|2x + 5| < 13 how do I solve and graph this absolute value inequality

Answer:

sqrt( 97)

Step-by-step explanation:

To find the distance between 2 points

d = sqrt( (x2-x1)^2 + (y2-y1)^2)

   = sqrt( (3-7)^2 + (8 - -1)^2)

    = sqrt( ( -4)^2 + (8+1)^2)

    = sqrt( 16+9^2)

   = sqrt(16+81)

  = sqrt( 97)

SOLUTION

We use sin

This is because the opposite and the adjacent sides are where we have known and unknown values

You can use the code SOH/ CAH / TOA to make the right choice of trigonometric ratio to use

The area of rectangle B can be calculated by dividing the area of rectangle A by 16cm. Therefore, the area of rectangle B is 128 cm^2.

Let's assume the length and width of rectangle B as Lb and Wb, respectively. According to the given information, the dimensions of rectangle A are four times the dimensions of rectangle B. This implies that the length and width of rectangle A are 4Lb and 4Wb, respectively.

The formula for calculating the area of a rectangle is A = length * width. In this case, the area of rectangle A is given as 2,048 cm2. Substituting the dimensions of rectangle A, we get:

2,048 = (4Lb) * (4Wb)

2,048 = 16Lb * Wb

To find the area of rectangle B, we need to determine the values of Lb and Wb. From the equation above, we can see that Lb * Wb equals 2,048 divided by 16. Simplifying the equation, we have:

Lb * Wb = 128

Therefore, the area of rectangle B is 128 cm^2, which is obtained by dividing the area of rectangle A by 16cm.

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Answer:

1/24

Step-by-step explanation:

Each time you take one marble out, the total decreases by 1

You take 1 marble out, it decreases from 10 to 9 and there are now 9 marbles left in the bag.

When you will take the next marble, it will be on a total of 9 and after you take it out the total decreases again by 1. You'd have 8 and so on.

Green = 3

Red = 5

Blue = 2

Probability of getting it in the order RGB =

\( \frac{3}{10} \times \frac{5}{9} \times \frac{2}{8} \: = \frac{30}{720} = \frac{1}{24} \)

Answer:

x=40

Step-by-step explanation:

Answer:

x = 32

Step-by-step explanation:

\(\frac{1}{2}\)x-10 = 6

Isolate the x.

\(\frac{1}{2}\)x = 6+10

Simplify.

\(\frac{1}{2}\)x = 16

(\(\frac{1}{2}\)x × 2 = \(\frac{2}{2}\)x) Find x.

\(\frac{2}{2}\)x = 16 × 2

Simplify.

\(\frac{2}{2}\)x = 32

Answer:

Solution

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The distance between two points (2, 3)

& (4, 1) is given by

distance

d=

(x

2

​

−x

1

​

)

2

+(y

2

​

−y

1

​

)

2

​

here (x

1

​

,y

1

​

)=(2,3) & (x

2

​

,y

2

​

)=(4,1)

d=

(4−2)

2

+(1−3)

2

​

=

2

2

+2

2

​

d=

4+4

​

d=

8

​

d=2

2

​

 distance

Step-by-step explanation:

444 ft traveled in 6 seconds.

If the car travels 74 ft in 1 second, all you have to do is multiply 74 by 6 to find the answer, which is 444 ft.

Answer:

put a point on the 9 (the line on the left of 10) and on the -6 (the line to the left of -5).

a. 9 is located to the right of -6

b. use the symbol >

Step-by-step explanation:

Answer:

let's use Pythagoras theorem,

h²=b²+l²

so,

ad²=ac²+dc²

6²=ac²+3²

36-9=ac²=27

√27 can be written as 3√3,

hence ac= 3√3

The minimum value and median are used in the five-number summary.

A box and whisker plot displays a "box" with its left edge at Q₁, right edge at Q₃, "center" at Q₂ (the median), and "whiskers" at the maximum and minimum.

Given:

A five-number summary.

That means minimum value, lower quartile (Q1), median value (Q2), upper quartile (Q3), and maximum value.

From the given choices:

The minimum value and median are the required measures.

Therefore, the minimum value and median are the required measures.

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Answer:

false

Step-by-step explanation:

Answer:

3(x+y) = 5x

Step-by-step explanation:

Answer:

a³ + 5c

Step-by-step explanation:

That would be, symbolically, a³ + 5c

Answer:She will need 12 and 1/2 cups of sugar

Step-by-step explanation:

Just set up a table and multiply 2 1/2 by 5 and you get 12 1/2

Answer:

To simplify the expression (-12x³ - 48x²) + (-4x), we can combine like terms by adding the coefficients of the same degree of x.

The expression simplifies to -12x³ - 48x² - 4x.

Therefore, the best answer from the choices provided is:

C. 16x² + 52x

The equation of the tangent to the curve at the point corresponding to θ = 0 is y = 1/2x - 1/2.

To find the equation of the tangent to the curve, we need to determine the slope of the tangent at the given point. We differentiate the equations of x and y with respect to θ:

dx/dθ = -sin(θ) + 2cos(2θ)

dy/dθ = cos(θ) - 2sin(2θ)

Substituting θ = 0 into these derivatives, we get:

dx/dθ = -sin(0) + 2cos(0) = 0 + 2 = 2

dy/dθ = cos(0) - 2sin(0) = 1 - 0 = 1

The slope of the tangent is given by dy/dx. Therefore, the slope at θ = 0 is:

dy/dx = (dy/dθ)/(dx/dθ) = 1/2

Using the point-slope form of a line, where the slope is 1/2 and the point is (x, y) = (cos(0) + sin(20), sin(0) + cos(20)) = (1, 0), we can write the equation of the tangent as:

y - 0 = (1/2)(x - 1)

Simplifying the equation, we get:

y = 1/2x - 1/2

Therefore, the equation of the tangent to the curve at the point corresponding to θ = 0 is y = 1/2x - 1/2.

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Step-by-step explanation:

it is a quadrilateral.

the sum of all angles in a quadrilateral is always 360°.

so,

360 = x + x + 2x + 7 + 2x + 5 = 6x + 12

348 = 6x

x = 348/6 = 58°

that's it.

Adjust the parameters as needed, such as the step size (h) and the final x-value (xn), and run the code to obtain the solution for y(x).

The resulting plot will show the solution curve.

To solve the given set of differential equations using the Runge-Kutta method in MATLAB, we need to convert the second-order differential equations into a system of first-order differential equations.

Let's define new variables:

y = y(x)

z = dz/dx

Now, we have the following system of first-order differential equations:

dy/dx = z (1)

dz/dx = -k/(2y) (2)

To apply the Runge-Kutta method, we need to discretize the domain of x. Let's assume a step size h for the discretization. We'll start at x = 0 and proceed until x = infinite.

The general formula for the fourth-order Runge-Kutta method is as follows:

k₁ = h f(xn, yn, zn)

k₂ = h f(xn + h/2, yn + k₁/2, zn + l₁/2)

k₃ = h f(xn + h/2, yn + k₂/2, zn + l₂/2)

k₄ = h f(xn + h, yn + k₃, zn + l₃)

yn+1 = yn + (k₁ + 2k₂ + 2k₃ + k₄)/6

zn+1 = zn + (l₁ + 2l₂ + 2l₃ + l₄)/6

where f(x, y, z) represents the right-hand side of equations (1) and (2).

We can now write the MATLAB code to solve the differential equations using the Runge-Kutta method:

function [x, y, z] = rungeKuttaMethod()

   % Parameters

   k = 1;              % Constant k

   h = 0.01;           % Step size

   x0 = 0;             % Initial x

   xn = 10;            % Final x (adjust as needed)

   n = (xn - x0) / h;  % Number of steps

   % Initialize arrays

   x = zeros(1, n+1);

   y = zeros(1, n+1);

   z = zeros(1, n+1);

   % Initial conditions

   x(1) = x0;

   y(1) = 0;

   z(1) = 0;

   % Runge-Kutta method

   for i = 1:n

       k1 = h * f(x(i), y(i), z(i));

       l1 = h * g(x(i), y(i));

       k2 = h * f(x(i) + h/2, y(i) + k1/2, z(i) + l1/2);

       l2 = h * g(x(i) + h/2, y(i) + k1/2);

       k3 = h * f(x(i) + h/2, y(i) + k2/2, z(i) + l2/2);

       l3 = h * g(x(i) + h/2, y(i) + k2/2);

       k4 = h * f(x(i) + h, y(i) + k3, z(i) + l3);

       l4 = h * g(x(i) + h, y(i) + k3);

       y(i+1) = y(i) + (k1 + 2*k2 + 2*k3 + k4) / 6;

       z(i+1) = z(i) + (l1 + 2*l2 + 2*l3 + l4) / 6;

       x(i+1) = x(i) + h;

   end

   % Plotting

   plot(x, y);

   xlabel('x');

   ylabel('y');

   title('Solution y(x)');

end

function dydx = f(x, y, z)

   dydx = z;

end

function dzdx = g(x, y)

   dzdx = -k / (2*y);

end

% Call the function to solve the differential equations

[x, y, z] = rungeKuttaMethod();

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The directional derivative of the function at the given point in the direction of the vector v are as follows :

\(\[D_{\mathbf{u}} f(\mathbf{a}) = \nabla f(\mathbf{a}) \cdot \mathbf{u}\]\)

Where:

- \(\(D_{\mathbf{u}} f(\mathbf{a})\) represents the directional derivative of the function \(f\) at the point \(\mathbf{a}\) in the direction of the vector \(\mathbf{u}\).\)

- \(\(\nabla f(\mathbf{a})\) represents the gradient of \(f\) at the point \(\mathbf{a}\).\)

- \(\(\cdot\) represents the dot product between the gradient and the vector \(\mathbf{u}\).\)

Now, let's substitute the values into the formula:

Given function: \(\(f(x, y) = 7e^x \sin y\)\)

Point: \(\((0, \frac{\pi}{3})\)\)

Vector: \(\(\mathbf{v} = \begin{bmatrix} -5 \\ 12 \end{bmatrix}\)\)

Gradient of \(\(f\)\) at the point  \(\((0, \frac{\pi}{3})\):\)

\(\(\nabla f(0, \frac{\pi}{3}) = \begin{bmatrix} \frac{\partial f}{\partial x} (0, \frac{\pi}{3}) \\ \frac{\partial f}{\partial y} (0, \frac{\pi}{3}) \end{bmatrix}\)\)

To find the partial derivatives, we differentiate \(\(f\)\) with respect to \(\(x\)\) and \(\(y\)\) separately:

\(\(\frac{\partial f}{\partial x} = 7e^x \sin y\)\)

\(\(\frac{\partial f}{\partial y} = 7e^x \cos y\)\)

Substituting the values \(\((0, \frac{\pi}{3})\)\) into the partial derivatives:

\(\(\frac{\partial f}{\partial x} (0, \frac{\pi}{3}) = 7e^0 \sin \frac{\pi}{3} = \frac{7\sqrt{3}}{2}\)\)

\(\(\frac{\partial f}{\partial y} (0, \frac{\pi}{3}) = 7e^0 \cos \frac{\pi}{3} = \frac{7}{2}\)\)

Now, calculating the dot product between the gradient and the vector \(\(\mathbf{v}\)):

\(\(\nabla f(0, \frac{\pi}{3}) \cdot \mathbf{v} = \begin{bmatrix} \frac{7\sqrt{3}}{2} \\ \frac{7}{2} \end{bmatrix} \cdot \begin{bmatrix} -5 \\ 12 \end{bmatrix}\)\)

Using the dot product formula:

\(\(\nabla f(0, \frac{\pi}{3}) \cdot \mathbf{v} = \left(\frac{7\sqrt{3}}{2} \cdot -5\right) + \left(\frac{7}{2} \cdot 12\right)\)\)

Simplifying:

\(\(\nabla f(0, \frac{\pi}{3}) \cdot \mathbf{v} = -\frac{35\sqrt{3}}{2} + \frac{84}{2} = -\frac{35\sqrt{3}}{2} + 42\)\)

So, the directional derivative \(\(D_{\mathbf{u}} f(0 \frac{\pi}{3})\) in the direction of the vector \(\mathbf{v} = \begin{bmatrix} -5 \\ 12 \end{bmatrix}\) is \(-\frac{35\sqrt{3}}{2} + 42\).\)

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ok

Result = 4 7/16

awnser im believe it is 24 i think

Answer:

20 units square

Step-by-step explanation:

do the Pythagoras theorem

a²=b²+c² ⇒ a=√b²+c²

if b is 4 and c is 2 an a is the unknown

so a=√(4)²+(2)²

a=√20

then get the rule of the area of the square

Area of the square= s²

s=a=√20 (a is the hypotenuse of the triangle and also a side in the square)

so s²=20

Area of the square=20 units square

Answer:

x = 8

Step-by-step explanation:

I hope this helps!

The statement "The decision maker controls the probability of making a Type I statistical error" is true.

1. Alpha and beta are directly related: This statement is false. Alpha (α) and beta (β) are not directly related. Alpha represents the significance level, which is the probability of rejecting the null hypothesis when it is true (Type I error). Beta represents the probability of failing to reject the null hypothesis when it is false (Type II error). They are separate probabilities and are influenced by different factors. Increasing one does not necessarily result in an increase in the other.

2. The alternative hypothesis should contain the equality: This statement is false. The alternative hypothesis is typically formulated to assert a difference or relationship between variables, and it does not include the equality. It represents the researcher's belief or expectation that there is a significant effect or relationship in the population.

3. The decision maker controls the probability of making a Type I statistical error: This statement is true. The decision maker, usually the researcher or statistician, has control over the significance level (α), which determines the threshold for rejecting the null hypothesis. By setting the significance level, the decision maker controls the probability of making a Type I error. A lower significance level reduces the chance of Type I error but increases the risk of Type II error, and vice versa.

4. Alpha represents the probability of making a Type II error: This statement is false. Alpha (α) represents the significance level and is the probability of making a Type I error, which is rejecting the null hypothesis when it is true. The probability of making a Type II error is denoted by beta (β). Alpha and beta are complementary probabilities that need to be considered together in hypothesis testing.

In conclusion, the statement that is true is "The decision maker controls the probability of making a Type I statistical error." The decision maker has the ability to set the significance level (α), which determines the maximum acceptable probability of making a Type I error. By controlling this probability, the decision maker can manage the level of risk associated with rejecting the null hypothesis incorrectly.

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Here, we want to solve the given equation

We can rewrite the equation as follows;

So, we have this as;

x+1 = -6 or x+1 = 6

x = -6-1 or x = 6-1

x = -7 or 5

9514 1404 393

Answer:

  12 liters

Step-by-step explanation:

The kerosene usage is assumed to be jointly proportional to the number of stoves and the number of hours. That is ...

  v = k·s·h . . . . . for s stoves running h hours

Then the value of k is ...

  k = v/(sh) = (16 L)/(12·14) = 2/21 . . . . liters per stove-hour

Then the volume of kerosene required for 7 stoves and 18 hours is ...

  v = (2/21)·s·h

  v = (2/21)(7)(18) = 12 . . . liters

We require both to ascertain whether the findings are independent, this criterion is applied.

Statistics frequently employs the binomial distribution as a discrete distribution. When compared to a binomial distribution, the normal distribution is continuous. The chance for 'x' success of an investigation in 'n' trials is represented by the binomial distribution.

As per the given information in the question,

The normal distribution can be used to approximate the binomial distribution. The situation when performing a normal approximation is as follows:

np ≥ 10 and,

np(1 - p) ≥ 10

This criterion is used to determine whether the results are independent.

We are aware that when n and p are combined, the results are independent.

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Answer:

(5,3)

Step-by-step explanation:

Evaluate (2x+3,y-1=5,3)

Then you will get 5,3

So then your answer will be (5,3)

Heres your answer! Enjoy :D

Answer:

x = 1, y = 4

Step-by-step explanation:

Equating the corresponding coordinates

2x + 3 = 5 ( subtract 3 from both sides )

2x = 2 ( divide both sides by 2 )

x = 1

and

y - 1 = 3 ( add 1 to both sides )

y = 4

This criterion can be defined based on the desired level of accuracy or when the change in the estimated parameters falls below a certain threshold.

When implementing a program for a nonlinear problem using the least square adjustment technique, it is essential to determine a termination condition. This condition dictates when the program should stop iterating and provide the final estimated parameters. A common approach is to set a convergence criterion, which measures the change in the estimated parameters between iterations.

One possible criterion is to check if the change in the estimated parameters falls below a predetermined threshold. This implies that the adjustment process has reached a point where further iterations yield minimal improvements. The threshold value can be defined based on the desired level of accuracy or the specific requirements of the problem at hand.

Alternatively, convergence can also be determined based on the objective function. If the objective function decreases below a certain tolerance or stabilizes within a defined range, it can indicate that the solution has converged.

Considering the chosen termination condition is crucial to ensure that the program terminates effectively and efficiently, providing reliable results for the nonlinear problem.

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fig 3 would take 18 triangle

fig 4 would take 30 small triangles

if its wrong i am sorry

Answer: