and BC = AD.

Using the Trigonometry once more, but this times with the edges of the rectangle, we can get d.

Lastly, by applying the right triangle's sides to the Pythagorean theorem, we may determine AC. ACD:

[tex]AC=\frac{500}{3}=10*\frac{5}{3}[/tex]

Therefore, |AC| = 10*(5/3)

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It took 24 days for the bank balance to increase from -$75 to $81 with daily deposits of $6.50.

Let's start by figuring out how much the bank balance increased by each day.

If the starting bank balance was -$75 and the ending bank balance was $81, then the total increase was:

$81 - (-$75) = $156

If she deposited $6.50 per day, then the bank balance increased by $6.50 each day.

So we can divide the total increase by the daily increase to find out how many days it took to reach $81:

$156 ÷ $6.50 per day = 24 days

Hence, the number of days is 24

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yes

im not sure though try it!

The length of the segment indicated is c = c = 9.92.

Pythagoras discovered that the square of the hypotenuse in a right-angled triangle with a 90° angle is equal to the sum of the squares of the other two sides.

The triangle has three sides: the hypotenuse, which is always the longest, the opposite, which doesn't touch the hypotenuse, and the adjacent (which is between the opposite and the hypotenuse).

a² = b² + c²

a = 19

b = 16.2

c or x =?

19² = 16.2² + c²

361 = 262.4 + c²

c² = 98.6

c = √98.6

c = 9.92

Therefore, the length of the segment indicated is c = 9.92.

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Answer:

$445.10

Step-by-step explanation:

The amount withheld for federal income tax depends on several factors, including Steve's filing status, income, and deductions. However, we can make an estimate based on some assumptions.

Assuming Steve is paid weekly and is paid for 52 weeks a year, his gross income would be:

$255.75 x 52 = $13,293

We also assume that Steve is claiming two allowances. Each allowance reduces the amount of taxable income subject to federal income tax withholding. For 2021, each allowance is equal to $4,300.

Therefore, Steve's taxable income for federal income tax purposes would be:

$13,293 - (2 x $4,300) = $4,693

To estimate the federal income tax withholding, we can use the IRS tax tables. For a single person claiming two allowances and earning $4,693 per week, the estimated federal income tax withholding would be:

$445.10

However, this is just an estimate, and the actual federal income tax withholding may be different based on Steve's specific circumstances. It's always best to consult with a tax professional for accurate tax advice.