12 times the difference of a number r and 7, how would you write this as a equation?

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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Given:

A figure of a right angle triangle.

To find:

The value of x.

Solution:

In a right angle triangle,

\(\tan \theta = \dfrac{Opposite}{Adjacent}\)

In the given triangle,

\(\tan (30^\circ) = \dfrac{x}{7}\)

\(\dfrac{1}{\sqrt{3}}=\dfrac{x}{7}\)

On multiplying both sides by 7, we get

\(\dfrac{7}{\sqrt{3}}=x\)

Therefore, the value of x is \(x=\dfrac{7}{\sqrt{3}}\).

ST. The statement is sometimes true. The dimension of the orthogonal complement of the null space of A is equal to the rank of A.

Since A is a 8 x 9 matrix of maximum rank, its rank is 8. Therefore, the dimension of the orthogonal complement of the null space of A is 1, if and only if the null space of A has dimension 7. This means that there are 7 linearly independent vectors that satisfy Ax = 0. It is possible for this to happen, but it is not always true. For example, if A is the identity matrix, then the null space of A is the zero vector, and the dimension of the orthogonal complement of the null space of A is 9, not 1. Therefore, the statement is not always true, but it is sometimes true, depending on the specific matrix A.

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Answer:

A

Step-by-step explanation:

The coordinates are (3,5),(7,-3),(0,-5),(-3,-4) and (-6,1). So the correct option is A

Based on the AA Similarity Theorem, triangles PQR and TSR are proven to be similar to each other because they have two pairs of corresponding angles that are congruent to each other.

The AA (Angle-Angle) Similarity Theorem states that if two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar. This means that the corresponding sides of the triangles are in proportion to each other.

With the information given, the proof that shows that the two triangles are similar as as follows:

Statements                                         Reasons                                        

1. ∠QPR ≅ ∠STR                                1. Given

2. QR ⊥ PT                                         2. Given

3. ∠QRP ≅ ∠SRT                               3. def. of perpendicular

4. ΔPQR ~ ΔTSR                                4. AA Similarity Theorem

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The dimensions of a scale drawing of a rectangular flag that is 40 centimeters by 72 centimeters using the scale 1:8 is 4 cm by 7.2 cm. Option C.

This is because a 1:8 scale means that for every actual unit of length, the corresponding length on the scale drawing is 8 times smaller.

Therefore, in order to find the dimensions of the scaled drawing of the flag, we must divide the actual dimensions (40 cm by 72 cm) by 8. The result is 4 cm by 7.2 cm.

It is important to make sure that you use the correct scale when attempting to determine the dimensions of a scaled drawing. If you use a different scale than the one intended, your result will be incorrect.

For example, if you use a 1:4 scale instead of a 1:8 scale, you will end up with a scaled drawing that has dimensions of 20 cm by 36 cm, which is double the correct answer.

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Answer:

16

Step-by-step explanation:

20-4=16

Step-by-step explanation:

You have selected the correct option

The growth rate of the bacterial colony after 3 hours is 32%, the population of a slowly growing bacterial colony after t hours is given by the function p(t) = 100 + 24t + 2t²

The growth rate of the colony is the rate of change of the population, which is given by the derivative of the function. The derivative of p(t) is p'(t) = 24 + 4t

The growth rate after 3 hours is p'(3) = 24 + 4 * 3 = 32. This means that the population of the colony is increasing by 32% after 3 hours.

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Answer:

6

Step-by-step explanation:

12 is the full length. point E marks 1/2 of the line. 12-6=6

if it's asking the length of d-e, then the answer is (6) because the entire length of line is twelve and in the top line e-f in 6 and 6-12=6

Answer:

737.75

Step-by-step explanation:

12.35h + .04c = salary

12.35 (45) + .04(4550) = salary

555.75 + 182 = salary

To find the argument of the complex number z = 1/16 - (sqrt(3)/16)i, we need to find the angle that the complex number forms with the positive real axis in the complex plane.

We can start by finding the magnitude of z, which is the distance between the origin and the point representing z in the complex plane:

|z| = sqrt( (1/16)^2 + (sqrt(3)/16)^2 )

= sqrt(1/256 + 3/256)

= sqrt(4/256)

= 1/4

Next, we can find the argument of z using the formula:

arg(z) = tan^(-1)(Im(z)/Re(z))

where Im(z) is the imaginary part of z, and Re(z) is the real part of z.

In this case, we have:

Re(z) = 1/16

Im(z) = -(sqrt(3)/16)

Therefore, we get:

arg(z) = tan^(-1)(Im(z)/Re(z))

= tan^(-1)(-(sqrt(3)/16)/(1/16))

= tan^(-1)(-sqrt(3))

= -60° (in degrees)

So, the argument of z is -60 degrees (or -π/3 radians).

Answer:

A

Step-by-step explanation:

Answer:

Option R

Step-by-step explanation:

The point S is the end point of ray.

What is line?

