Zohar is using scissors to cut a rectangle with a length of 5x – 2 and a width of 3x + 1 out of a larger piece of paper. The perimeter of the rectangle is 2(5x – 2) + 2(3x + 1). If x = 4 centimeters, what is the total distance Zohar needs to cut with the scissors?a. (5x-2) (3x+1); 31 centimeters b. (5x-2) (3x+1); 36 centimeters c. 2(5x-2) 2(3x+1); 62 centimeters d. 2(5x-2) 2(3x+1); 70 centimeters

(i) The remainder is -12.

(ii) Concluded that x - 3 is a factor of p(x).

(iii) It can be express p(x) as (x - 3)(x² - x + 1).

c) The equation x(x - 2)² = 3 has only one real root, which is x = 3.

(i) To find the remainder when p(x) = x³ - 4x² + 4x - 3 is divided by x + 1, we can use synthetic division, which is shown in the attached image.

Here, the remainder is -12.

(ii) According to the Factor Theorem, if (x - a) is a factor of a polynomial p(x), then p(a) = 0.

Substitute x = 3 into p(x) to verify if x - 3 is a factor:

p(3) = 3³ - 4(3)² + 4(3) - 3

= 27 - 36 + 12 - 3

= 0

Since p(3) = 0, we can conclude that x - 3 is a factor of p(x).

(iii) Using the factor we found in part (ii), we can divide p(x) by (x - 3) using long division or synthetic division:

We obtain a quotient of x² - x + 1 and no remainder.

Therefore, we can express p(x) as (x - 3)(x² - x + 1).

(c) Now let's consider the original equation x(x - 2)² = 3.

We know that x = 3 is a root of p(x) = x³ - 4x² + 4x - 3, which means it satisfies the equation p(x) = 0.

Hence, x = 3 is a solution to the equation x(x - 2)² = 3.

Since (x - 3) is a factor of p(x) and the quadratic factor (x² - x + 1) does not have any real roots, the equation x(x - 2)² = 3 has only one real root, which is x = 3.

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a) An example of a polynomial of degree 5 for which x=1 is a critical number but not a local minimum nor a local maximum is:

P(x) = (x-1)^2(x-2)(x+1)(x+3)

To see why x=1 is a critical point but not a local minimum nor a local maximum, we can compute the first and second derivatives of P(x):

P'(x) = 2(x-1)(x-2)(x+1)(x+3) + (x-1)^2(x+1)(x+3) + (x-1)^2(x-2)(x+3) + (x-1)^2(x-2)(x+1)

P''(x) = 2(x-2)(x+1)(x+3) + 2(x-1)(x+1)(x+3) + 2(x-1)(x-2)(x+3) + 2(x-1)(x-2)(x+1) + 4(x-1)(x-2)(x+1)(x+3)

We can see that P'(1) = 0, so x=1 is a critical point. To determine whether it's a local minimum or maximum, we need to look at the sign of P''(1). However, computing P''(1) gives us:

P''(1) = 2(1-2)(1+1)(1+3) + 2(1-1)(1+1)(1+3) + 2(1-1)(1-2)(1+3) + 2(1-1)(1-2)(1+1) + 4(1-1)(1-2)(1+1)(1+3) = 16

Since P''(1) is positive, we know that x=1 is not a local maximum or a local minimum, but rather an inflection point.

b) To determine the intervals on which f(x) = (x-2)(x+3) is decreasing and increasing and find local minima and maxima, we can compute the first and second derivatives of f(x):

f'(x) = 2x+1

f''(x) = 2

We can see that f''(x) is always positive, so f(x) is always concave up. Therefore, any critical points of f(x) will be local minima. To find the critical points, we set f'(x) = 0:

2x+1 = 0

x = -1/2

So x=-1/2 is the only critical point of f(x). To determine whether it's a local minimum or not, we can look at the sign of f'(x) on either side of x=-1/2:

When x < -1/2: f'(x) < 0, so f(x) is decreasing.

When x > -1/2: f'(x) > 0, so f(x) is increasing.

Therefore, we know that x=-1/2 is a local minimum of f(x).

c) To determine the intervals on which f(x) = (x+1)(x-2)(x+3) is decreasing and increasing and find local minima and maxima, we can compute the first and second derivatives of f(x):

f'(x) = 3x^2-2x-7

f''(x) = 6x-2

To find the critical points of f(x), we set f'(x) = 0:

3x^2-2

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The nth harmonic number is defined as the sum of the reciprocals of the first n positive integers. We can calculate the nth harmonic number using the formula Hn=1+1/2+1/3+...+1/n.

Sure, I'll be glad to help you out!In mathematics, the nth harmonic number is defined as the sum of the reciprocals of the first n positive integers.

The nth harmonic number is defined to be:

$$H_n=1+\frac{1}{2}+\frac{1}{3}+\cdots+\frac{1}{n}$$

Now,  to understand the concept in detail.

For this purpose, let's consider an example:

If we want to find the 5th harmonic number, then we use the formula as shown below:

$$H_5=1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}$$

Simplifying the above expression we get:

$$H_5=\frac{1}{1}+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}$$$$\frac{1}{1}+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}=\frac{60}{60}+\frac{30}{60}+\frac{20}{60}+\frac{15}{60}+\frac{12}{60}$$$$

=\frac{137}{60}$$

Therefore, the 5th harmonic number is 2.2833.

Now, The nth harmonic number is defined as the sum of the reciprocals of the first n positive integers. We can calculate the nth harmonic number using the formula Hn=1+1/2+1/3+...+1/n.

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Answer:

A glide reflection is a two-step procedure in which the translation normally occurs along the line of reflection after the reflection.

A reflection is a single action, such as the reflection across y = x in the blue pre-image and the black dotted-line picture below.

A glide reflection is a two-step procedure in which the translation normally occurs along the line of reflection after the reflection.

In such situation, the blue pre-image is reflected across y = x and then translated by a factor of two to form the green picture.

The figure appears to be moving along the line after several repetitions.

A sine wave resembles the sine from zero to pi that has been repeatedly translated from "pi, 0" across the x-axis.

See the attachment. (Pre-image in blue Dots indicate reflection. Glider reflection picture is green.)

Cheers,

ROR

Answer:

A glide reflection is a two-step procedure in which the translation normally occurs along the line of reflection after the reflection.

Step-by-step explanation:

The normal curve can be used as an approximation to the binomial probability of at most 85 out of 136 DVDs malfunctioning, with the probability of a given DVD malfunctioning being 98%. The necessary conditions for using the normal curve as an approximation have been verified and met.

Probability is a measure of the likelihood of a certain event occurring. It is expressed as a number between 0 and 1, with 0 indicating that the event is impossible and 1 indicating that the event is certain. Probability is used to make predictions, assess risk, and make decisions in a variety of disciplines such as mathematics, finance, science, and engineering.

To verify the necessary conditions for a normal curve to be used as an approximation to the binomial probability, we must check if np ≥ 10 and nq ≥ 10, where n is the number of trials and p and q are the probabilities of success and failure, respectively. In this case, n = 136, p = 0.98 and q = 0.02. Thus, np = 134.08 ≥ 10 and nq = 2.72 ≥ 10.

Therefore, the necessary conditions for a normal curve to be used as an approximation to the binomial probability have been met. This means that the normal curve can be used as an approximation to the binomial probability of at most 85 out of 136 DVDs malfunctioning, with the probability of a given DVD malfunctioning being 98%.

In conclusion, the normal curve can be used as an approximation to the binomial probability of at most 85 out of 136 DVDs malfunctioning, with the probability of a given DVD malfunctioning being 98%. The necessary conditions for using the normal curve as an approximation have been verified and met, and so the normal curve is a valid approximation in this case.

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Answer:

Josh has played 12 MORE matches then her. Not 12 TIMES as many matches. The correct answer would be he haas played 12 more matches then her or 3 times as many matches as her.

Step-by-step explanation:

The distance between two locations on the same line of latitude can be calculated by summing the total distance between the points in degrees and multiplying it by the statute miles per degree for the shared line of latitude.

To calculate the distance in miles between two locations on the same line of latitude, we first need to find the total distance between the points in degrees. In the case of location A, which is 60°N, 30°W, and location B, which is 60°N, 50°E, the total distance between the two points is 80 degrees (50°E - 30°W).

Next, we need to multiply the sum of the degrees by the statute miles per degree for the shared line of latitude. Since the line of latitude is 60°N, we need to determine the statute miles per degree at that latitude.

