Its factorial math pleaseHelp.

The expression cos x/cot x simplifies to sin x by utilizing trigonometric identities and canceling out the common cosine terms in the numerator and denominator.

To simplify the expression cos x/cot x, we need to utilize trigonometric identities. Cotangent (cot x) is the reciprocal of the tangent function, so we can rewrite cot x as 1/tan x.

Now, substituting 1/tan x for cot x in the expression cos x/cot x, we have:

cos x / (1/tan x)

To divide by a fraction, we multiply by its reciprocal. Therefore, multiplying cos x by tan x, we get:

(cos x)(tan x)

Using the identity tan x = sin x / cos x, we can substitute sin x / cos x for tan x:

(cos x)(sin x / cos x)

The cos x term in the numerator and denominator cancels out, leaving us with:

sin x

Therefore, the simplified expression for cos x / cot x is sin x.

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Answer:

A.

Step-by-step explanation:

The vertical line test is a way of finding out if a relation is a function.

Graph the relation.

Then imagine a vertical line moving from left to right over the graph of the relation.

If the vertical line intersects at most one point of the graph in any position you place the vertical line, then the relation is a function.

This function passes the vertical test since it never intersects more than one point on the vertical line at a time.

Answer: A.

Answer:

6%

Step-by-step explanation:

Tax rate = sales tax / price

We Take

(3.54 ÷ 59) x 100 = 6%

So, the state sales tax rate in Florida is 6%

None of the provided options accurately describe the relationship between the sides of the original square and the scale model.

Based on the information given, the scale model was created using a factor of 4. This means that each dimension of the scale model is 1/4 of the corresponding dimension of the original square.

The original square has sides measuring 8 feet.

To determine the length of each side of the scale model, we divide the length of the corresponding side of the original square by the scale factor:

Length of each side of the scale model = 8 feet / 4 = 2 feet.

Now, let's evaluate the given options:

a) Each side of the original square is the length of each side of the scale model.

This option is incorrect because the length of each side of the original square is 8 feet, whereas the length of each side of the scale model is 2 feet.

b) Each side of the original square is 4 times the length of each side of the scale model.

This option is incorrect because the length of each side of the original square is not 4 times the length of each side of the scale model. In fact, it is 4 times larger.

c) Each side of the original square is the same length as each side of the scale model.

This option is incorrect because, as mentioned earlier, the length of each side of the original square is 8 feet, whereas the length of each side of the scale model is 2 feet.

d) Each side of the original square is 4 feet less than the scale model.

This option is incorrect because the length of each side of the original square is not 4 feet less than the scale model. In fact, it is 6 feet larger.

Based on the evaluation, none of the provided options accurately describe the relationship between the sides of the original square and the scale model.

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Answer:

P(t) = 800 * 0.98^t

Step-by-step explanation:

If the population of a species in a preserve is 800, and it is expected to decrease at a rate of 2% each year, we can use the exponential decay model to represent the population after t years:

P(t) = P (1 - r)^t

P = initial population (800 in this case)

r = decay rate (2% or 0.02 as a decimal)

t = time

Substituting the given values into the formula, we get:

P(t) = 800 * (1 - 0.02)^t

P(t) = 800 * 0.98^t

So, the equation is P(t) = 800 * 0.98^t

The equation for exponential decay is given by:

where:

Substituting the given values, we get:

Simplifying this equation, we get:

[tex]\blue{\overline{\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}}[/tex]

Answer: The aim of this question is to find the first-order partial derivatives of an implicit function made up of two independent variables.

Step-by-step explanation:

a) Completing the table of values for y = x² - 2x - 3:

x | y

-2 | 11

-1 | 2

0  | -3

1  | -4

2  | -3

3  | 2

b) i) Comparing the values in the table to the equation y = x² - 2x - 3, we can see that the corresponding curve is Curve A.

ii) To estimate the value of y when x = 2.5, we can interpolate using the nearby points in the table. Looking at the table, we see that when x is between 2 and 3, the corresponding y values are -3 and 2. Since x = 2.5 lie halfway between these two values, we can estimate the value of y to be approximately halfway between -3 and 2, which is -0.5.

iii) To find the values of x when y = 1, we need to solve the equation x² - 2x - 3 = 1. Rearranging the equation, we get x² - 2x - 4 = 0. This is a quadratic equation, which can be factored as (x - 4)(x + 1) = 0. Setting each factor to zero, we find x = 4 and x = -1.

In summary:

a) Completing the table, we have:

x | y

-2 | 11

-1 | 2

0  | -3

1  | -4

2  | -3

3  | 2

b) i) Curve A matches the equation y = x² - 2x - 3.

ii) The estimated value of y when x = 2.5 is approximately -0.5.

iii) The values of x when y = 1 are x = 4 and x = -1.

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Answer:

Step-by-step explanation:

Direction or acceleration

Answer:

The correct answer for me is 2.5926

Answer:

48

Step-by-step explanation:

Answer:

24

Step-by-step explanation:

*Assuming that OM is a perpendicular bisector*

The correct answer is 24.

A perpendicular bisector splits the line segment, AC, in half directly, making one side 12 and the other side also 12.

So, AC in total is 24 units.

Hope this helps! :)

To solve the equation (17-3x)/(x-3)(x-4) = (x+1)/(x-4), we need to first simplify both sides of the equation and then find the values of x that satisfy the equation.

Let's start by simplifying the equation. We notice that both sides have a common denominator of (x-4), so we can eliminate it by multiplying both sides of the equation by (x-4):

[tex](x-4) * (17-3x) = (x-4) * (x+1)[/tex]

Expanding the equation, we get:

[tex]17x - 4x - 3x^2 + 12 = x^2 - 3x + x - 4[/tex]

Simplifying further, we have:

[tex]-3x^2 + 13x + 12 = x^2 - 2x - 4[/tex]

Bringing all terms to one side, we get:

[tex]-3x^2 - x^2 + 13x + 2x + 12 + 4 = 0[/tex]

Combining like terms, we have:

[tex]-4x^2 + 15x + 16 = 0[/tex]

Now, we have a quadratic equation. To solve it, we can either factor it, complete the square, or use the quadratic formula. However, the given equation is not easily factored.

Using the quadratic formula, x = [tex](-b ± \sqrt(b^2 - 4ac)) / (2a),[/tex] where a = -4, b = 15, and c = 16, we can calculate the solutions for x.

x = (-15 ± √(15^2 - 4 * -4 * 16)) / (2 * -4)

x = (-15 ± √(225 + 256)) / -8

x = (-15 ± √481) / -8

Therefore, the solutions for x are:

x ≈ 4.28 and x ≈ -0.53

These are the values of x that satisfy the given equation (17-3x)/(x-3)(x-4) = (x+1)/(x-4).

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The graph of the translated funciton is on the image at the end.

We start with the absolute value funciton:

f(x) = -|x|

And we want to graph the translated function:

g(x) = -|x - 4| - 3

So we can write:

g(x) = f(x - 4) - 3

That is a translation of 4 units to the right and 3 units down, so the graph of the function is the one you can see below.

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The equation of the circle with center (9,8) and touching the x-axis is given as follows:

(x - 9)² + (y - 8)² = 64.

The equation of a circle of center [tex](x_0, y_0)[/tex] and radius r is given by:

[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]

The coordinates of the center for this problem are given as follows:

(9,8).

Hence:

(x - 9)² + (y - 8)² = r².

The radius of a circle represents the distance between the center of the circle and a point on the circumference of the circle, and since it touches the x-axis(y = 0), the measure is given as follows:

r = 8 - 0

r = 8 units.

Thus the equation is given as follows:

(x - 9)² + (y - 8)² = 8²

(x - 9)² + (y - 8)² = 64.

The problem asks for the equation of the circle with the given features.

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To find a quarter of the difference between N8450 and N1290, we first need to calculate the difference between the two values, and then divide that difference by 4.

The difference between N8450 and N1290 can be calculated by subtracting N1290 from N8450:

N8450 - N1290 = N7160

Now, we have the difference of N7160. To find a quarter of this difference, we divide it by 4:

N7160 / 4 = N1790

Therefore, a quarter of the difference between N8450 and N1290 is N1790.

In other words, if we take N8450 and subtract N1290 from it, the result is N7160. And if we divide this difference by 4, we get N1790.

It's important to note that the "N" in the values N8450, N1290, N7160, and N1790 likely refers to some currency or numerical unit. Without further context, we cannot determine the exact nature of this unit, but the calculations presented demonstrate how to find a quarter of the difference between two given values.

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Answer:

c = 8

Step-by-step explanation:

Using the Intersecting Chords Theorem, we can form the following equation and solve for c:

[tex]ab=cd\\(10)(8.8)=11c\\88=11c\\c=8[/tex]

The correct answer is Miguel is 8 years old.

We are given that Josué is 2 years older than his brother Miguel. So, if we let Miguel's age be "x," Josué's age would be "x + 2".

María, who is the mother of both Josué and Miguel, has three times the age of the older sibling. Therefore, María's age would be "3(x + 2)".

The sum of the ages of the three individuals is 48 years. Setting up the equation:

x + (x + 2) + 3(x + 2) = 48

Simplifying the equation:

x + x + 2 + 3x + 6 = 48

5x + 8 = 48

Solving for x:

5x = 40

x = 8

Therefore, Miguel is 8 years old.Llamemos "x" a la edad de Miguel. Según la información dada, Josué tiene 2 años más que Miguel, lo que significa que su edad es "x + 2". María, por otro lado, tiene el triple de la edad del mayor de ellos, es decir, "3(x + 2)".

La suma de las edades de los tres es de 48 años, por lo tanto, podemos establecer la ecuación:

x + (x + 2) + 3(x + 2) = 48

Resolviendo la ecuación, encontramos:

x + x + 2 + 3x + 6 = 48

5x + 8 = 48

5x = 40

x = 8

Por lo tanto, Miguel tiene 8 años.

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JetBlue can recognize the change fee revenue of $250 immediately and the additional travel costs revenue of $50 on August 15th when the customer flies.

JetBlue can recognize revenue for the ticket sold on May 1st, 2019, when the customer postpones the flight until August 15th and pays an additional $300, under the following conditions:

1. The change fee of $250 is recognized as revenue immediately when the change is made. This is because the change fee represents the consideration received by JetBlue for modifying the ticket.

2. The increased travel costs of $50 ($300 - $250) should be allocated to the new flight date, which is August 15th. JetBlue can recognize this portion of the revenue on August 15th when the customer actually flies.

The initial ticket cost ($0 if forfeited completely) is not recognized as revenue since it represents breakage, and revenue is recognized when the service is provided (i.e., when the customer flies).

Therefore, JetBlue can recognize the change fee revenue of $250 immediately and the additional travel costs revenue of $50 on August 15th when the customer flies.

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Based on an annual income of $53,698 and deductions for FICA, federal tax withholding, and state tax withholding, the calculated allowed housing expense is approximately $11,572.84.

To calculate the allowed housing expense for the year, we need to determine the net income after deducting FICA (7.65%), federal tax withholding (11.5%), and state tax withholding (9%) from the annual income of $53,698.

First, let's calculate the deductions:

FICA deduction: 7.65% of $53,698 = $4,111.97

Federal tax withholding: 11.5% of $53,698 = $6,177.07

State tax withholding: 9% of $53,698 = $4,832.82

Next, subtract the deductions from the annual income:

Net income = $53,698 - $4,111.97 - $6,177.07 - $4,832.82 = $38,576.14

The allowed housing expense is generally recommended to be around 30% of the net income. To calculate this, we multiply the net income by 0.3:

Allowed housing expense = 0.3 * $38,576.14 = $11,572.84

However, it appears there is a discrepancy between the provided answer of $10,802.96 and the calculated value of $11,572.84. The difference could be due to rounding or other factors not accounted for in the given information. To reconcile this difference, we would need additional details or clarification.

In conclusion, based on the given information, the calculated allowed housing expense for the year is $11,572.84.

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The answer is $(x-7)(x-3)$.

Given expression is $x^2-10x+21=-10x+21$We can factor this expression by splitting the middle term. That means we have to find two numbers which, when multiplied, will give us $21$ and when added will give us $-10$.That means we have to find two numbers $a$ and $b$ such that $ab=21$ and $a+b=-10$.The numbers are $-3$ and $-7$.Now, let's write $-10x$ as $-3x-7x$.$$x^2-3x-7x+21$$$$x(x-3)-7(x-3)$$$$(x-7)(x-3)$$Thus, the given expression can be factorised as $$(x-7)(x-3)$$

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If we can determine the ratio of corresponding sides between the two triangles, such as StartFraction PQ Over EF EndFraction or StartFraction PR Over EF EndFraction, we would have sufficient information to prove the similarity.

To prove that △DEF is similar to △PQR using the SSS (Side-Side-Side) similarity theorem, we need one additional piece of information.

In this case, we are given that StartFraction DF Over PR EndFraction = StartFraction FE Over RQ EndFraction = three-halves. We also know that DE ≅ PQ and ∠D ≅ ∠P. However, to apply the SSS similarity theorem, we need to establish a ratio of corresponding sides between the two triangles.

To find this additional information, we can examine the ratios involving the remaining sides. We have StartFraction DE Over EF EndFraction = three-halves and StartFraction DE Over PQ EndFraction = three-halves.

Without this additional information, we cannot establish the necessary ratios of corresponding sides, and therefore, we cannot prove that △DEF is similar to △PQR using the SSS similarity theorem.

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Juan's three children, aged 6, 8, and 9, are to receive 667 World Cup figurines as a reward for their school performance.

To distribute the 667 World Cup figurines proportionally among Juan's three children based on their ages, we need to calculate the proportion of figurines each child should receive.

Total figurines: 667

Let's calculate the proportion for each child:

Child 1 (6 years old):

Proportion = (Age of Child 1) / (Sum of Ages of all children)

Proportion = 6 / (6 + 8 + 9) = 6 / 23

Child 2 (8 years old):

Proportion = (Age of Child 2) / (Sum of Ages of all children)

Proportion = 8 / (6 + 8 + 9) = 8 / 23

Child 3 (9 years old):

Proportion = (Age of Child 3) / (Sum of Ages of all children)

Proportion = 9 / (6 + 8 + 9) = 9 / 23

Now, let's calculate the number of figurines each child will receive based on their proportions:

Child 1:

Figurines = Proportion of Child 1 * Total figurines

Figurines = (6 / 23) * 667

Child 2:

Figurines = Proportion of Child 2 * Total figurines

Figurines = (8 / 23) * 667

Child 3:

Figurines = Proportion of Child 3 * Total figurines

Figurines = (9 / 23) * 667

After performing the calculations, we will have the number of figurines each child should receive.

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Note the translated question is Juan has 3 children of 6, 8 and 9 years old. To reward their performance at school, Juan wants to give them 667 World Cup figurines. To make the delivery more fair, Juan distributes the figurines proportionally, according to the ages of his children.

To calculate the value of h(2), we need to use the given information and equations. Let's break down the problem step by step.

Given:

[tex]ƒ(x) = g(x) + h(x)\\g(x) = x^2 + 3y\\ƒ(x) = x^3[/tex]

We want to find h(2), which means we need to determine the value of h when x = 2.

First, let's substitute the given expressions for g(x) and ƒ(x) into the equation ƒ(x) = g(x) + h(x):

[tex]x^3 = (x^2 + 3y) + h(x)[/tex]

Now, we can isolate h(x) by moving the other terms to the other side of the equation:

[tex]h(x) = x^3 - (x^2 + 3y)[/tex]

Since we want to calculate h(2), we substitute x = 2 into the equation:

[tex]h(2) = 2^3 - (2^2 + 3y)\\ = 8 - (4 + 3y)\\ = 8 - 4 - 3y\\ = 4 - 3y[/tex]

Therefore, h(2) is equal to 4 - 3y.

The value of h(2) depends on the value of y. Without any additional information or an equation relating to y, we cannot determine a specific value for h(2). However, we have expressed it in terms of y as 4 - 3y.

If you have any further information about y or any other equations or constraints related to h(x), please provide them so that we can calculate a specific value for h(2).

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The correct answer is 3/2. In this case, x = 3/2, and its square, (3/2)^2 = 9/4, is rational. x satisfies the given condition.option (c)

To explain further, we need to understand the properties of rational and irrational numbers.

A rational number can be expressed as a fraction of two integers, while an irrational number cannot be expressed as a fraction and has non-repeating, non-terminating decimal representations.

In the given options, (a) √5102.0 (£) and (b) √2 are both irrational numbers.

Their squares, (√5102.0)^2 and (√2)^2, would also be irrational, violating the given condition. On the other hand, (d) 4/5 is rational, and its square, (4/5)^2 = 16/25, is also rational.

Option (c) 3/2 is rational since it can be expressed as a fraction. Its square, (3/2)^2 = 9/4, is rational as well.

Therefore, (c) 3/2 is the only option where x is rational, but its square is irrational, satisfying the condition mentioned in the question.

In summary, the number x that satisfies the given condition, where x^2 is irrational but x is rational, is (c) 3/2.option (c)

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Answer:

Adding +6 in turn

Step-by-step explanation:

-13+6=(-7)

(-7)+6=(-1)

(-1)+6=5

5+6=11

11+6=17

17+6=23

23+6=29

29+6=35

........... And so on

The probability of choosing a book with blue on its cover and replacing it before choosing a book with white on its cover is 15/256, or approximately 0.059.

To find the probability of choosing a blue book and then a white book, we need to consider the total number of books and the number of blue and white books in the given scenario.

The total number of books on the shelf is:

5 blue + 6 red + 1 orange + 3 white + 1 blue and white = 16 books

The probability of choosing a blue book and replacing it before choosing a white book can be calculated by dividing the number of favorable outcomes by the total number of possible outcomes.

The number of favorable outcomes is the number of blue books, which is 5. After choosing a blue book and replacing it, the probability of choosing a white book is 3, as there are 3 white books left.

Therefore, the probability of choosing a blue book and then a white book can be calculated as:

[tex](5/16) \times (3/16) = 15/256[/tex]

The probability calculation is based on the assumption that each book is equally likely to be chosen and that the events of choosing each book are independent of each other.

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Answer:

it is

exactly 15 points

that will be included in the construction

To construct a perpendicular line using a point on the line, the following steps need to be followed:

1. Draw a line that passes through the given point and is perpendicular to the given line.

2. This perpendicular line should intersect the given line at a 90-degree angle.

3. Use a protractor to measure the angle between the given line and the perpendicular line.

4. Divide this angle in half to determine the angle that the perpendicular line should make with the given line.

5. Draw a line at this angle from the given point, and this line will be perpendicular to the given line.

Answer:

Grogg's dad is 22

Step-by-step explanation:

Let D = dad's current age

Let g = Grogg's current age

6(d - 7) = g - 7 → 6d - 42 = g - 7 → 6d -35 = g

4(d - 3) = g - 3 → 4d -12 = g - 3 → 4d -9 = g

Set the two equations equal to each other and solve for d

6d - 35 = 4d - 9  Subtract 4d from both sides

2d -35 = -9  Add 35 to both sides

2d = 44  Divide both sides by 2

d = 22

Helping in the name of Jesus.

Answer:

Step-by-step explanation:

d = current dad age

g = current grogg age

d-7 = 6(g-7)

d-3 = 4(g-3)

Let's solve the first equation first:

Add 7 to both sides: d - 7 +7 = 6g - 42 + 7 so d = 6g - 35

Substitude d = 6g - 35 for d in d - 3 = 4g - 12

(6g-35)-3 = 4g-12 = 6g-38 = 4g-12

Subtract 4g from both sides: 2g - 38 = -12

Add 38 to both sides: 2g = 26

Easy: g = 13

And now substitude g in for any equations.

d-3 = 52-12

d = 43