A line has length but no width, making it a one-dimensional figure. A line is made up of a collection of points that can be stretched indefinitely in opposing directions. Two points in a two-dimensional plane determine it.

According to the given information,

A ray's endpoint is a single point that denotes the conclusion of a line segment. In this instance, only one of the three lines that extend from point S contains a ray's terminus.

We must comprehend a ray's qualities in order to establish which location is the endpoint of a ray.

A ray originates at a single place and travels in one direction indefinitely. The beginning of the line segment is the endpoint of a ray.

We can see from the provided lines that the vertical line runs from point S via point R. Since it doesn't go on forever in one direction, this is not a ray example.

Similar to the vertical line,

The horizontal line also extends from point S through point T,

But it does not go on forever.

The third line is a ray because it is infinitely long in one direction and extends right and up from point S via point U.

Therefore, point S, the beginning of the line, is the endpoint of this ray.

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Answer:

  (X_1, X_2) = (2, 4)

  Z = 110

Step-by-step explanation:

You want a graphical solution to ...

  minimize Z = 15 X_1 +20 X_2

  subject to ...

A graph of the reverse of the inequalities is attached. This makes the feasible solution region be white (rather than shaded multiple times), so its vertices are easier to see. (The dashed lines are part of the solution space.)

The vertex of the solution space that minimized the objective function is (X_1, X_2) = (2, 4). The minimum value of Z is 110.

The following can be answered by the concept of Maxima and Minima.

The absolute extrema of the function f(x) = x^2 – 2x on the given intervals are:

(a) [−1, 2]: Minimum at (-1, 3), Maximum at (2, 0)

(b) (1, 3]: Minimum at (1, -1), Maximum at (3, 3)

(c) (0, 2): Minimum at (1, -1), Maximum at (0, 0)

(d) [1, 4): Minimum at (2, -2), Maximum at (1, -1)

To find the absolute extrema of a function on a given interval, we need to find the critical points of the function and evaluate the function at the critical points as well as the endpoints of the interval.

Firstly, we find the critical points of f(x) by taking its derivative and setting it equal to zero:

f'(x) = 2x - 2 = 0

x = 1

Now, we evaluate f(x) at the critical point and the endpoints of each interval:

(a) [−1, 2]:

f(-1) = 3

f(1) = -1

f(2) = 0

(b) (1, 3]:

f(1) = -1

f(3) = 3

(c) (0, 2):

f(0) = 0

f(1) = -1

f(2) = 0

(d) [1, 4):

f(1) = -1

f(2) = -2

f(4) = 8

Therefore, we can conclude that the absolute extrema of f(x) on each interval are as follows:

(a) [−1, 2]: Minimum at (-1, 3), Maximum at (2, 0)

(b) (1, 3]: Minimum at (1, -1), Maximum at (3, 3)

(c) (0, 2): Minimum at (1, -1), Maximum at (0, 0)

(d) [1, 4): Minimum at (2, -2), Maximum at (1, -1)

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Answer:450

Step-by-step explanation:

The correct answer is option (F) 450 cm

For a circle with radius 'r' and the central angle 'θ' (in radians), an arc length 's' is,

s = r × θ

C = 2 × π × r

We have been given that the length of xy (the minor arc) is 15 cm and angle = 12°.

⇒ θ = 0.209 radians

Let r be the radius of the circle.

xy = 15

⇒ r × θ = 15

⇒ r × 0.209 = 15

⇒ r = 71.77 cm

The circumference of the circle is,

C = 2 × π × r

⇒ C = 2 × π × 71.77

⇒ C = 450.95

⇒ C ≈ 450 cm

Therefore, the circumference of the circle is option (F) 450 cm

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Answer:

127 degrees f

Step-by-step explanation:

-117 + ? = 10

The value of 'E' in the algebraic equation is -2

Algebraic equation is a mathematical statement in which two expressions are set equal to each other.

Therefore, let solve for 'E' in the equation 0.75(8+e)=2−1.25e

Use 0.75 to open the bracket

6 + 0.75e = 2 -1.25e

Collect the like terms

0.75e+1.25e = 2-6

2e = -4

Divide both sides by 2

2e/ 2 = -4/2

e =-2

Therefore, the value of 'E' in the equation is -2

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Answer:

Because it is terminating.

Step-by-step explanation:

0.71875 is rational because it is terminating (has a clear end). If it were a bunch of random numbers that never ended, then it would be irrational.

0.71875 is a rational number because it is a terminating and non-repeating decimal.

Rational numbers are numbers that can be written as the ratio of two integers. For example: 1/2, 3/4, are rational numbers

Irrational numbers, any real number that cannot be expressed as the quotient of two integers—that is, p/q, where p and q are both integers. For example, there is no number among integers and fractions that equals Square root of√2.

Now,the given number is 0.71875

Here we see that digits after decimal 71875 stops,

hence the given number can be convert into fraction of the form a/b

So,

0.71875 = 71875/100000

So 0.71875 can be expressed in the form of a/b

Therefore 0.71875 is rational because it is a terminating and non-repeating decimal.

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Answer:

Step-by-step explanation:

You want two methods of choosing points on the line with slope 1/2 through A(-1, 2).

Writing the equation in standard form, we can find the x- and y-intercepts. To get there, we can start from point-slope form:

  y -k = m(x -h) . . . . . . line with slope m through point (h, k)

  y -2 = 1/2(x -(-1)) . . . . . using given slope and point

  2y -4 = x +1 . . . . . . . . . . multiply by 2

  x -2y =  -5 . . . . . . . . . . . . add -1 -2y

Setting x=0 tells us the y-intercept is ...

  0 -2y = -5

  y = -5/-2 = 5/2

So, the y-intercept is (0, 5/2).

Setting y=0 tells us the x-intercept is ...

  x -2(0) = -5

  x = -5

So, the x-intercept is (-5, 0).

It will be convenient to choose an arbitrary y-value to find another point on the line. We can pick y = 6, for example, Then the corresponding x-value is ...

  x -2y = -5

  x = -5 +2y = -5 +2(6) = 7

Another point on the line is (7, 6).

__

Additional comment

If we were to choose an arbitrary value for x, we would want it to be odd, so the corresponding y-value would be an integer. We chose to pick an arbitrary value of y so we didn't have to worry about how to make the x-value an integer.

<95141404393>

9514 1404 393

Answer:

  114°

Step-by-step explanation:

Angles LOM and MON are a linear pair, so are supplementary.

  x + 66 = 180

  x = 180 -66 = 114

The measure of ∠x is 114°.

The simplified value of the given expression 0 + (1/2)×(2. 219^2)*9. 81 is 24.143810005.

To simplify the expression, we can use the Order of Operations (PEMDAS): 1. Parentheses 2. Exponents 3. Multiplication 4. Division 5. Addition 6. Subtraction. Hence, to simplify the expression 0 + (1/2)×(2.219^2)*9.81, we need to follow the order of operations (PEMDAS).

1. The parentheses must be solved first: (2.219^2) = 4.924361

2. The exponents are solved next: there are none in this expression

3. The multiplication must be carried out next: 4.924361x9.81 = 48.30405741

4. The division is done next: (1/2)x48.30405741 = 24.143810005

5. The addition and subtraction are carried out last: 0 + 24.143810005 = 24.143810005

Therefore, the simplified expression is 24.143810005.

Note: The question is incomplete. The complete question probably is: Simplify the question 0 + (1/2)×(2. 219^2)*9. 81

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Answer:

X is 28

Step-by-step explanation:

All angles in a triangle ad up to 180 degrees.

85 + 67=152

180-152=28.

Hope it helped.

Answer:

28

Step-by-step explanation:

All triangles equal 180.

85+67=152

180-152=28

Your answer is 28

Hey there!

Assuming you meant:

5^3

IF SO, LETS SOLVE FOR IT!

5^3

= 5 * 5 * 5

= 25 * 5

= 25 + 25 + 25 + 25 + 25

= 50 + 50 + 25

= 100 + 25

= 125

Therefore, your answer is mostly likely:

125

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

The y-coordinate of the solution of the system is -10.

What is the linear equation?

A linear equation is an equation that describes a straight line in a two-dimensional space. It is a mathematical expression that relates two variables, usually x and y, such that one variable is a function of the other. The general form of a linear equation is:

y = mx + b

To find the y-coordinate of the solution of the system:

3x - y = 22 ...(1)

y = x - 14 ...(2)

We can substitute the expression for y from equation (2) into equation (1) to eliminate y:

3x - (x - 14) = 22

Simplifying this equation:

3x - x + 14 = 22

2x + 14 = 22

Subtracting 14 from both sides:

2x = 8

Dividing both sides by 2:

x = 4

Now we can substitute x = 4 into equation (2) to find the corresponding value of y:

y = x - 14

y = 4 - 14

y = -10

Therefore, the y-coordinate of the solution of the system is -10.

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Answer:

Step-by-step explanation:

40 l of 60% sugar syrup becomes 40 l of 45% sugar syrup if x l is drained and replaced with distilled water. Sugar content is then:

10 liters solution was replaced with distilled water

The solution to the inequality -3 < 2x - 3 is given as follows:

x > 0.

The inequality for this problem is defined as follows:

-3 < 2x - 3.

It can be rewritten as follows:

2x - 3 > -3.

We isolate the variable x, similarly to an equality, as follows:

2x > 0

x > 0/2

x > 0.

Hence all the options that have positive numbers are solutions to the inequality−3<2x−3.

The problem is incomplete, hence the answer was given on general terms.

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Answer:

1/2 inch: 3 feet

Step-by-step explanation:

It says in the bottom right corner.

Answer:2tt

Step-by-step explanation:

huh

Answer:

La respuesta correcta es B)

Ambos son pentágonos ordinarios pero no son exactamente idénticos