Suppose that the tangent line to the curve y = f (x) at the point (-9, -67) has equation y = -4 + 7x. If Newton's method is used to locate a root of the equation f(x) = 0 and the initial approximation is X1 = -9, find the second approximation x2: = = = = = (b) Suppose that Newton's method is used to locate a root of the equation f(x) 0 with initial approximation X1 9. If the second approximation is found to be X2 = -9, and the tangent line to f(x) at x = 9 passes through the point (17,2), find f(9). = (c) Use Newton's method with initial approximation X1 = - 9 to find x2, the second approximation to the root of the equation x3 = 3x – 8. = Problem #5(a): Enter your answer symbolically, as in these examples Problem #5(b): Enter your answer symbolically, as in these examples Problem #5(c): Enter your answer symbolically, as in these examples

Answer:

D)  The y-axis only tests whether x = 0 has been mapped to more than one y coordinate.

Step-by-step explanation:

The y-axis is a vertical line and intersects the x-axis (horizontal line) at the origin (0, 0) when both x and y are zero.

Vertical line test

A graph represents a function if and only if all vertical lines intersect the graph at most once.

Therefore, the strategy of using only the y-axis as the vertical line in the vertical line test is flawed because the y-axis only tests whether x = 0 has been mapped to more than one y-coordinate.

Answer:

NaN x \(100^{0}\)

Step-by-step explanation:

Answer: Approx 4.6

Step-by-step explanation:

5 necklaces, each 11/12 feet

(5*11)/12

55/12

a. Because the population diameter of tennis balls is approximately normally distributed, the sampling distribution of samples of size 10 will also be approximately normal b. The probability that the sample mean is less than 2.53 inches is approximately 0.1736.

a. The correct answer is A. Because the population diameter of tennis balls is approximately normally distributed, the sampling distribution of samples of size 10 will also be approximately normal.

b. To calculate the probability that the sample mean is less than 2.53 inches, we need to calculate the z-score and find the corresponding cumulative probability from the standard normal distribution.

First, we calculate the z-score using the formula:

z = (X - μ) / (σ / √n)

Where X is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size.

Plugging in the values, we have:

z = (2.53 - 2.55) / (0.06 / √10)

Calculating this, we find:

z ≈ -0.9428

Next, we look up the cumulative probability corresponding to this z-score using a standard normal distribution table or a statistical calculator. The cumulative probability for a z-score of -0.9428 is approximately 0.1736.

Therefore, the probability that the sample mean is less than 2.53 inches is approximately 0.1736.

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Answer:

y=4500x+32000

Step-by-step explanation:

If they are increasing at a constant rate of 4500 then that is the coefficient of x, and if they received a 32000$ donation then that is the y-intercept so you add that to 4500x to get this equation.

Hope this answer helped!

5285 meters x 0.001 = 5.285 km

Multiplying the length in meters by 0.001 converts it to kilometers.

Answer:

Step-by-step explanation:

Sorry I can't explain how it is done. It is very difficult to explain on paper.

Rate of change of function  on the interval  is; 6.

Step-by-step explanation:

Given the function:  on the interval

Rate of change of function: Let f be the function defined on the interval , then the rate of change of function A(x) is given by:

A(x) =

at x = 2;

h(2) =

and at x = 4

h(4) =

then, by the definition of rate of change of function:

A(x) =

Substitute the value of h(2) = 4 and h(4) = 16 we have;

Therefore, the rate of change of function is 6.

Answer:

18.50 ft

Step-by-step explanation:

Add 1.25 to the length:

3 + 1.25 = 4.25

The formula for the perimeter of a rectangle is: L + L + W + W.

To find the perimeter quicker, multiply the length and width by 2, then add.

5.00(2) = 10.00

4.25(2)= 8.50

10.00 + 8.50 = 18.50

By applying the Simplex Method or Big M Method to the given problem, the optimal solution for minimizing the objective function Z = 4x₁ + 2x₂ subject to the given constraints is obtained. The optimal solution for the given problem is Z = -27, x₁ = 6, and x₂ = 3.

To solve the given problem using the Simplex Method or Big M Method, we follow these steps:

Step 1: Convert the problem into standard form:

Introduce slack variables to convert inequalities into equations.

Express any unrestricted variables as the difference of two non-negative variables.

The given problem can be converted into the following standard form:

Minimize Z = 4x₁ + 2x₂

subject to:

3x₁ + x₂ + s₁ = 27

-x₁ - x₂ = 21

x₁ + 2x₂ + s₂ = 30

x₁, x₂, s₁, s₂ ≥ 0

Step 2: Set up the initial Simplex tableau:

Construct the initial tableau using the coefficients of the objective function and the constraints:

  | Cj   | x₁ | x₂ | s₁ | s₂ | RHS |

------------------------------------

Z  | -4   |  0 |  0 |  0 |  0 |  0  |

------------------------------------

s₁ |  0   |  3 |  1 |  1 |  0 | 27  |

------------------------------------

s₂ |  0   |  1 |  2 |  0 |  1 | 30  |

------------------------------------

Step 3: Perform iterations of the Simplex Method:

We start with the initial tableau and iterate until we reach an optimal solution. I will provide the final tableau directly:

| Cj   | x₁ |  x₂ |  s₁ |  s₂ |  RHS |

----------------------------------------

Z  | -2   | 0  |  0  |  1  | -2  |  -27 |

----------------------------------------

x₁ |  1   | 1  |  0  | -1  |  1  |   6  |

----------------------------------------

s₂ |  0   | 0  |  1  | -0.5|  0.5|   3  |

----------------------------------------

The optimal solution is obtained when all the coefficients in the Z row (except Cj) are non-positive. I

n this case, Z = -27, x₁ = 6, and x₂ = 3. The objective function is minimized when x₁ = 6 and x₂ = 3, resulting in Z = -27.

Therefore, the optimal solution for the given problem is Z = -27, x₁ = 6, and x₂ = 3.

Note: The steps provided above show the general process of solving a linear programming problem using the Simplex Method or Big M Method. The exact calculations and iterations may vary depending on the specific values and coefficients in the problem.

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The sentence that includes a transition showing that the ideas are similar to the ideas in the previous sentence is: "In addition, forests provide natural beauty." Option C

The transition phrase "In addition" indicates that the information being presented is related or similar to the previous sentence. It suggests that there is an additional point or aspect that supports the idea discussed earlier.

Transitional words and phrases are used to create coherence and establish logical connections between ideas in a text. They help readers understand the flow of information and the relationships between different parts of a written work.

In this case, the transition "In addition" signals that the sentence will provide another reason or benefit associated with forests. It indicates that the new information will complement or support the idea expressed in the previous sentence.

Other transitional phrases, such as "However," "Conversely," and "In contrast," introduce contrasting ideas or points of view, which are different from the previous sentence. These transitions indicate a shift in the direction or a contradiction between the ideas being presented.

Option C

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Answer:

The #4 graph represents

Step-by-step explanation:

i plugged the inequalitites into desmos.

(see below)

Answer:

Step-by-step explanation:

just use division

-2 is the value of linear equation .

What in mathematics is a linear equation?

An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.

                     Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

= 3a - 4a^2 + 5b

PUT a = -2 and b=4

= 3 * -2 - 4 * (-2)² + 5 * 4

= -6 - 16 + 20

=  - 22 + 20

= - 2

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Answer:

10.5

Step-by-step explanation:

2.99 divided by 2 = 1.495 x 7 = 10.465, rounded is 10.5.

Answer:

x = 12

Step-by-step explanation:

\((4x - 5) \degree +(3x + 11) \degree = 90\degree \\(complementary \: \angle s) \\ \\ (4x - 5 + 3x + 11)\degree = 90\degree \\ \\ (7x + 6)\degree = 90\degree \\ \\ 7x + 6 = 90 \\ \\ 7x = 90 - 6 \\ 7x = 84 \\ \\ x = \frac{84}{7} \\ \\ x = 12\)

Answer:

0.5 years

Step-by-step explanation:

Answer:

28

Step-by-step explanation: You need to divide 7 by 1/4. Whenever you divide fractions you keep the first number as it is, change the sign to multiplication and write the reciprocal of the second fraction which is you have to flip the fraction. It is going to be 7 times 4/1. Which is 28/1 which is 28.

Answer:

Thomas draws a triangle with side lengths of 5 centimeters and 12 centimeters and one angle of 90°.  The length of the longest side of the triangle is not known.

How many different triangles can be drawn with these dimensions? Explain your reasoning.

Step-by-step explanation:your weclome

The number of triangles that can be drawn with these dimensions will be one.

The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.

Thomas draws a triangle with side lengths of 5 centimeters and 12 centimeters and one point of 90° The length of the longest side of the triangle isn't known.

The longest side of the triangle is given as,

H² = P² + B²

H² = 12² + 5²

H² = 144 + 25

H² = 169

H = 13 cm

If the three dimensions of the triangle are known, then the number of possible triangles is only one.

The number of triangles that can be drawn with these dimensions will be one.

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A parallel line would contain the same slope and have a different y-intercept.

Using the slope of the original line you would start with:

Y = -5x + b, where b is the new y-intercept.

Using the given point replace x and y and solve for b:

-9 = -5(-4) + b

Simplify:

-9 = 20 + b

Subtract 20 from both sides

-29 = b

Now replace b in the equation to get:

Y = -5x -29

Answer: sample of 100

:3

Answer:

The equation in point-slope form is: y - 5 = 4(x - 2).

The equation in standard form is: 4x - y + 3 = 0.

Answer:

Standard form

4x - y = 3

Step-by-step explanation:

Point slope form of a line equation is:
y - y1 = m(x - x1)

where
(x1, y1) is a point on the line and m is the slope

The standard form of a line equation is:
Ax + Bc = C
where
A, B, C are integers

Slope Point Form

Given
(x1, y1) = (2, 5)
m = 4

The slope-point equation is
y - y1 = m(x - x1)

which is

y - 5 = 4(x - 2)

Expanding the bracket on the right side:
y - 5 = 4x  - 8

Move constant -5 to the right to become +5
y = 4x - 8 + 5 = 4x - 3

Move 4x to left becoming -4x

y - 4x = -3

or

-4x + y = -3

same as

4x - y = 3

This is the standard form with A = -4, B = 1 and C = 13

In Isosceles ΔABC, m AB and m BC are congruent to each other.

We have,

Isosceles ΔABC is inscribed in D.

By the property of inscribed angles,

When an angle is inscribed in a circle, its measure is half the measure of the arc it intercepts.

In the case of an isosceles triangle inscribed in a circle, the base angles intercept congruent arcs, which means that they have equal measures.

Since the triangle is isosceles, the base angles are also congruent to each other.

Therefore, the two base angles are congruent and intercept congruent arcs, which means that they have the same measure.

So, we can conclude that in an isosceles triangle inscribed in a circle, the base angles are congruent, and therefore the two sides opposite to them (mAB and mBC) are congruent as well.

Hence, If isosceles triangle ABC is inscribed in circle D, then we can conclude that mAB and mBC are congruent, which means that they have the same measure.

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Answer:

\(x = 7 \sqrt[3]{2} \)

The graph of the function is attached

The domain is the set of all real numbers and the range is (-∝, 2]

From the question, we have the following parameters that can be used in our computation:

Function of the ramp height: f(x) = -1/2|x - 24| + 2

Next, we plot the ramp height function, f(x) = -1/2|x - 24| + 2 on a graph

See attachment for the graph of the function

The key features to explore here are the domain

The above equation is an absolute value equation

An absolute value equation can take any value as its input

This means that the domain is the set of all real numbers

When represented as an interval, we have

The domain is (-∝, ∝)

For the range

Here, we have

f(x) = -1/2|x - 24| + 2

The above equation is an absolute value function

An absolute value function represented as

y = a|x - h| + k

Where

Vertex = (h, k)

So, we have

Vertex = (24, 2)

Remove the x value

y = 2

Because the leading coefficient is negative, then the vertex is a maximum

i.e. (-∝, 2]

So, the range is (-∝, 2]

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Answer:

Triangle STU is not similar to Triangle VWU

Step-by-step explanation:

For two triangles to be similar, they both should have the same angle measures. To find out if they have the same angle measures, we have to solve for the unknown angles. Remember, a triangle is worth 180°.

Triangle STU:

Triangle VWU:

As you can see, the angles don't have the same angle measures. Thus, they are not similar.

The distance of the boat from its starting point is 156.226 .

According to the question

A boat sails on a bearing of 63 degree for 124 miles

i.e

By making 63 degree covers 124 miles

therefore ,

In figure below

AC = 124 miles

Then turns and sails 201 miles on a bearing of 192 degree

therefore ,

In figure below

CD = 201 miles  

Now,

According to the sum of triangle

∠ACB + ∠ABC + ∠BAC = 180°

∠ACB + 90° + 63° = 180°

∠ACB = 27°

CE = 180°  (Straight line )

therefore,

∠DCE = 192°  -  180°

          = 12°

As ∠C = 90°

therefore

∠ACD = ∠C - ∠DCE - ∠ACB

          = 90° - 12°- 27 °

          = 51°

Now,

The distance of the boat from its starting point = AD

By using Law of Cosines

As

The Law of Cosines can be used to find the unknown parts of an oblique triangle(non-right triangle), such that either the lengths of two sides and the measure of the included angle is known (SAS) or the lengths of the three sides (SSS) are given.

The Law of Cosines (also called the Cosine Rule) says:

c² = a² + b² − 2ab cos(C)

As we have 2 sides and one angle available we can use   Law of Cosines

Therefore,

by substituting the value

(AD)² = (AC)² + (CD)² − 2(AC)(CD) cos(∠ACD)

(AD)² = (124)² + (201)² − 2*124*201 cos(51)

AD = 156.226

Hence, the distance of the boat from its starting point is 156.226 .

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Answer:

$68000

Step-by-step explanation:

Answer:

$6800

Step-by-step explanation:

30x1600+10x2000

=48000+2000

=68000