Chapter 5 Lesson 1 Adding and Subtracting Polynomials

Answer:

y=2(x+4)-3

Step-by-step explanation:

To make it parallel to y=2x+4, the slope needs to be the same

Point-slope form is: y=m(x-x1)+y1

In this case,

m = 2

x1 = -4

y1 = -3

So when put into point-slope form, it is y=2(x+4)-3

Answer:

None of the above

Step-by-step explanation:

The absolute value of a-b is equal to none of the above. say A was -4, and b was -1. -4 minus -1 is -3. absolute value of -3 is 3. so lets see if any problems equal 3. |a+b| = 5 (absolute value of -4+-1). a-b is -3. ((-4)-(-1))

The new coordinates is A'(-1,5) which is glide reflection of point A(-3,-3) where the translation is (x+2,y) and the line of reflection is y = 1.

Glide Reflection, it is known as composition of transformations.

In glide reflection, before reflected over a line it translation is first performed on the figure.

The coordinate of A are given as (-3,-3).

The rule of translation is (x, y) → (x+2,1)  and the line of reflection is y=1.

Now,

Applying the rule of translation, we get;

A = (-3, -3) → (-3+2, -3) = (-1, -3)

Since, -3 which is 4 unit below line of reflection,

then,

after reflection, over the line  y=1 we get, the reflected point A' would be 4 units above line of reflection

so, A' (-1, 1+4) =(-1, 5)

Therefore, the coordinate of A' (-1, 5).

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the mean absolute deviation of the set {16, 10, 22, 18, 4, 18, 14, 24, 16, 22} is 4.68.

To find the mean absolute deviation of a set of numbers, we first need to calculate the mean of the set.

The mean of the set {16, 10, 22, 18, 4, 18, 14, 24, 16, 22} is:

Mean = (16 + 10 + 22 + 18 + 4 + 18 + 14 + 24 + 16 + 22) / 10 = 16.4

Next, we need to calculate the absolute deviation of each number from the mean. The absolute deviation is the absolute value of the difference between the number and the mean.

The absolute deviations for each number in the set are:

|16 - 16.4| = 0.4

|10 - 16.4| = 6.4

|22 - 16.4| = 5.6

|18 - 16.4| = 1.6

|4 - 16.4| = 12.4

|18 - 16.4| = 1.6

|14 - 16.4| = 2.4

|24 - 16.4| = 7.6

|16 - 16.4| = 0.4

|22 - 16.4| = 5.6

Now, we need to find the mean of the absolute deviations.

Mean absolute deviation = (0.4 + 6.4 + 5.6 + 1.6 + 12.4 + 1.6 + 2.4 + 7.6 + 0.4 + 5.6) / 10

Mean absolute deviation = 4.68

Therefore, the mean absolute deviation of the set {16, 10, 22, 18, 4, 18, 14, 24, 16, 22} is 4.68.

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Answer:

A=∫

1

3

x

2

dx

A=[

3

x

3

]

1

3

A=(

3

27

−

3

1

)

A=

3

26

Therefore , the solution of the given problem of angles comes out to be x has a value of 150°.

The two sides of a tilt in Euclidean geometry are actually spherical faces that divide at the centre and top of barrier. At the point where two rays meet, they might combine to form an angle. Angle is another outcome of two entities interacting. They mirror dihedral forms the most. A two-dimensional curve can be created by arranging two line beams in various configurations at their ends.

Here,

Since AE and BD are parallel, we can calculate the value of angle ABD using the alternate internal angles theorem:

=> BCD x ABD = 180

=>ABD = 150°, ABD + 30° Equals 180°.

Now, we can use the knowledge that a triangle's angles sum to 180 degrees to determine what angle AED is worth:

180° from ABD + AED + EDC is 150° from

=>AED + 180° is 180°.

=>AED = -150°

=>AED Plus BAE = 180

=> BAE + 30° = 180°

=> BAE = 150°

In order to determine the value of angle AEB, we can use the knowledge that the angles in a triangular sum to 180°:

=>AED 180° BAE AEB

=> AEB + 150° + 30° = 180°

=>AEB = 0°

.Points A, E, and B are collinear because angle AEB is 0°, and angle x equals angle ECD:

=> Angle BCD x = 180° - 30° x = 150° x = ECD = 180°

Consequently, x has a value of 150°.

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Therefore , the solution of the given problem of probability comes out to be 3 flights will depart on time is roughly 0.311, the likelihood that at most 4 flights will depart on time is roughly 0.672,

Finding the likelihood that a claim is true or that a specific event will occur is the primary objective of the branch of mathematics known as parameter estimation. Any number between range 0 but rather 1, where 1 is usually used to symbolise certainty and 0 is typically used to represent possibility, may be utilized to represent chance. A probability diagram shows the chance that a specific event will occur. .

Here,

=> P(X = k)  = (n choose k) * p * k * (1-p) (n-k)

where p is the chance of success and (1-p) is the probability of failure, (n choose k) is the binomial coefficient, and P(X = k) is the probability of k successes in n trials.

The likelihood that precisely 3 planes will depart on time is:

P(X = 3)

=> (6 choose 3) * 0.60 * 0.40 * 0.311

The likelihood that up to 4 planes depart on time is:

=> P(X <= 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)

         = > (6 choose 0) * 0.60^0 * 0.40^6 + (6 choose 1) * 0.60^1 * 0.40^5 + (6 choose 2) * 0.60^2 * 0.40^4 + (6 choose 3) * 0.60^3 * 0.40^3 + (6 choose 4) * 0.60^4 * 0.40^2

         ≈> 0.672

The likelihood that at least three planes will depart on time is:

P(X >= 3) = 1 - P(X < 3)

         = 1 - P(X = 0) - P(X = 1) - P(X = 2)

         = 1 - (6 choose 0) * 0.60^0 * 0.40^6 - (6 choose 1) * 0.60^1 * 0.40^5 - (6 choose 2) * 0.60^2 * 0.40^4

         ≈ 0.695

=> P(X>=3) = 1 - P(X3) = 1 - P(X0) - P(X = 1) - P(X = 2)

=>  1 - (6 choose 0) (6 choose 0) * 0.60^0 * 0.40^6 - (6 choose 1) (6 choose 1) * 0.60 * 0.40 * 6 (select 2) * 0.60 * 0.40 * 4

≈> 0.695

Therefore, the likelihood that precisely 3 flights will depart on time is roughly 0.311, the likelihood that at most 4 flights will depart on time is roughly 0.672, and the likelihood that at least 3 flights will depart on time is roughly 0.695.

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Simplifying the expression, we get: ∫(49 - 5x^2) dx ∫(3x^2 - 1) dx = (44/3)x^3 + 48x + C

what is integration?

Integration is a fundamental concept in calculus that involves finding the integral of a function. The integral of a function is essentially the opposite of differentiation, and it involves finding the area under the curve of the function.

we have:

∫(a - bx^2) dx = ax - (b/3)x^3 + C

where C is the constant of integration.

Applying this formula to the first integral, we have:

∫(49 - 5x^2) dx = 49x - (5/3)x^3 + C1

where C1 is the constant of integration for the first integral.

Similarly, applying Theorem 8.2 to the second integral, we have:

∫(3x^2 - 1) dx = x^3 - x + C2

where C2 is the constant of integration for the second integral.

Therefore, the indefinite integral of the given expression is:

∫(49 - 5x^2) dx ∫(3x^2 - 1) dx = 49x - (5/3)x^3 + C1 + x^3 - x + C2

where C = C1 + C2 is the constant of integration for the entire expression.

Therefore Simplifying the expression, we get:

∫(49 - 5x^2) dx ∫(3x^2 - 1) dx = (44/3)x^3 + 48x + C

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The first and fifth expressions are equal to the fraction, the second expression is less than the fraction and the third, fourth, and sixth expressions are greater than the fraction.

In this case, to better understand the numbers and expressions given, let's simplify each of the expressions.

3/4 or 0.75

Firs expression: 7/7 x 3/ 4 = 1 x 0.75 = Equal to

Second expression: 1/3 x 3/4 = 0.33 x 0.75 = 0.24 = Less than

Third expression: 9/7 x 3/4 =  1.28 x 0.75 = 0.96 = Greater than

Fourth expression: 3/4 x 3/4 = 0.75 x 0.75 = 1.5 = Greater than

Fifth expression: 5/5 x 3/4 = 1 x 0.75 = 0.75 = Equal to

Sixth expression: 5/2 x 3/4 = 2.5 x 0.75 = 1.5= Greater than

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The equation given is:

396 = 66t

This equation relates the distance traveled (396 miles) to the rate of travel (66 miles per hour) and the time it takes to travel that distance (t hours).

We can rearrange this equation to solve for the constant of proportionality, which is the rate of travel:

66t = 396

Dividing both sides by 66, we get:

t = 6

Therefore, the constant of proportionality in the equation is 66. The correct answer is C.

