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The solutions of the equation  x² + 2x + 10 = - 3x + 4 are  x=-2 and x=-3

The given equation is x² + 2x + 10 = - 3x + 4.

Take all the terms to the left side

x² + 2x + 10+3x-4=0

Combine the like terms

x²+5x+6=0

x²+2x+3x+6=0

Take out the factors

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

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

x=-2 and x=-3

Hence, x=-2 and x=-3 are the solutions of the equation  x² + 2x + 10 = - 3x + 4.

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The force of the block on the rope is 35 N and it's downward. This force is acting downwards because the block is being lowered with a downward acceleration of `2.8 m/s²` by means of a rope.Thus, the correct option is 35 N. down.

The force of the block on the rope is the force due to gravity acting on it. This force is given by

`F=mg`,

where m is the mass of the block, g is the acceleration due to gravity and F is the force due to gravity acting on the block.In this case, the block is being lowered with a downward acceleration of

`2.8 m/s²`.

The acceleration of the block is given as

`a=2.8 m/s²`.

We need to find the force of the block on the rope. The force of the block on the rope is the force due to gravity acting on the block. The mass of the block is

`5-kg`.

Therefore, we can find the force due to gravity acting on the block as follows:

F = mg = 5 kg × 9.8 m/s² = 49 N

The force of the block on the rope is `49 N`.

This force is acting downwards because the block is being lowered with a downward acceleration of `2.8 m/s²` by means of a rope.Thus, the correct option is 35 N. down.

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Answer:

Option D.

Step-by-step explanation:

It is given that function g(x) represented by the graph. In the graph parabola opening down passing through (0,2), (-1.5,4.25), and (-3.5,0).

We need find the solutions of g(x) shown in the graph.

An ordered pair is called a solution of a function if it lie on graph of that function.

So, all the points lie on graph of function g(x) are the solutions of function g(x).

Therefore, the correct option is D.

Answer:

D

Step-by-step explanation:

I took the test

Inadequate authentication is a common weakness in software systems where the software fails to sufficiently prove the claimed identity of a user or actor. This can lead to unauthorized access and security risks.

Inadequate authentication is a common weakness in software systems, where the software fails to adequately prove a user's or actor's claimed identity. This can occur when the software does not verify a user's identity with sufficient accuracy or fails to ensure that the user is who they claim to be. This can lead to unauthorized access to sensitive information and resources, as well as data manipulation and other malicious activities. Unauthorized access can have serious consequences, such as data breaches, identity theft, and financial losses. To prevent these risks, software developers should ensure that their authentication systems are secure, reliable, and difficult to bypass. This includes implementing multi-factor authentication, using strong passwords, and regularly updating authentication systems.

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Answer: smaller

Step-by-step explanation:

hope this helpsss

Answer:

The answer to this question depends on the values of the numbers involved. In general, when you multiply a number by a fraction, the product will be smaller than the largest factor if the fraction is less than 1. For example, if you multiply 5 by 1/2, the product is 2.5, which is smaller than 5. On the other hand, if you multiply a number by a fraction that is greater than 1, the product will be larger than the largest factor. For example, if you multiply 5 by 2/1, the product is 10, which is larger than 5.

In conclusion, the size of the product obtained from multiplying a number by a fraction depends on the values of the numbers involved and can be either smaller or larger than the largest factor.

Option B is correct, the inequality which represents the  length of segment AB is greater than  length of segment AD is 9x-16>1.5x+42

The given rectangle is ABCD.

The length of segment AB is 9x-16 units

The length of segment AD is 1.5x+42 units

We have to find the inequality which represents the  length of segment AB is greater than  length of segment AD

> is the symbol used to represent greater than

AB>AD

9x-16>1.5x+42

Hence, option B is correct, the inequality which represents the  length of segment AB is greater than  length of segment AD is 9x-16>1.5x+42

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As the sample size rises, the width of a 95% confidence interval for a sample proportion decreases.

If the sample size is four times greater than the initial sample size but the sample percentage remains constant, the breadth of the 95% confidence interval is reduced by around a factor of two.

This is due to the fact that the standard error, which defines the width of the confidence interval, is proportional to the sample size squared. When the sample size is multiplied by four, the square root of the sample size multiplies by two, resulting in a lower standard error and a smaller confidence range.

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Answer:

-3(2x+3)=21 does not become -6x+9=21 because wrong foiling.

Step-by-step explanation:

When you distribute -3 with 2x+3 you multiply both values by -3.

-3*2x = -6x

-3*3 = -9 <- This is where the error is. It's -9, not +9.

The area of the trapezoidal tarp in the hotel is 47.3 square inches.

How do determine the area of the trapezoid?

From the complete question, the parallel sides are 10ft and 12ft.

Evaluate,

The height (h) is computed using the cosine function shown below:

This gives

Make h the subject:

Evaluate:

So, we get:

Evaluate:

Therefore, the area of the trapezoidal tarp in the hotel is 47.3 square inches.

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The complete question is given below:
A hotel builds an isosceles trapezoidal pool for children. it orders a tarp to cover the pool when not in use. what is the area of the tarp?

to find the height. first find that d is 60,45, or 120. this means the height of the trapezoid is approximately 2.5,4.3, or 3.5 feet. so the area of the tarp is approximately 47.3,30.0 or 38.5 square feet.

Answer:

Perimeter: 26 ft

Area: 36 ft

Step-by-step explanation:

There are two sides with the length of 4, the other two sides have a length of 9. Perimeter means to add up all of the sides. 9+9+4+4 = 26

The area means the length times width, 9× 4 = 36

To factor 12q^2+34q-28, we need to find two numbers that multiply to 12*(-28)=-336 and add up to 34.

We can start by listing all the factors of -336:

1, -1, 2, -2, 3, -3, 4, -4, 6, -6, 7, -7, 8, -8, 12, -12, 14, -14, 16, -16, 21, -21, 24, -24, 28, -28, 42, -42, 48, -48, 56, -56, 84, -84, 112, -112, 168, -168, 336, -336

Now, we need to find two numbers from this list that add up to 34. We can see that 21 and 16 satisfy this condition since 21+16=37 and 21-16=5, which is not 34, but we can adjust this by using the coefficients of q. Specifically, we can use the fact that 34=21q+16q, and then we can write:

12q^2+34q-28 = 12q^2+21q+16q-28

Now, we can factor by grouping:

= (12q^2+21q) + (16q-28)

= 3q(4q+7) + 4(4q+7)

= (3q+4)(4q+7)

Therefore, the factorization of 12q^2+34q-28 is:

12q^2+34q-28 = (3q+4)(4q+7)

Answer:

Length = 107cm, Width = 20cm

Step-by-step explanation:

Length = L

Width = W

Then, from first statement:

L = 5W + 7. (eqn1)

From second statement:

2(L + W) = 254. (eqn2)

solving the equations:

substitute (eqn1) into (eqn2) for L.

2(5W + 7 + W) = 254

6W + 7 = 127

6W = 127 - 7

6W = 120

W = 120/6

W = 20.

from (eqn1);

L = 5W + 7

L = 5(20) + 7

L = 107

The MATLAB program uses the fixed-point iteration method to find a real root of the equation 4x + cos(x) - e* = 0. It starts with an initial approximation of xo = 1 and iteratively applies the function g(x) = e* - cos(x) until convergence. The program also calculates the absolute and relative percentage error for the obtained root.

Here is an example MATLAB program that implements the fixed-point iteration method to find the real root of the given equation:

function root = fixedPointIteration()

   e_star = % Enter the desired value for e* here

   xo = 1; % Initial approximation

   % Set the tolerance for convergence

   tolerance = 1e-6;

   % Initialize variables

   x = xo;

   previous_x = xo;

   iteration = 0;

   % Perform the fixed-point iteration

   while true

       iteration = iteration + 1;

       x = e_star - cos(previous_x);

       % Calculate the absolute and relative percentage errors

       abs_error = abs(x - previous_x);

       rel_error = abs_error / abs(x);

       % Check for convergence

       if abs_error < tolerance

           break;

       end

       previous_x = x;

   end

   % Display the results

   disp('Root:')

   disp(x)

   disp('Absolute Error:')

   disp(abs_error)

   disp('Relative Error (%):')

   disp(rel_error * 100)  

   root = x;

end

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The term "resilience" encompasses the psychological processes and traits that enable individuals to deal with traumas and recover their healthy and effective functioning.

To understand resilience more deeply, let's consider a mathematical analogy.

Just as mathematical equations can be adjusted or modified to solve different problems, individuals need to adapt their coping mechanisms to match the specific demands of a trauma. Being adaptable allows people to assess the situation, identify necessary adjustments, and find effective strategies for recovery.

Resilience is not solely about returning to a pre-trauma state but also involves personal growth and transformation. In mathematics, this growth can be compared to solving a complex problem that requires expanding one's knowledge and skills.

It's important to note that resilience is not a fixed trait, but rather a dynamic process that can be developed and strengthened over time. Just as mathematical skills can be improved through practice and learning, individuals can cultivate resilience through various interventions, such as therapy, support groups, self-care practices, and building healthy relationships.

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The total charge for the rooms will be $197.55.

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Given,

The charge for one room = $21.95

Total number of rooms = 3+2+4=9 rooms

Total charges for the room= Charge for one room × total number of room

Substitute the values:-

The total charge for the room = 21.95 × 9 = 197.55

Hence, the total charge for the room is 197.55

The complete question is given below:-

Landon Elliot fumigates rooms and charges $21.95 per room. on Monday, he fumigated 3 rooms in one house, 2 in another, and 4 in a third. find his total charges.