The Earth's circumference at the equator is approximately 24,901 miles, and since a circle is divided into 360 degrees, the distance per degree at the equator is approximately 69.17 miles (24,901 miles / 360 degrees).

Multiplying the total distance in degrees (80 degrees) by the statute miles per degree (69.17 miles), we find that the distance between the two locations is approximately 5,533.6 miles.

Similarly, for location C, which is 30°S, 60°W, and location D, which is 30°S, 90°E, the total distance between the points is 150 degrees (90°E - 60°W). Since the line of latitude is 30°S, we use the same statute miles per degree value (69.17 miles).

Multiplying the total distance in degrees (150 degrees) by the statute miles per degree (69.17 miles), we find that the distance between the two locations is approximately 10,375.5 miles.

Therefore, the distance between locations A and B is approximately 5,533.6 miles, and the distance between locations C and D is approximately 10,375.5 miles, when calculated using the given method.

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The system of equations general solution is denoted by the following notation:

\(\[x = c_1 \cdot e^{\sqrt{51}t} \cdot \begin{pmatrix} 1 \\ \sqrt{51} - 5 \end{pmatrix} + c_2 \cdot e^{-\sqrt{51}t} \cdot \begin{pmatrix} 1 \\ -\sqrt{51} - 5 \end{pmatrix}\]\)

where t stands for the independent variable (time) and c_1 and c_2 are arbitrary constants.

What is Linear algebra?

The study of vector spaces and linear transformations is the focus of the mathematical field known as linear algebra. It includes the geometric and algebraic characteristics of matrices and vectors.

Vectors are used in linear algebra to describe quantities that have both a magnitude and a direction. They can be multiplied by one another, scaled using scalars, and put through a variety of procedures. Contrarily, matrices are rectangular arrays of numbers that can be used to represent a variety of mathematical structures, including systems of equations and linear transformations.

Let's begin by reformatting the system of equations into a matrix form in order to get the general solution:

\(\[x' = \begin{pmatrix} 5 & 1 \\ -26 & -5 \end{pmatrix} x\]\)

where x is the (x, y) column vector.

We can determine the eigenvalues and eigenvectors of the coefficient matrix (5 1; -26 -5) to solve this system.

We begin by computing the eigenvalues by resolving the defining equation:

\(\[\det(A - \lambda I) = 0\]\)

where A is the matrix of coefficients and I is the matrix of identities.

The characteristic equation is \(\(\begin{pmatrix} 5 & 1 \\ -26 & -5 \end{pmatrix}\)\) using the coefficient matrix.

\(\[\begin{vmatrix} 5 - \lambda & 1 \\ -26 & -5 - \lambda \end{vmatrix} = 0\]\)

Increasing the determinant's scope:

\(\((5 - \lambda)(-5 - \lambda) - (-26)(1) = 0\)\)

Simplifying:

\(\((\lambda - 5)(\lambda + 5) - 26 = 0\)\(\lambda^2 - 25 - 26 = 0\)\(\lambda^2 - 51 = 0\)\)

We obtain two eigenvalues after solving for :

\(\(\lambda_1 = \sqrt{51}\)\(\lambda_2 = -\sqrt{51}\)\)

Then, for each eigenvalue, we identify the matching eigenvectors.

If \(\(\lambda_1 = \sqrt{51}\):\((A - \lambda_1 I)v_1 = 0\)\)

Changing the values:

\(\((5 - \sqrt{51})v_1 + v_2 = 0\)\(-26v_1 + (-5 - \sqrt{51})v_2 = 0\)\)

We can use the free variable v_1 = 1 to solve these equations:

\(\(v_2 = \sqrt{51} - 5\)\)

As a result,\(\(v_1 = \begin{pmatrix} 1 \\ \sqrt{51} - 5 \end{pmatrix}\).\) is the eigenvector corresponding to _1 = sqrt(51).

