In your opinion, which is the best and simplest way to factor polynomials (including quadratics)? Explain why you chose this method compared to other methods. Are there some exceptions to this, maybe a polynomial that might factor better with another method?

The measures ∠2 = 135°, ∠5 = 45°, ∠6 = 135°, ∠4 = 45° and  ∠3 = 135°.

An angle is formed when two straight lines or rays meet at a common endpoint.

The angle ∠1 = 45° is given.

Types of the angles are as follows;

Supplementary angle - Two angles are said to be supplementary angles if their sum is 180 degrees.

Corresponding angle - If two lines are parallel then the third line. The corresponding angles are equal angles.

Vertically opposite angle - When two lines intersect, then their opposite angles are equal.

Alternate angle - If two lines are parallel then the third line will make z -angle and z-angles are equal angles with the parallel lines.

∠1 + ∠2 = 180°    (Supplementary angle)

45° + ∠2 = 180°

∠2 = 135°

∠1 = ∠5 = 45°   (Corresponding angle)

∠2= ∠6 = 135°

∠4 = 45° (Alternate angle)

∠3 = 135°   (Alternate angle)

Hence, the measures ∠2 = 135°, ∠5 = 45°, ∠6 = 135°, ∠4 = 45° and  ∠3 = 135°.

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The camp charge per week = slope = $25 per week.

The slope is also referred to as the unit rate which is given as: m = change in y / change in x.

From the given scenario, let:

x = number of weeks

y = camp charges

We will therefore have these two points:

(6, 190) and (9, 265)

Use the two points to find the slope, which is the swimming camp charge per week:

Camp charge per week (m) = change in y / change in x = 265 - 190 / 9 - 6

= 75/3

= $25 per week.

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The cost of one rose shrub costs $12 and one pot of ivy costs $24, respectively.

It takes two equations with two variables to solve a system of equations. The variables can then be solved for using algebraic techniques like substitution or elimination.

Let x be the cost of one rose bush and y be the cost of one pot of ivy.

From Mei's purchase, we have:

3x + y = 36

From Ming's purchase, we have:

9x + 8y = 168

Use the first equation to solve for y:

y = 36 - 3x

Substituting this into the second equation, we get:

9x + 8(36 - 3x) = 168

9x + 288 - 24x = 168

-15x = -120

x = 8

Substituting x = 8 into equation of y, we get:

y = 24

Hence, the cost of one rose bush is $8, and the cost of one pot of ivy is $24.

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Answer:

q - 8

Step-by-step explanation:

q - 8

Answer:

q=0

Step-by-step explanation:

There are 1 and 3/5 of 5/8 in 1, if Its supposed to be a mixed number.

What is a mixed number?

A mixed number is a combination of a whole number and a fraction. It is written in the form of "a b/c" where a is the whole number, b is the numerator of the fraction, and c is the denominator of the fraction.

To answer your second question, we can divide 1 by 5/8 as follows:

1 ÷ 5/8 = (1 x 8) ÷ 5 = 8/5

We can then write 8/5 as a mixed number by dividing the numerator (8) by the denominator (5) and writing the remainder as the fraction part.

8 ÷ 5 = 1 with a remainder of 3, so we write the answer as:

1 3/5

Therefore, there are 1 and 3/5 of 5/8 in 1.

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If a poisson process rate was 1.5 (15 events in 10 min) with a mean of 0.387, then

a) p(no events for 3 min) - 0.0498

b) p(1 event in 1 min) - 0.3347

c) p(>= 1 event in 1 min) - 0.7769

d) uncertainty for a, b, c - For a), σ = 1.732 and for b) and c), σ = 1.225

A Poisson process is a stochastic process that counts the number of events in a given time interval. It is characterized by two parameters: the rate, λ, which is the average number of events in a given time interval, and the mean, μ, which is the average number of events in the entire process.

a) The probability of no events in 3 minutes is given by the Poisson probability mass function:

P(X = 0) = (λt)^0 * e^(-λt) / 0! = e^(-λt)

Where t is the time interval (3 minutes), and λ is the rate (1.5 events per minute). Plugging in the values gives:

P(X = 0) = e^(-1.5 * 3) = 0.0498

b) The probability of 1 event in 1 minute is given by the Poisson probability mass function:

P(X = 1) = (λt)^1 * e^(-λt) / 1! = λt * e^(-λt)

Where t is the time interval (1 minute), and λ is the rate (1.5 events per minute). Plugging in the values gives:

P(X = 1) = 1.5 * e^(-1.5) = 0.3347

c) The probability of at least 1 event in 1 minute is given by the complement of the probability of no events:

P(X >= 1) = 1 - P(X = 0) = 1 - e^(-λt)

Where t is the time interval (1 minute), and λ is the rate (1.5 events per minute). Plugging in the values gives:

P(X >= 1) = 1 - e^(-1.5) = 0.7769

d) The uncertainty for each of the probabilities is given by the standard deviation of the Poisson distribution:

σ = sqrt(λt)

For a), the standard deviation is:

σ = sqrt(1.5 * 3) = 1.732

For b) and c), the standard deviation is:

σ = sqrt(1.5 * 1) = 1.225

Therefore, the uncertainty for each of the probabilities is given by the standard deviation.

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Answer:

d>500

t>130

Step-by-step explanation:

For the first problem:

we must set up an inequality to answer :D soooo:

d>500

the same thing goes for the second one:

t>130

Hope this is right!

The order of the number from least to greatest will be -12, |3|, |-4|, 10. Then the correct option is D.

It is the order of the numbers in which a smaller number comes first and then followed by the next number and then the last number will be the biggest one.

The numbers are given below.

|-4|, 10, -12, |3|

Determine the absolute value of the numbers, then we have

|-4| = 4

10 = 10

-12 = -12

|3| = 3

The order of the number from least to greatest will be given as,

-12, 3, 4, 10

-12, |3|, |-4|, 10

Thus, the correct option is D.

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Answer:

I don't know dude...............

The measure of the 2 angle in the triangle is 55 degrees.

In geometry, a kite is a quadrilateral with two pairs of adjacent sides that are equal in length. This means that a kite is a special type of quadrilateral called a "tangential quadrilateral" because its sides can be inscribed in a circle.

If one angle of a triangle is a right angle (90 degrees) and another angle is 35 degrees, then the sum of the three angles in the triangle is 180 degrees.

Therefore, the measure of the third angle can be found by subtracting the sum of the other two angles from 180 degrees:

Third angle = 180 degrees - 90 degrees - 35 degrees

Third angle = 55 degrees

So the measure of the 2 angle in the triangle is 55 degrees.

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Answer:

The total travel time is the sum of the time it takes to travel in the morning and the time it takes to travel in the evening.

Total travel time = (morning travel time) + (evening travel time)

= (4x + 13) + (10x - 2)

= 14x + 11

Therefore, the total travel time is 14x + 11. Answer: B.

Answer:

B: 14x+11

Step-by-step explanation:

i took the test and got it right

40000000

Step-by-step explanation:

ezy Peasy lemon squeeze

Answer:40,000,000

Step-by-step explanation:

its just like 2 divided by 8 which is 4 then just add all your zeros

The graph and the solution to the system of inequalities are added as attachments

System 1

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

x ≤ -3

y < 5/3x + 2

The above system is a system of inequalities that contain two linear inequalities

Next, we plot the graph

One of the points in the shaded region is (-4, -5)

System 2

Here, we have the following system

y ≤ -5/2x - 2

y < -1/2x + 2

The above system is a system of inequalities that contain two linear inequalities

Next, we plot the graph

One of the points in the shaded region is also (-4, -5)

System 3

Here, we have the following system

y ≥ 2/3x + 3

y > -4/3x - 3

The above system is a system of inequalities that contain two linear inequalities

Next, we plot the graph

One of the points in the shaded region is also (4, 7)

See attachment for the graph of the inequalities

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Assuming a constant rate of production, 360 workers can produce approximately 7200 widgets in 20 hours.