(a)   25-44

(b)   45-64

(a) The 2×3 table of local odds ratios for the association between age group and education level is as follows:

The odds ratio corresponding to the strongest of these pairwise associations is 1.78, which indicates that adults aged 45-64 are 78% more likely to have a high school diploma than adults who are 25-44.

(b) The 2×3 table of odds ratios for the association between age group and education level when treating the youngest age group and highest education level as the baseline categories for comparison is as follows:

The odds ratio corresponding to the strongest of these pairwise associations is 1.48, which indicates that adults aged 25-44 are 48% more likely to have a high school diploma than adults aged 45-64.

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Combined translation, rotation, reflection, and enlargement to create a vibrant average pattern on fabric that represents me.

My design would consist of a colorful pattern with a variety of forms, including circles, triangles, squares, and stars. I would mix several transformations, such as translation, rotation, reflection, and enlargement, to get this design. I would first create the shapes and then move them across the cloth using translation and transformation. The forms would then be rotated using the rotation transformation. I would also apply the reflection transformation to the same forms to produce a mirror appearance. Ultimately, I would enhance certain forms while reducing others using the transformation. The cloth would have a distinctive and dynamic appearance that symbolizes me as a person thanks to this mix of alterations.

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Answer:

We can use the Pythagorean theorem to find the length of the hypotenuse:

c^2 = a^2 + b^2

where c is the length of the hypotenuse, and a and b are the lengths of the other two sides.

Plugging in the given values, we get:

c^2 = 16^2 + 10^2

c^2 = 256 + 100

c^2 = 356

Taking the square root of both sides, we get:

c = sqrt(356)

c ≈ 18.9

Therefore, the length of the hypotenuse is approximately 18.9 cm.

The measure of the smaller angle is 10 degrees. We find the measure of the larger angle, we can substitute x = 10 into the expression, the measure of the larger angle is 170 degrees.

When two angles form a linear pair, they are adjacent angles that share a common side and form a straight line. The sum of the measures of these two angles is always 180 degrees.

Let x be the measure of the smaller angle in this problem. Since the ratio of the measures of the two angles is 1:17, we can express the measure of the larger angle in terms of x by multiplying 17 to x. Thus, the measure of the larger angle is 17x.

To find the value of x, we can use the fact that the sum of the measures of the two angles is 180 degrees. So we have:

x + 17x = 180

Simplifying the equation, we get:

18x = 180

Dividing both sides by 18, we obtain:

x = 10

Therefore, the measure of the smaller angle is 10 degrees. To find the measure of the larger angle, we can substitute x = 10 into the expression we derived earlier for the measure of the larger angle:

17x = 17(10) = 170 degrees

Hence, the measure of the larger angle is 170 degrees.

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The sample space can then be written as: S = {(Y,U), (Y,T), (Y,C), (W,U), (W,T), (W,C), (R,U), (R,T), (R,C)}Thus, the sample space consists of nine possible outcomes or options.
The sample space for this experiment is composed of all the possible combinations of the two variables (paint color and finish). The possible combinations are:

Therefore, the sample space is {Y + U, Y + T, Y + C, W + U, W + T, W + C, R + U, R + T, R + C}.
Here, the experiment involves choosing a paint color and a finish for a game room and entertainment center respectively. We are given that there are three paint color options and three finish options. Therefore, the sample space can be written as follows:

Let Y, W, and R represent the paint colors yellow, white, and red respectively. Let U, T, and C represent the finish options unfinished, teak, and cherry respectively.

Each outcome is an ordered pair, where the first element represents the paint color option and the second element represents the finish option.

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The probability that a randomly chosen individual will experience actual unfavorable effects is roughly 0.9025, or 90.25%.

The percentage of genuine positive results—both true positive and true negative—in the chosen population is represented by the accuracy score's numerical number. 99% of the time, whether the test result is positive or negative, it is accurate.

We can write: Applying the law of total probability

P(B|¬A) = P(B|¬A,¬T)P(¬T|¬A) + P(B|¬A,T)P(T|¬A),

To calculate P(B|¬A,¬T), the probability that the test is negative given that the person does not have Covid-19 and the test is negative, we can use the complement rule:

P(B|¬A,¬T) = 1 - P(¬B|¬A,¬T),

P(¬B|¬A,¬T) = 1 - P(B|¬A,¬T) = 1 - 0.95 = 0.05.

P(B|¬A) = P(B|¬A,¬T)P(¬T|¬A) + P(B|¬A,T)P(T|¬A)

= (1 - P(¬B|¬A,¬T))P(¬T|¬A) + P(B|¬A,T)P(T|¬A)

= (1 - 0.05) x 0.95 + 0 x 0.1

= 0.9025.