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Answer:

42 cm A

Step-by-step explanation:

Answer:

f(x) = -x^2 + x + 13 find f(9) = -59

Hope this helps :)

Answer:

f(9)= -59

Step-by-step explanation:

First, put 9 into x; which gives you...

f(9)= (-9)^2+9+13

f(9)= -81+9+13

f(9)= -59

Answer:

Can't be done

Step-by-step explanation:

3a = 9 divide both sides by 3

a = 3

that is not equivalent to a = 1

can't be done

Answer:

They aren't equivalent; a = 3

Step-by-step explanation:

If a = 1, then the expression will show:

3(1) = 9

3 × 1 does not equal 9.

3 × 3 equals 9.

The expression and variable are not equivalent.

A must equal 3 to be equivalent as that's the only was to equal 9 from this expression.

Answer:

x+11.5

Step-by-step explanation:

4x² +7x-2=0

16x+7x-2=0

23x-2=0

      +2  +2

23x=2

23x/2

x= 11.5

I hope these help.

The single simplified fraction is (m + n)(p + m) / 2m.

To simplify the expression

\((3m^2 - 3n^2) / (m^2 + mp)÷ (6m - 6n) / (p + m)\)

we need to invert the second fraction and multiply by the first.

\((3m^2 - 3n^2) / (m^2 + mp) \times (p + m) / (6m - 6n)\)

We can then factor out a 3 from the numerator and the denominator, and cancel out the (m - n) terms. 3(m + n)(m - n) / 3m(m - n) x (p + m) / 6(m - n)

Simplifying further, we can cancel out the 3's and the (m - n) terms. (m + n) / m x (p + m) / 2

The simplified expression is (m + n)(p + m) / 2m.

To simplify the given expression, we invert the second fraction and multiply it by the first. Then we factor out common terms and cancel out like terms. We simplify the expression to obtain the single fraction (m + n)(p + m) / 2m.

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Answer:

sas

The answer is the first one, sas.

To improve the design of this experiment, the researchers could have used a double-blind design, where both the participants and the researchers are unaware of the group allocation.

In the given experiment, the researchers have not employed any form of blinding, which could be a potential source of bias. Blinding is a critical aspect of experimental design, where the participants or the researchers are unaware of the group allocation or the treatment being administered. Blinding is used to eliminate any potential sources of bias that may arise due to the expectations or beliefs of the researchers or participants. In this particular study, the lack of blinding could have led to two possible sources of bias. Firstly, the participants in the first group who received the meditation session could have had higher expectations of improvement in their flexibility due to the meditation. These expectations could have led to higher motivation and effort during the flexibility measurement, leading to an artificial improvement in their flexibility scores. Secondly, the researchers who were measuring the flexibility of the participants could have been biased towards finding a difference between the groups due to their knowledge of the group allocation. This could have led to a subconscious alteration in the measurement process, leading to a false conclusion about the effect of meditation on flexibility.

hence To improve the design of this experiment, the researchers could have used a double-blind design, where both the participants and the researchers are unaware of the group allocation. For instance, the participants could have been assigned a unique identification number, and the researchers could have used coded labels to differentiate the groups. This would have eliminated any potential sources of bias due to expectations or beliefs and would have made the results more reliable.

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The maximum amount of profit the company can make is 9274

Differentiation is the rate of change of one quantity with respect to the other.

It is the ratio of the change in one quantity, usually the dependent quantity to the change in another related quantity, usually the independent quantity.

Analysis:

y= -6x^2 + 600x - 5726

differentiating the equation,

dy/dx = -12x + 600

for maximum selling price, dy/dx = 0

-12x + 600 = 0

12x = 600

x = 50

The maximum selling price is 50, so substituting x to find y

y = -6(50)(50) + 600(50) - 5726 = 9274

In conclusion, the maximum amount of profit the company can make is 9274.

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Step-by-step explanation:

if AB and CD are parallel then

90 -x +83 +46 = 180 --> x= 39

Answer:

x = 39

Step-by-step explanation:

Using the properties of parallel lines, then

x + 44 = 83 ( subtract 44 from both sides )

x = 39

Answer:

Use the distance formula to determine the distance between two points.

Exact Form:

4 √ 10

The distance between points (-8, 5) and (4, 9) is 4√10.

A coordinate plane is a plane in which a set of two number lines are represented, horizontal line is called x-axis and vertical line is called y-axis.

The given points are,

P(-8, 5) and Q(4, 9)

To find the distance between points P(-8, 5) and Q(4, 9),

Use formula,

The distance between two points A(x₁, y₁) and B(x₂, y₂)

Distance\(AB =\sqrt{(x_2-x_1)^2+ (y_2-y_1)^2}\)

Distance between P(-8, 5) and Q(4, 9),

\(PQ = \sqrt{(4+8)^2 + (9-5)^2}\\\\PQ = \sqrt{12^2+4^2}\\\\ PQ = \sqrt{144 + 16}\\\\PQ = \sqrt 160\\\\PQ = 4\sqrt10\\\)

The distance between points P(-8, 5) and Q(4, 9) is 4√10.

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Answer:

x = 16

Step-by-step explanation:

(5x + 14)° + (x + 19)° + (2x + 19)° = 180°

8x + 52 = 180

8x = 128

x = 16