The problem asks how many widgets can be produced by 360 workers in 20 hours. To solve this problem, we need to use the formula:

widgets = rate x time x workers

We know the time is 20 hours and the number of workers is 360. We need to find the rate at which the workers can produce widgets. Let's assume that each worker can produce one widget in one hour, so the rate is 1 widget per worker-hour.

Substituting the values, we get:

widgets = 1 x 20 x 360

widgets = 7200

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The component form of bar (xY) = [[36],[30]] and aph bar (xY) = [[36, 30]]

To express bar (xY) in component form, we need to multiply the matrices x and Y together. The result will be a 2x1 matrix, which is the component form of bar (xY).

First, we multiply the first row of x by the first column of Y:

[-9] * [-4] = 36

Next, we multiply the second row of x by the second column of Y:

[10] * [3] = 30

Now we can put these two results together to get the component form of bar (xY):

bar (xY) = [[36],[30]]

To aph bar (xY), we simply take the transpose of the matrix. This means that we switch the rows and columns:

aph bar (xY) = [[36, 30]]

So the final answer is:

bar (xY) = [[36],[30]]
aph bar (xY) = [[36, 30]]

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The volume of the oblique cone is  5887.5 ft³.

A cone is a three-dimensional geometric shape with a smooth and curving surface and a flat base, with an increase in the height radius of a cone decreasing to a certain point.

The volume of a cone is (1/3)πr²h.

The total surface area of a cone is πr(r + l).

The curved surface area is πrl.

We know, The volume of an oblique cone is, (1/3)×B×h.

Where h = height and B = area of the base.

Here the area of the base is, π(15)² = 706.5 ft², and the height is 25 feet.

Therefore, The volume is,

= (1/3)×706.5×25.

= 5887.5 ft³

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1.  A transition matrix is regular if there is a positive integer k such that P^k has all positive elements.

2. The value of x2 =  [128,295, 44,557]T.

3. The value of x = [0.701, 0.299, 0]T .

1. P is a regular transition matrix because it has all positive elements, meaning that it is possible for any state to transition to any other state.

2. To find the state vector x2, we need to multiply the initial state vector x0 by the transition matrix P twice:
x2 = P^2 * x0
= P * P * x0
= P * [72 * 10 + 75 * 7, 32 * 10 + 31 * 7]T
= P * [945, 457]T
= [72 * 945 + 75 * 457, 32 * 945 + 31 * 457]T
= [128,295, 44,557]T

3. To find the steady state vector, we need to solve the equation Px = x for x. This means that we need to find the eigenvector of P corresponding to the eigenvalue

1. We can do this by finding the null space of (P - I), where I is the identity matrix:

(P - I)x = 0
=> [71 -75 0, -32 30 0, 0 0 -1]x = 0
=> x = c[75, 32, 0]T, where c is a constant.

To find the steady state vector, we need to normalize this eigenvector so that it sums to 1:
x = [75/107, 32/107, 0]T
= [0.701, 0.299, 0]T

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Answer:

3

Step-by-step explanation:

cuz ik

The product of ((2)/(3)x+(4)/(3)) and (2x+(5)/(6)) as a trinomial in simplest form is (4/3)x^2 + (13/9)x + (10/9).

To express the product of ((2)/(3)x+(4)/(3)) and (2x+(5)/(6)) as a trinomial in simplest form, we need to multiply the two binomials using the distributive property.

First, we will multiply the first term of the first binomial by each term of the second binomial:
(2/3)x * 2x = (4/3)x^2
(2/3)x * (5/6) = (10/18)x = (5/9)x

Next, we will multiply the second term of the first binomial by each term of the second binomial:
(4/3) * 2x = (8/3)x
(4/3) * (5/6) = (20/18) = (10/9)

Now we will combine like terms:
(4/3)x^2 + (5/9)x + (8/3)x + (10/9) = (4/3)x^2 + (13/9)x + (10/9)

Therefore, the product of ((2)/(3)x+(4)/(3)) and (2x+(5)/(6)) as a trinomial in simplest form is (4/3)x^2 + (13/9)x + (10/9).

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The constant term is 8, which means that the y-intercept of the graph of g is (0, 8).

In mathematics, a function is a rule that assigns a unique output value for every input value in a set. It is a relation between a set of inputs and a set of possible outputs, with the property that each input is related to exactly one output. Functions are widely used in various fields of mathematics, science, engineering, and technology to model and analyze real-world situations, to describe how quantities depend on one another, and to solve problems.

Here,

If we set k=4, the function g(x) becomes:

g(x) = k(x+2) = 4(x+2)

The value of k affects the slope of the graph of g compared to the graph of f. In this case, since k=4, the slope of the graph of g is 4 times the slope of the graph of f.

The slope of the graph of f is 1, since the coefficient of x is 1. Therefore, the slope of the graph of g is:

4 * 1 = 4

This means that the graph of g is steeper than the graph of f.

The y-intercept of the graph of f is 2, since the constant term is 2. Setting k=4 does not affect the y-intercept of the graph of g, since the constant term remains the same:

g(x) = 4(x+2) = 4x + 8

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The required length of side CD is 22 units.

Since the perimeter of the rectangle is 80 units, we can use the formula for the perimeter of a rectangle, which is:

perimeter = 2(length + width)

In this case, we know that the perimeter is 80 units, so we can write:

80 = 2(length + width)

We also know that CD is a side of the rectangle, so it must be either the length or the width. Let's assume that CD is the length, so we can write:

CD = 4z + 2

Substituting this expression for the length into the formula for the perimeter, we get:

80 = 2(4z + 2 + width)

Simplifying the right-hand side, we get:

80 = 8z + 4 + 2width

Subtracting 4 from both sides, we get:

76 = 8z + 2width

Dividing both sides by 2, we get:

38 = 4z + width

Now we can use the fact that CD is a side of the rectangle to substitute for width. Since the opposite side of the rectangle must also have length 4z + 2, we can write:

width = 3z + 3

Substituting this into the previous equation, we get:

38 = 4z + 3z + 3

Simplifying the right-hand side, we get:

38 = 7z + 3

Subtracting 3 from both sides, we get:

35 = 7z

Dividing both sides by 7, we get:

5 = z

Now we can substitute this value of z into the expression for CD:

CD = 4z + 2 = 4(5) + 2 = 22

Therefore, the length of side CD is 22 units.

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The determinant of the inverse of an invertible matrix is the reciprocal of the determinant of the original matrix.

Determinants: The determinant of an invertible matrix A is a scalar value that is used to indicate the invertibility of the matrix. If the determinant of A is non-zero, then the matrix is invertible. The determinant of the inverse of an invertible matrix is the reciprocal of the determinant of the original matrix. In other words, det(A−1)=det(A)1​.

To prove this, we can use the property of determinants that det(AB)=det(A)det(B) for any two square matrices A and B. Since A is an invertible matrix, we know that AA−1=I, where I is the identity matrix. Taking the determinant of both sides of this equation gives us:

det(AA−1)=det(I)

Using the property of determinants mentioned above, we can rewrite the left-hand side of the equation as:

det(A)det(A−1)=det(I)

Since the determinant of the identity matrix is 1, we can simplify the equation to:

det(A)det(A−1)=1

Dividing both sides of the equation by det(A) gives us:

det(A−1)=det(A)1​

Therefore, the determinant of the inverse of an invertible matrix is the reciprocal of the determinant of the original matrix.

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Answer:108.73

Step-by-step explanation: To get the total sales tax you add box of the taxes together wich gives you 7.75%, then you find the total amount of money he spent, which was 1402.96. Lastly you find 7.75% of 1402.96 which is 108.73

Among Jack, Pandu and  Sam, Pandu scored the best as his marks scored percentage is 60%.

In mathematics, a percentage is a number or ratio that can be expressed as a fraction of 100. If you need to calculate the percentage of a number, divide the number by the whole number and multiply by 100. Percentages therefore mean 1 in 100. The word percent means around 100. Represented by the symbol '%'. 

Solution according to the information given:

Jack's percentage = (5/10)×100

                               = 50%

Sam's percentage = (22/40)×100

                               = (11/20)×100

                               = 55%

Pandu's percentage = (12/20)×100

                                  = 60%

Thus, Pandu scored the best marks by scoring 60%.

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The volume of the rectangular prism is 11.28 feet³.

In terms of geometry, a rectangular prism is a polyhedron having two parallel, congruent bases. It also goes by the name cuboid. A rectangular prism is made up of six rectangles, each with twelve edges.

We are given that a rectangular prism has the following dimensions:

Length (l) = 4.7 feet

Width (w) = 1.5 feet

Height (h) = 1.6 feet

We know that

Volume (V) = [tex]l \times w \times h[/tex]

From this, we get

⇒V = [tex]4.7 \times 1.5 \times 1.6[/tex]

⇒V = 11.28 feet³

Hence, the volume of the rectangular prism is 11.28 feet³.

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Answer: Your answer is 11.28 ft³

Step-by-step explanation: 4.7 x 1.5 x 1.6 = 11.28 you have to do it in this order also I did the k12 quiz here's proof.

Hope it helped :D

The diagonals are 17.4 inches

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

DH = 10, HK = 8.2, KB = 6, HR = 8 and KY = 6.8

Given that DHB is a right triangle, we have

DB² = HB² + DH²

So, we have

DB² = (8.2 + 6)² + 10²

DB² = 301.64

Take the square root

DB = 17.4

The triangles DBY and RYB are congruent triangles

So, we have

RY = 17.4

The figure is an isosceles triangle, and the length does not meet the regulation

This is so because the length is less than the required 20 inches

The two non-parallel sides of an isosceles triangle are of equal length

So, we have

1/2x + 5 = 2x - 4

Evaluate the like terms

3/2x = 9

This gives

x = 9 * 2/3

x = 6

So, we have

KR = 1/2x + 5

This gives

KR = 1/2 * 6 + 5

KR = 8

So, the value of KR is 8 units

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There are 24 five-pound bags of potatoes in the crate.

The crate contains a total of 6 bags of potatoes weighing 10 pounds each, which is a total of 60 pounds.

So, the remaining weight of the crate is 180 pounds - 60 pounds = 120 pounds.

Let's assume that there are x five-pound bags of potatoes in the crate.

Therefore, the total weight of these x bags of potatoes would be 5x pounds.

We know that the weight of the entire crate is 180 pounds,

60 pounds (weight of 6 bags of 10-pound potatoes) + 5x pounds (weight of x 5-pound bags of potatoes) = 180 pounds (weight of the entire crate)

60 + 5x = 180

5x = 180 - 60

5x = 120

x = 24

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Answer:

[tex]x = \frac{y}{3} - 1[/tex]

Step-by-step explanation:

[tex]1. \: 4y - 8 - 4 = 12x \\ 2. \: 4y - 12 = 12x \\ 3. \: \frac{4y - 12}{12} = x \\ 4. \: \frac{4(y - 3)}{12} = x \\ 5. \: \frac{y - 3}{3} = x \\ 6. \: - 1 + \frac{y}{3} = x \\ 7. \: \frac{y}{3} -1 = x \\ 8. \: x = \frac{y}{3}-1[/tex]

[tex](\stackrel{x_1}{-2}~,~\stackrel{y_1}{-4})\hspace{10em} \stackrel{slope}{m} ~=~ \cfrac{1}{2} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-4)}=\stackrel{m}{ \cfrac{1}{2}}(x-\stackrel{x_1}{(-2)}) \implies y +4= \cfrac{1}{2} (x +2) \\\\\\ y+4=\cfrac{1}{2}x+1\implies {\Large \begin{array}{llll} y=\cfrac{1}{2}x-3 \end{array}}[/tex]