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The function value is csc 330° = -2.

Function establishes the relationship between input and output. The x-intercept, y-intercept, and slope of any function are calculated using function formulas. You could also figure out the vertex of a quadratic function. Moreover, a graph of the function can be created for a range of x values.

Since the sine of 360 degrees (which has a sine of 0) is similar to 30 degrees being subtracted from it, we can determine using the unit circle that the sine of 330 degrees is equal to -1/2 and thus the sine function is negative in the fourth quadrant. The reciprocal of sine 330 degrees, which is -2/1 or -2, is the cosecant of 330 degrees.

Thus, csc 330° = -2.

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The required angle of the incline of the hill, to the nearest degree, is 37 degrees.

We can use trigonometry to find the angle of the incline of the hill.

we can see that Nick has hiked 10 miles up the hill, and is now at point A. His starting point is at point O, which is 8 miles east of A. Let's call the angle at A, between the incline of the hill and the horizontal ground, theta.

We can use the tangent function to find theta:

[tex]$$\tan(\theta) = \frac{h}{8}$$[/tex]

where h is the height of the hill (the distance from A to the horizontal ground at O).

We know that Nick hiked 10 miles up the hill, so we can use the Pythagorean theorem to find h:

[tex]$$h^2 = 10^2 - 8^2 = 36$$[/tex]

Therefore,

[tex]$$h = \sqrt{36} = 6$$[/tex]

Substituting into the equation for tangent, we get:

[tex]$\tan(\theta) = \frac{6}{8} = 0.75$$[/tex]

To find the angle whose tangent is 0.75, we can use the arctangent function:

[tex]$$\theta = \arctan(0.75)$$[/tex]

Using a calculator, we find that

[tex]$$\theta \approx 36.87^{\circ}$$[/tex]

Therefore, the angle of the incline of the hill, to the nearest degree, is 37 degrees.

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In mathematics, the word "of" is also regarded as one of the arithmetic operations, denoting multiplication between brackets. So far, 312440 copies have been sold.

A number or ratio that can be expressed as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The percentage therefore refers to a part per hundred. Per 100 is what the word percent means.
In mathematics, the word "of" is also regarded as one of the arithmetic operations, denoting multiplication between brackets.
We are given that the copies sold on first release date= 42800 copies.

And this is the 7.3 of the number of copies sold on date.

So, let the number of copies sold out on date is x.

Therefore, x= 7.3*42800 OR [tex]x= \frac{73}{10} * 42800= 73*4280= 312440[/tex]

Hence, the number of copies sold out on the date are 312440.

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Answer: (3/6) then (2/6)

Step-by-step explanation:

FRACTIONS: YOU TIMES IT SO THE DENOMINATOR IS THE SAME APPLY THE NUMBER YOU TIMED BY THE NUMERATOR.

Answer:

Step-by-step explanation:

[tex]sin45=\frac{x}{4}[/tex]      [tex](sin=\frac{opposite}{hypotenuse})[/tex]

[tex]x=4sin45[/tex]    

  [tex]=\frac{4}{\sqrt{2}}[/tex]

  [tex]=\frac{4}{\sqrt{2}}\times\frac{\sqrt{2}}{\sqrt{2}}[/tex]

  [tex]=\frac{4\sqrt{2} }{2}[/tex]

  [tex]=2\sqrt{2}[/tex]

[tex]cos45=\frac{y}{4}[/tex]     [tex](cos=\frac{adjacent}{hypotenuse})[/tex]

[tex]y=4cos45[/tex]

  [tex]=\frac{4}{\sqrt{2}}[/tex]

  [tex]=2\sqrt{2}[/tex]

After 12 years, Ariana would have 366.65 more in her account than Kylie, to the nearest dollar.

The formula used to calculate the amount of money Ariana would have in her account after 12 years is [tex]A = Pe^rt[/tex], where A is the amount of money, P is the principal amount (initial investment), e is the mathematical constant (2.71828), r is the rate at which interest is compounded, and t is the time (in years).

Kylie's total amount after 12 years would be calculated using [tex]A = 2800(1.055)^12[/tex], while Ariana's total amount would be calculated using [tex]A = 2800(2.71828)^(0.0575*12)[/tex].

After substituting the values into the formulas, Kylie would have 4,841.22 in her account and Ariana would have 5,207.87 in her account. This means that Ariana would have 366.65 more than Kylie in her account, to the nearest dollar.

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In total, there are 8! (8 factorial) ways that the 8 finalists can stand on the stage. 8! = 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 40,320. This means that there are 40,320 possible combinations in which the 8 finalists can stand on the stage.

To calculate this, we can use the formula n!, which stands for n factorial. n! is the product of all the numbers from n down to 1, so 8! is 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1. This formula can be used to find the total number of combinations that 8 people can stand in on the stage.
It's important to remember that the order matters in this case, so a configuration where the finalists are standing in a line is different from a configuration where they are standing in a circle.
In conclusion, there are 40,320 ways in which the 8 finalists can stand on the stage. This can be determined by using the formula n!, which stands for n factorial.

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The submarine will take 14 seconds to safely reach the surface.

Speed is a measure of how quickly an object is moving, calculated as the distance traveled per unit time.

The submarine rises 183 feet, which means its depth decreases by 183 feet. Therefore, its depth is now 375 - 183 = 192 feet below sea level.

The submarine then dives 228 feet, which means its depth increases by 228 feet. Therefore, its depth is now 192 + 228 = 420 feet below sea level.

To reach the surface, the submarine needs to ascend a distance of 420 feet.

The speed of the submarine is given as 30 feet per second. Therefore, the time it will take for the submarine to reach the surface can be calculated as:

[tex]Time = \frac{Distance}{Speed} = \frac{420}{30}[/tex]

= 14 seconds

Therefore, it will take the submarine 14 seconds to safely reach the surface.

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Since, the triangle FGH is a right angle triangle, The angles of the ∠F = 62°, ∠G = 90° and ∠H = 28°.

Right Angle Triangle:

A right triangle (American English) or right triangle (UK), or more formally an orthogonal triangle, formerly known as a right triangle, is a triangle in which one angle is a right angle (i.e. say an angle of 90 degrees), i.e. two of its sides are perpendicular. The relationship between the sides of a right triangle and the other angles is the basis of trigonometry.

According to the Question:

Interior angles of a triangle add up to 90 degrees

∠F + ∠ G + ∠H = 180

⇒ 9x - 1 + 90 + 3x + 7 = 180

⇒ 12x + 96 = 180

⇒ 12x = 180 - 96

⇒ 12x = 84

⇒ x = 84/12

⇒ x = 7

Therefore,

∠F = 9x - 1 = 9(7) - 1 = 63 - 1 = 62

And, ∠G = 90

And, ∠ H = 3x + 7 = 3(7) + 7 = 21 + 7 = 28

If we add the angles :

62 + 90 + 28 = 180°

Complete Question:

Triangle FGH is a right triangle. Angle G is a right angle, m∠F = 9x – 1, and m∠H = 3x + 7. What is m∠F?

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The probability of correctly answering both questions with random guesses is 5.6%.

There are 6 possible answers, so the probability of randomly guessing the correct answer is 1/6. Similarly, for the second question, there are 3 possible answers, so the probability of randomly guessing the correct answer is 1/3.

Since the two questions are independent events, meaning that the outcome of one question does not affect the outcome of the other question, we can find the probability of both events occurring by multiplying their probabilities together. Therefore, the probability of randomly guessing both answers correctly is:

P(both answers correct) = P(first answer correct) * P(second answer correct)

= (1/6) * (1/3)

= 1/18

The probability is 1/18 or about 0.056 or 5.6% when rounded to one decimal place.

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The correlation here in the provided graph is a positive trend and the equation for line of best fit will be as follows:

y = 1/4x

Correlation is a statistical method for determining the association or relationship between two variables. To put it another way, the correlation coefficient formula facilitates the calculation of the correlation coefficient, which assesses the degree to which one variable depends on another.

The correlation coefficient is a numerical indicator of correlation. Between -1 and 1, the correlation coefficient is found. An inverse association between two variables is shown by a negative correlation coefficient. A high correlation coefficient means that the two variables directly affect one other's values. There is no association between the two variables, according to a zero-correlation coefficient.

Here in the question,

The graph shows a positive trend as its increasing upwards. The equation for the line of best fit will be y =1/4x.

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Answer:

see below

Step-by-step explanation:

[tex]SA = 2\pi r \ \ (h+r)[/tex]

[tex]130=2(3.14)(7\div2)(h+(7\div2))[/tex]

[tex]130\div(2(3.14)(7\div2)) = h+(7\div2)[/tex]

[tex]5.91=h+(7\div2)[/tex]

[tex]h = 5.91-3.5[/tex]

Answer Below: