Perform the addition or subtraction and simplify.
x
x2 + x − 2
−
9
x2 − 5x + 4

The scalar equation of the plane is -5x - 2y = 5.

To find the scalar equation for the plane passing through the points P1=(−3, 5, 3), P2=(−5, 0, 6), and P3=(−1, 10, −1), we need to follow these steps:

1. Find the vectors P1P2 and P1P3 by subtracting the corresponding coordinates of the points:
P1P2 = P2 - P1 = (-5 - (-3), 0 - 5, 6 - 3) = (-2, -5, 3)
P1P3 = P3 - P1 = (-1 - (-3), 10 - 5, -1 - 3) = (2, 5, -4)

2. Find the normal vector to the plane by taking the cross product of P1P2 and P1P3:
n = P1P2 x P1P3 = (-5 * (-4) - 3 * 5, 3 * 2 - (-2) * (-4), -2 * 5 - (-5) * 2) = (-5, -2, 0)

3. Find the scalar equation of the plane by substituting one of the points and the normal vector into the general equation of a plane:
ax + by + cz = d
-5 * (-3) + (-2) * 5 + 0 * 3 = d
d = 5

Therefore, the scalar equation of the plane is -5x - 2y = 5.

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Larry will need an annual rate of return of approximately 1.35% (rounded to two decimal places) to reach his goal of $3,500 in 20 years, if interest is compounded continuously.

The formula for continuous compounding is [tex]A = Pe^{rt}[/tex], where A is the amount of money at the end of the investment period, P is the initial principal, e is Euler's number (approximately 2.71828), r is the annual interest rate, and t is the time in years.

In this case, Larry has P = $3,000 and needs A = $3,500 in t = 20 years. We can solve for r by rearranging the formula:

[tex]r = ln(A/P)/(t)[/tex]

Plugging in the values, we get:

[tex]r = ln(3500/3000)/(20) = 0.0135[/tex] or 1.35%

Therefore, Larry will need an annual rate of return of approximately 1.35% (rounded to two decimal places) to reach his goal of $3,500 in 20 years, if interest is compounded continuously.

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Using long division . The quotient of  (4x^3-6x^2-4x+8) divided by (2x-1) is: 2x^2 - 2x - 2 with a remainder of 7.

Let use long division to determine the quotient of (4x^3-6x^2-4x+8) divided by (2x-1).

Long division:

   2x^2  - 2x  - 2

    --------------------

2x - 1 | 4x^3  - 6x^2  - 4x  + 8

       - (4x^3  - 2x^2)

       --------------

            -4x^2  - 4x

            +  (4x^2  - 2x)

            --------------

                      -2x  + 8

                      -(-2x  + 1)

                      --------

                               7

Therefore, the quotient of (4x^3 - 6x^2 - 4x + 8) divided by (2x - 1) is:

2x^2 - 2x - 2 with a remainder of 7.

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Answer:

Proofs attached to answer

Step-by-step explanation:

Proofs attached to answer

According to the information, the ratio of taco shells and cups of chicken is 9:4.

To identify the ratio of Taco shells and cups of chicken we must take into account the information in the image. In this case we must count how many units of each element we have. So we have 9 Taco shells and 4 cups of chicken.

According to the above, the ratio would be 9:4, that is to say that for every 9 taco shells that we have, we would have to use 4 cups of chicken. Therefore, if we want to double or triple the recipe we must use the following ingredients:

Double

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The surface area of the solids are listed below:

In this problem we find three cases of unfolded solids, whose surface area must be determined. The surface area is the sum of the areas of all faces of the solid. The area formulas for the triangle and the rectangle are, respectively:

Rectangle

A = b · h

Triangle

A = 0.5 · b · h

Where:

Now we proceed to determine the surface area of the solids are listed below:

Case 1

A = (9 in)² + 0.5 · (9 in)²

A = 81 in² + 40.5 in²

A = 121.5 in²

Case 2

A = 4 · (10 cm) · (2 cm) + (2 cm)²

A = 80 cm² + 4 cm²

A = 84 cm²

Case 3

A = 3 · (8 ft) · (10 ft) + 2 · (8 ft) · (5 ft)

A = 240 ft² + 80 ft²

A = 320 ft²

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The variable in the equation? x + 2 = 8 is 'x'.

An expression is a grouping of terms that have been joined together using mathematical operations such as subtraction, addition, multiplication, and division. In mathematics, the terms involved in an expression are:

We have the Equation: x+ 2 = 8.

as, we know that Equation is the combination of variables, Operation, numbers and Equal Sign,

So, the variable is x

and, Number is 8

and, Operation is +

Thus, the Variable in equation is x.

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As the value of x (time in seconds) increases, the height of the soccer ball decreases until it hits the ground at x=3.

what is domain of the function?

The domain of a function is the set of all possible values of the input variable (independent variable) for which the function is defined. It is the set of all x-values for which the function produces a valid output. In order to determine the domain of a function, one needs to consider any restrictions or limitations that the function may have.

The given problem is related to the motion of a soccer ball kicked by Lin. The height of the soccer ball (in feet) is a function of time (in seconds), and it is represented by a graph.

Domain: The domain of the function is the set of all possible values of the input variable (time in seconds). In this case, the soccer ball was in the air for 3 seconds, so the domain is [0, 3], which means that the height function is defined for all values of time between 0 and 3 seconds, including 0 and 3.

Range: The range of the function is the set of all possible values of the output variable (height of the soccer ball in feet). In this case, the soccer ball reached a height of approximately 30 ft while it was in the air. Therefore, the range of the function is [0, 30], which means that the height of the soccer ball is defined for all values between 0 and 30 feet, including 0 and 30.

Line of symmetry: The line of symmetry is a vertical line that passes through the vertex of the parabola (in this case, the highest point that the soccer ball reaches). The parabolic graph of the soccer ball's height function is symmetric with respect to the vertical line passing through the midpoint of the domain. Since the domain is [0, 3], the midpoint is (3/2, 0), so the line of symmetry is x = 3/2.

As the value of x (time in seconds) increases, the height of the soccer ball decreases until it hits the ground at x=3. As the value of x decreases from 3 to 0, the height of the soccer ball increases from 0 to 30 and then decreases again as it hits the ground. The rate of change of the height of the soccer ball is not constant but rather depends on the shape of the parabolic graph of the height function.

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o(a) = o(a-1) for any element a ∈ G.</p>,o(a) = o(a-1) for both the finite and infinite order cases

<p>Let G be a group and a ∈ G. To show that o(a) = o(a-1), we need to consider both the finite and infinite order cases.</p>
Finite order</p>
<p>If a has finite order, then there exists a positive integer n such that a^n = 1. We want to show that (a-1)^n = 1 as well. By the binomial theorem, we have:</p>
<p>(a-1)^n = a^n - na^(n-1) + (n(n-1)/2)a^(n-2) - ... + (-1)^n</p>
<p>Since a^n = 1, we can simplify this to:</p>
<p>(a-1)^n = 1 - na^(n-1) + (n(n-1)/2)a^(n-2) - ... + (-1)^n</p>
<p>All of the terms except for the last one are multiples of a, so they will all cancel out when we multiply by a^n. This leaves us with:</p>
<p>(a-1)^n * a^n = (-1)^n * a^n</p>
<p>Since a^n = 1, this simplifies to:</p>
<p>(a-1)^n = (-1)^n</p>
<p>If n is even, then (-1)^n = 1, so (a-1)^n = 1. If n is odd, then (-1)^n = -1, so (a-1)^n = -1. But since a-1 is an element of G, it must have an inverse, so (a-1)^n = 1. Therefore, o(a) = o(a-1) in the finite order case.</p>
Infinite order</p>
<p>If a has infinite order, then there is no positive integer n such that a^n = 1. We want to show that there is also no positive integer n such that (a-1)^n = 1. Suppose there exists such an n. Then we have:</p>
<p>(a-1)^n = 1</p>
<p>Multiplying both sides by a^n gives us:</p>
<p>(a-1)^n * a^n = a^n</p>
<p>But this is equivalent to:</p>
<p>(a^n - 1)^n = a^n</p>
<p>Since a has infinite order, a^n ≠ 1 for any positive integer n. Therefore, there is no positive integer n such that (a-1)^n = 1, so o(a) = o(a-1) in the infinite order case as well.</p>
<p>In conclusion, o(a) = o(a-1) for both the finite and infinite order cases. Therefore, o(a) = o(a-1) for any element a ∈ G.</p>

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Answer:

Step-by-step explanation

First divide 29.6 by 8.  Your answer will be 3.7.

[tex]\left \{ {{2y-x=-9} \atop {y=2x-3}} \right. \iff \left \{ {{2(2x-3)-x=-9} \atop {y=2x-3}} \right. \iff \{ {{4x-6-x=-9} \atop {y=2x-3}} \right. \\[/tex]

[tex]\{ {{3x=-9+6} \atop {y=2x-3}} \right. \iff \{ {{3x=-3} \atop {y=2x-3}} \right. \iff \{ {{x=-1} \atop {y=2x-3}} \right. \\[/tex]

[tex]\{ {{x=-1} \atop {y=2(-1)-3}} \right \iff \{ {{x=-1} \atop {y=-2-3}} \right \implies \bf \{ {{x=-1} \atop {y=-5}}[/tex]

[tex]\implies (x, \ y) = (-1, \ -5)[/tex]

1. The median of the sample is obtained through the expression 3+5 / 2. The correct answer is option b.

2. The mean of the ungrouped data distribution is 1.98. The correct answer is option C.

1. The median of a set of data is the middle value when the data is arranged in ascending or descending order. In this case, the data set is (1.9, 3, 5, 7). The middle values are 3 and 5, so the median is the average of these two values, which is (3+5) / 2 = 4.

2. The mean of a set of data is the sum of all the data values divided by the number of data values. In this case, the mean is [(3.2)(2) + (1.3)(5) + (2.4)(3)] / (2+5+3) = 19.8 / 10 = 1.98.

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When ff. is written it refers to the page or line mentioned and two or more pages or lines after it or a set of numbers as a function.

What is set?

A set is a clearly defined group of things in mathematics. Set names and symbols begin with a capital letter.

According to set theory, a set's constituent parts can be anything, including humans, alphabetic letters, numbers, shapes, variables, etc.

The types of set are:

Empty Set or Null set: It has no element present in it.Example: A = {} is a null set.

Finite Set: It has a limited number of elements.Example: A = {1,2,3,4}

Infinite Set: It has an infinite number of elements.Example: A = {x: x is the set of all whole numbers}

Equal Set: Two sets that have the same members.Example: A = {1,2,5} and B={2,5,1}: Set A = Set B

Subsets: A set ‘A’ is said to be a subset of B if each element of A is also an element of B.Example: A={1,2}, B={1,2,3,4}, then A ⊆ B

Universal Set: A set that consists of all elements of other sets present in a Venn diagram.Example: A={1,2}, B={2,3}, The universal set here will be, U = {1, 2,3}

Hence, ff(x) means that you have to replace x with f(x) in f(x).

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By applying velocity concept, it can be concluded that the height of the object is 48 feet at 1 second and 3 seconds.

Velocity is the distance traveled, and the direction in which the distance is changing. It can also be described as the instantaneous rate of change of a moving object.

velocity = Δs / Δt  , where:

Δs = distance change

Δt  = time change

The height of the object is given by the equation h = -16t² + 64t.

We need to find the time t when the height is 48 feet.

To do this, we can plug in the value of h and solve for t:

 h = -16t² + 64t

48 = -16t² + 64t

 0 = -16t² + 64t - 48

Dividing by -16 gives us:

0 = t² - 4t + 3

  = (t - 3)(t - 1)

Therefore, the possible values of t are 1 and 3 seconds.

So, the height of the object is 48 feet at 1 second and 3 seconds.

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It will take 5.00 seconds for the object to reach a height of 48 feet.

To answer this question, we need to use the equation given: h = -16t2 + 64t. We know that the height is 48 feet and need to calculate the number of seconds it will take to reach this height.

We can rearrange the equation to solve for t, which will give us the number of seconds it takes to reach 48 feet:

48 = -16t2 + 64t

To solve for t, we can use the quadratic formula:

t = (-64 ± √(642 - 4(-16)(48))) / (2(-16))

After simplifying, we get:

t = (8 ± √384) / -32

Therefore, the two solutions are t = 5.00 seconds and t = -6.25 seconds.

Since the object is being propelled upwards, the only solution that makes sense is t = 5.00 seconds.

Therefore, it will take 5.00 seconds for the object to reach a height of 48 feet.

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Teh type of plate was served are 242 child's plates and 212 adult's plates.

To solve this problem, we can use a system of equations. Let x be the number of child's plates and y be the number of adult's plates.

We can write two equations to represent the information given in the problem:

x + y = 454 (the total number of plates served)

3.50x + 7.40y = 2415.80 (the total amount of money collected)

Now we can use the first equation to solve for one of the variables in terms of the other.

For example, we can solve for x in terms of y:

x = 454 - y

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

3.50(454 - y) + 7.40y = 2415.80

Simplifying and solving for y, we get:

1589 - 3.50y + 7.40y = 2415.80 3.90y = 826.80 y = 212

Now we can use this value of y to find x: x = 454 - 212 = 242 So there were 242 child's plates and 212 adult's plates served.

Rounded to the nearest whole person, the answer is 242 child's plates and 212 adult's plates.

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The width of the rectangular prism as required to be determined is 12 centimetres.

As evident in the task content; the rectangular prism is 6 centimeters long and 16 centimeters high while Its volume is 1,152 cubic centimeters.

Since for rectangular prisms;

Volume = length × width × height

Where,

Length = 6 centimeters

Width = w

Height = 16 centimeters

So,

Volume = length × width × height

1152 = 6 × w × 16

w = 1152 / 96

w = 12 centimeters

Ultimately the width of the rectangular prism in discuss is;12 centimetres.

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The area of the sign is 35 square feet. The solution has been obtained by using the area of the trapezoid.

The entire area occupied by the sides of a trapezoid is its area. A trapezoid's area is determined by how many unit squares fit inside of it.

We know that area of the trapezoid is

Area (A) = (a + b ) * h/ 2

Now, here we are given the following:

a = 8

b = 6

h = 5

Now, on substituting these values in the formula, we get

⇒A = (8 + 6 ) * 5 / 2

⇒A = (14 * 5) / 2

⇒A = 70 / 2

⇒A = 35 square feet

Hence, the area of the sign is 35 square feet.

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The graph of g(x) = 3x² + 6 is steeper and shifted upward compared to the graph of f(x) = x².

A graph can be defined as a pictorial representation or a diagram that represents data or values.

The graphs of g(x) = 3x² + 6 and f(x) = x² are both quadratic functions, which means that their graphs are parabolas.

However, they have different coefficients and constant terms, which means that they will have different shapes and positions.

Here, the graph of g(x) = 3x² + 6 is steeper and shifted upward compared to the graph of f(x) = x².

Both graphs have a vertex at the origin, but g(x) has a larger coefficient of x², which makes it steeper, and an added constant term, which shifts it upward.

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The complex zeros of the polynomial function are -1, -2, -2, 1.5, and -4.

To find the complex zeros of the polynomial function, we need to use synthetic division and the quadratic formula.

First, let's use synthetic division to find one of the zeros:

-1 | 2 15 29 24 80
| -2 -13 -16 -8
|_____________________
2 13 16 8 72

Now, we have a new polynomial: 2x^(4)+13x^(3)+16x^(2)+8x+72

Let's use synthetic division again to find another zero:

-2 | 2 13 16 8 72
| -4 -18 -4 -8
|_____________________
2 9 -2 4 64

Now, we have a new polynomial: 2x^(3)+9x^(2)-2x+4

Let's use synthetic division one more time to find another zero:

-2 | 2 9 -2 4
| -4 -10 4
|_____________________
2 5 -12 0

Now, we have a new polynomial: 2x^(2)+5x-12

We can use the quadratic formula to find the remaining zeros:

x = (-b ± √(b^(2)-4ac))/(2a)

x = (-(5) ± √((5)^(2)-4(2)(-12)))/(2(2))

x = (-5 ± √(121))/(4)

x = (-5 ± 11)/(4)

x = (-5 + 11)/(4) or x = (-5 - 11)/(4)

x = 6/4 or x = -16/4

x = 1.5 or x = -4

So, the complex zeros of the polynomial function are -1, -2, -2, 1.5, and -4.

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Based on the information provided, it can be concluded that Manuel measured the height.

The height of a triangle ( a shape with three sides, three angles, and three vertices) can be defined as the distance between the vertex and the opposite. The vertex refers to the highest point of the triangle, which is usually at the top. In the case of the triangle presented, the height is five and this was correctly obtained by Manuel when he measured the distance from the vertex to its base.

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The logarithmic expression can be rewritten as a single logarithm with the same base as [tex]log_{4} (12.8)[/tex].

To rewrite the logarithmic expression as a single logarithm with the same base means that we have to do logarithmic expression simplification.

To do so, we can use the logarithmic properties:

[tex]log_{b} (a)[/tex] + [tex]log_{b} (c)[/tex] = [tex]log_{b} (ac)[/tex]

[tex]log_{b} (a)[/tex] - [tex]log_{b} (c)[/tex] = [tex]log_{b} (a/c)[/tex]

b · [tex]log_{a} (x)[/tex] = [tex]log_{a} (x^{b} )[/tex]

Using these properties, we can rewrite the given expression:

9 · [tex]log_{4} (2)[/tex] - [tex]log_{4} (40)[/tex] = [tex]log_{4} (2^{9} )[/tex] - [tex]log_{4} (40)[/tex]

= [tex]log_{4} (512)[/tex] - [tex]log_{4} (40)[/tex]

= [tex]log_{4} (512/40)[/tex]

= [tex]log_{4} (12.8)[/tex]


So the logarithmic expression can be rewritten as a single logarithm with the same base as [tex]log_{4} (12.8)[/tex]

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The number of ID numbers that can be made out of 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 is 3265920.


To find the number of ID numbers that can be made, we can use the permutation formula:

P(n,r) = n! / (n-r)!

Where n is the total number of digits available and r is the number of digits in the ID number.

In this case, n = 10 (the digits 0-9) and r = 8 (the number of digits in the ID number).

Plugging these values into the formula gives us:

P(10,8) = 10! / (10-8)!

P(10,8) = 10! / 2!

P(10,8) = 3628800 / 2

P(10,8) = 1814400

However, we need to subtract the number of ID numbers that start with 0, since these would not be valid eight-digit numbers. To find this number, we can use the permutation formula again with n = 9 (the digits 1-9) and r = 7 (the remaining digits in the ID number):

P(9,7) = 9! / (9-7)!

P(9,7) = 9! / 2!

P(9,7) = 362880 / 2

P(9,7) = 181440

Subtracting this from the total number of ID numbers gives us:

3265920 - 181440 = 3084480

So the number of ID numbers that can be made out of 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 is 3084480.

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Answer: 1/3

Step-by-step explanation: so there is six cards total and only two of them are even so 2/6 and that can go to 1/3

1/3

There are 2 even numbers, and the total is 6. So 2/6 in the simplest form is 1/3.

The total number of entities depicted by the given requirements is the sum of the number of students, teachers, and classrooms, which is 100 + 10 + 5 = 115. Hence, the answer is (C) 115.

What is the algebraic operation?

An algebraic expression in mathematics is an expression that is made up of variables and constants, along with algebraic operations (addition, subtraction, etc.). Expressions are made up of terms.

The question asks us to determine the number of entities depicted by the given requirements, which include School XYZ keeping track of its 100 students, 10 teachers, and 5 classrooms.

An entity can be defined as a distinct object or concept that is represented in a system, such as a database or software application.

In this case, the entities can be identified as follows:

Students: There are 100 students in the school, and each student can be considered as a separate entity.

Teachers: There are 10 teachers in the school, and each teacher can be considered as a separate entity.

Classrooms: There are 5 classrooms in the school, and each classroom can be considered separate.

Therefore, the total number of entities depicted by the given requirements is the sum of the number of students, teachers, and classrooms, which is 100 + 10 + 5 = 115. Hence, the answer is (C) 115.

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Answer:

28 units

Step-by-step explanation:

To find the area of a rectangle, multiply the base by its height.

Area = b · h

Area = 7 · 4

Area = 28 units

The equation expressed with x and y to find the tourist's average speed over the whole distance he walked is (5x + 4y) / (x + y)

Average speed = Total distance traveled / Total time taken

Distance = speed × time

= 5 km/h × x

= 5x km/h

Distance = speed × time

= 4 km/h × y

= 4y km/h

Average speed = Total distance traveled / Total time taken

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

Therefore, the tourist's average speed over the whole distance he walked is represented by (5x + 4y) / (x + y)

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Answer:

the answer is A

So basically it's simple just use some scientific calculator and put the number one by one with the bracket because there's a rule of mathematics which we call BODMAS

The percentage increase in the new monthly payment is a 35.5% decrease compared to the old monthly payment.

The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.

Here,
The original monthly payment per thousand dollars of the loan is $10.67. So, for a loan amount of x dollars, the original monthly payment can be written as:

10.67 x (x/1000) = 0.01067x

The term (x/1000) is used to convert the loan amount from dollars to thousands of dollars.

Jim has been paying this monthly payment for 4 years or 48 months. So, the total amount he has paid towards the loan is:

48 x 0.01067x = 0.51216x

At the end of 4 years, Jim owes the bank $70,000. So, we can write:

x - 0.51216x = 70000

0.48784x = 70000

x = 143391.99 (rounded to the nearest cent)

Now, we can use the new interest rate and monthly payment information to find the new monthly payment.

The new monthly payment per thousand dollars of the loan is $11.72. So, for a loan amount of x dollars, the new monthly payment can be written as:

11.72 x (x/1000) = 0.01172x

The new interest rate is 13%, which is applied to the remaining loan amount of $70,000. So, the new loan amount can be written as:

0.13 x 70000 + 70000 = 79100

Therefore, the new monthly payment for the loan amount of $79,100 is:

0.01172 x 79100 = $927.11 (rounded to the nearest cent)

To find the percentage increase in the new monthly payment, we can use the formula:

% increase = (new value - old value) / old value x 100

% increase = (927.11 - 1437.32) / 1437.32 x 100

% increase = -35.5%

Therefore, the percentage increase in the new monthly payment is a 35.5% decrease compared to the old monthly payment.

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The solution to the inequality 6x + 9 ≥ −(x − 9) is x ≥ 0, and the solution set in interval notation is [0, ∞).

To solve the inequality 6x + 9 ≥ −(x − 9), we need to first distribute the negative sign on the right side of the inequality. This gives us:

6x + 9 ≥ -x + 9

Next, we need to isolate the variable on one side of the inequality. We can do this by adding x to both sides and subtracting 9 from both sides:

7x ≥ 0

Finally, we can divide both sides by 7 to solve for x:

x ≥ 0

Now, we can write the solution set in interval notation. Since x is greater than or equal to 0, the solution set is [0, ∞).

So, the solution to the inequality 6x + 9 ≥ −(x − 9) is x ≥ 0, and the solution set in interval notation is [0, ∞).

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The solutions to the equation are x = π/2 and x = 11π/6. We can write these as a list separated by commas:

X = π/2, 11π/6

To solve the equation 2 sin^2 (x) – sin(x) – 1=0 for all solutions 0 < x < 2π, we can use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

In this case, a = 2, b = -1, and c = -1. Plugging these values into the quadratic formula gives us:

x = (-(-1) ± √((-1)^2 - 4(2)(-1))) / (2(2))

Simplifying the expression inside the square root gives us:

x = (1 ± √(1 + 8)) / 4

x = (1 ± √9) / 4

x = (1 ± 3) / 4

This gives us two possible values for x:

x = (1 + 3) / 4 = 1

x = (1 - 3) / 4 = -0.5

Now we need to find the values of x that satisfy the original equation and are within the given range of 0 < x < 2π. To do this, we can use the inverse sine function:

x = sin^-1(1) = π/2

x = sin^-1(-0.5) = -π/6

Since we are looking for solutions within the range of 0 < x < 2π, we need to add 2π to the nagetive solution to get a positive value:

x = -π/6 + 2π = 11π/6

Therefore, the solutions to the equation are x = π/2 and x = 11π/6. We can write these as a list separated by commas:

X = π/2, 11π/6

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