In the same way, for \(\(\lambda_2 = -\sqrt{51}\):\((A - \lambda_2 I)v_2 = 0\)\)

Changing the values:

\(\((5 + \sqrt{51})v_3 + v_4 = 0\)\(-26v_3 + (-5 + \sqrt{51})v_4 = 0\)\)

We can use the free variable\(\(v_3 = 1\)\) to solve these equations:

\(\(v_4 = -\sqrt{51} - 5\)\)

As a result, \(\(v_2 = \begin{pmatrix} 1 \\ -\sqrt{51} - 5 \end{pmatrix}\).\) is the eigenvector corresponding to\(\(\lambda_2 = -\sqrt{51}\)\)

The system of equations general solution is denoted by the following notation:

\(\[x = c_1 \cdot e^{\sqrt{51}t} \cdot \begin{pmatrix} 1 \\ \sqrt{51} - 5 \end{pmatrix} + c_2 \cdot e^{-\sqrt{51}t} \cdot \begin{pmatrix} 1 \\ -\sqrt{51} - 5 \end{pmatrix}\]\)

where t stands for the independent variable (time) and c_1 and c_2 are arbitrary constants.

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Answer:

the answer is either B or C but I think it's C

Answer:

They trees on school property have no correlation with the students score on standardized tests

Step-by-step explanation:

this problem made no sense but hopefully this helps

Answer:

Step-by-step explanation:

Mass = volume * density

Mass  = 12*25 = 300 g

Answer:

300 g

Step-by-step explanation:

density = mass / volume

25g/cm^3 = mass / 12 cm^3

25 * 12 = mass

300 = mass

Answer:

THE LAST ONE

Step-by-step explanation:

it doesn't pass the vertical line test

Answer:

35

Step-by-step explanation:

10-20=-10

-10+45=+ 35

Answer:35

Step-by-step explanation:10-20=-10+45=35

Answer:

I think the answer is 2.56 = x

Step-by-step explanation:

pls like, vote, and give brainliest!

The inequality to show the values of [w] that will not exceed the weight limit of the elevator is w + 1643 ≤ 2000. On solving the inequality, we get w ≤ 357. The graph of the inequality is attached.

        ≤ : less than or equal to

        ≥ : greater than or equal to

        < : less than

        > : greater than

        ≠ : not equal to

Given is the maximum load for a certain elevator is 2000 pounds. The total weight of the passengers on the elevator is 1400 pounds. A delivery man who weighs 243 pounds enters the elevator with a crate of weight [w].

        1400 + 243 + w ≤ 2000

        w + 1643 ≤ 2000

        w + 1643 ≤ 2000

        w ≤ 2000 - 1643

        w ≤ 357

Therefore, the inequality to show the values of [w] that will not exceed the weight limit of the elevator is w + 1643 ≤ 2000. On solving the inequality, we get w ≤ 357. The graph of the inequality is attached.

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Answer:

180

Step-by-step explanation:

The 12 th square number is

12² = 12 × 12 = 144

The 6 th square number is

6² = 6 × 6 = 36

Thus

sum = 144 + 36 = 180

Answer:

-35

Step-by-step explanation:

Since there are  parentheses, you start with that. 3+4=7

Now, -5 x 7 =-35

Answer:

-35

hope this helps

have a good day :)

Step-by-step explanation:

3+4=7

-5 x 7=-35

Answer:

y = 4x + 31

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (- 8, - 1 ) and (x₂, y₂ ) = (- 7, 3 )

m = \(\frac{3-(-1)}{-7-(-8)}\) = \(\frac{3+1}{-7+8}\) = \(\frac{4}{1}\) = 4 , then

y = 4x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (- 7, 3 ) , then

3 = - 28 + c ⇒ c = 3 + 28 = 31

y = 4x + 31 ← equation of line

The surface area of the triangular prism is 152 sq, ft.

A triangular prism is a three-dimensional (3D) object having two identical triangle-shaped faces joined by three rectangular faces. The bases are the triangle faces, while the lateral faces are the rectangular faces. The top and bottom (faces) of the prism are other names for the bases.

The surface area of the triangular prism is given as:

SA = bh + (b1 + b2 + b3)l

Here, b = 6, h = 4, b1 = b2 = 5, b3 = 6 and l = 8.

Substituting the values we have:

SA = (6)(4) + (5 + 5 + 6) (8)

SA = 24 + (16)(8)

SA = 152 sq. ft.

Hence, the surface area of the triangular prism is 152 sq, ft.

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Lines that have the same slope are said to be parallel, and if the slope of one line is equal to the negative reciprocal of the slope of the other, the two lines are said to be perpendicular; otherwise, they are merely intersecting lines.

A line's slope in mathematics is defined as the ratio of the change in the y coordinate to the change in the x coordinate.

Both the net change in the y-coordinate and the net change in the x-coordinate are denoted by y and x, respectively.

m = Δy/Δx = dy/dx = change in y/change in x

where "m" represents a line's slope.

Additionally, the slope of the line may be shown as

tan θ = Δy/Δx

A line's slope often indicates the steepness and direction of the line.

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m = Δy/Δx = dy/dx = change in y/change in x

where "m" represents a line's slope.

Additionally, the slope of the line may be shown as

tan θ = Δy/Δx

Answer:

The range is 8

Step-by-step explanation:

Recall that the range of a data set is the distance between the maximum and the minimum, therefore:

Range = Maximum - Minimum = 9 - 1 = 8

Answer:

Subtract the minimum data value from the maximum data value to find the data range. In this case, the data range is

9−1=8

Step-by-step explanation:

So therefore,the range is 8

Answer:

\(4.\\\text{E. }x=5, x=-6,\\\\5.\\\text{A. }x=7, x=-3\\\\\text{18.}\\\text{D. No mistakes.}\)

Step-by-step explanation:

For \(a=|b|\), there are two cases:

\(\begin{cases}a=b,\\a=-b\end{cases}\)

Question 4:

Given \(5|2x+1|=55\),

Divide both sides by 5:

\(|2x+1|=11\)

Divide into two cases and solve:

\(\begin{cases}2x+1=11,2x=10, x=\boxed{5}\\-(2x+1)=11,2x+1=-11, 2x=-12, x=\boxed{-6}\end{cases}\)

Therefore, the solutions to this equation are \(\boxed{\text{E. }x=5, x=-6}\).

Question 5:

Given \(\frac{1}{2}|4x-8|-7=3\),

Add 7 to both sides:

\(\frac{1}{2}|4x-8|=10\)

Multiply both sides by 2:

\(|4x-8|=20\)

Divide into two cases and solve:

\(\begin{cases}4x-8=20,4x=28, x=\boxed{7}\\-(4x-8)=20, 4x-8=-20, 4x=-12, x=\boxed{-3}\end{cases}\)

Therefore, the solutions to this equation are \(\boxed{\text{A. }x=7, x=-3}\)

Question 18:

There are no mistakes in the solution shown. The answer properly isolates the term with absolute value with no algebraic mistakes. Following that, the answer divides the equation into both absolute value cases and solves algebraically correctly. Therefore, the correct answer is \(\boxed{\text{D. No mistakes.}}\)

In a normal distribution, with 10.03% of items below 35 kg and 89.97% below 70 kg, we need to find the mean and standard deviation of the distribution.

Let's denote the mean of the distribution as μ and the standard deviation as σ. In a normal distribution, we can use the properties of the standard normal distribution (with mean 0 and standard deviation 1) to solve this problem.

The given information allows us to calculate the z-scores corresponding to the weights of 35 kg and 70 kg. The z-score represents the number of standard deviations an observation is from the mean. Using z-scores, we can find the cumulative probabilities from a standard normal distribution table.

For the weight of 35 kg, the z-score can be calculated as (35 - μ) / σ. Using the standard normal distribution table, we can find the cumulative probability associated with this z-score, which is 10.03%.

Similarly, for the weight of 70 kg, the z-score can be calculated as (70 - μ) / σ. The cumulative probability associated with this z-score is 89.97%.

By looking up the corresponding z-scores in the standard normal distribution table, we can determine the z-values. Solving the equations (35 - μ) / σ = z1 and (70 - μ) / σ = z2, we can find the mean μ and standard deviation σ of the distribution.

In this way, we can use the properties of the standard normal distribution to calculate the mean and standard deviation of the given normal distribution based on the provided cumulative probabilities.

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Answer:

Part A: 4.5 cups

Part B: 3

Step-by-step explanation:

Part A:

We will have to find how many muffins he will make first if he uses all 7 cups.

# of muffins = 7/(2 + 1/3) = 3

Cups of sugar = 3 * (1 +1/2) = 4.5 cups

Part B:

We solved this in Part A

The number of muffins is 3

Answer:

the same:

a= b x h

22 x 12 =264

=[264cm]

Step-by-step explanation: