(n^4-14n^3+51n^2-19n-30)/(n-8) Synthetic Division

The length of the rectangular prism is 4/5x.

What is a rectangular prism?

Six faces make up the three-dimensional shape of a rectangular prism (two at the top and bottom and four are lateral faces). The prism has rectangular shapes on each of its faces. There are therefore three sets of identical faces in this picture. A cuboid is another name for a rectangular prism because of its shape.

We know that Volume of a rectangular prism is a product of length, height and width.

We are given volume as (7/x)-(3/5x).

The width(w) is 2/x and the height(h) is 4/x

Using the formula, we get

⇒ V = lwh

⇒ (7/x)-(3/5x) = l * (2/x) * (4/x)

⇒ l = [(7/x)-(3/5x)] / [(2/x) * (4/x)]

⇒ l = (32/5x) /(8/x^2)

⇒ l = 4/5x

Hence, the length of the rectangular prism is 4/5x.

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The logarithmic function that describes the graph is given as follows:

[tex]f(x) = \log_2{(x + 1)}[/tex]

The parent logarithmic function is defined as follows:

f(x) = log(x).

Which, no matter the base, has the vertical asymptote given as follows:

x = 0.

The vertical asymptote of the graphed function is given as follows:

x = -1.

Hence:

[tex]f(x) = \log_a{(x + 1)}[/tex]

When x = 3, f(x) = 2, hence the base a is obtained as follows:

[tex]2 = \log_a{(4)}[/tex]

Meaning that:

a² = 4.

a = 2.

And the function is then defined as follows:

[tex]f(x) = \log_2{(x + 1)}[/tex]

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The answers to all parts are shown below.

To determine the quantity or percentage of something in terms of 100, use the percentage formula. Per cent simply means one in a hundred. Using the percentage formula, a number between 0 and 1 can be expressed. A number that is expressed as a fraction of 100 is what it is. It is mostly used to compare and determine ratios and is represented by the symbol %.

Given:

7. CP of sound system = 499

loss= 45%

So, the selling price = 499 - 45% of 499

                                  = R 274.45

8. original price is =1084

The new price = 1084 + 8% of 1084

                                  = R 1,170.72

9. Percentage decreased

= ( 747 - 599) / 747 x 100

= 19.81%

10. Mandisa left with

= 1000 - (228.95 + 573.38)

= R 197.67

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Given the expressions, f(x)=√x+5, g(x)=3x-7, and h(x)=5x, the answer to f(g(5)) is 8. This is because when g(5) is substituted into f(x) we get f(g(5))=f(3x-7)=√(3x-7)+5. When 5 is substituted for x, this simplifies to f(g(5))=√(-2)+5 which equals 8.

The answer to g(f(78)) is 60. This is because when 78 is substituted into f(x) we get f(78)=√78+5 which simplifies to f(78)=9. When 9 is substituted into g(x) we get g(f(78))=3x-7 which simplifies to g(f(78))=3(9)-7 which equals 60.

Finally, the answer to h(g(f(2))) is 83. This is because when 2 is substituted into f(x) we get f(2)=√2+5 which simplifies to f(2)=3. When 3 is substituted into g(x) we get g(f(2))=3x-7 which simplifies to g(f(2))=3(3)-7 which equals 8. When 8 is substituted into h(x) we get h(g(f(2)))=5x which simplifies to h(g(f(2)))=5(8) which equals 83.

In summary, the answers to f(g(5)), g(f(78)), and h(g(f(2))) are 8, 60, and 83 respectively.

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The height of the highest point of the trajectory and the horizontal distance the golf ball travels before hitting the ground will be 360 .6 meters

Apparently, x is the distance from the place where the ball is impacted on the ground.

The ball's horizontal speed, given by s, can be calculated using the equation cos(50) = s/60, where s = 38.5 mps.

Size is represented by f(x). The highest point of the parabola would be at -b/2a = -1.19/-.0066 = 180.3 metres, meaning the ball has moved 180.3 metres.

Input 107.28 metres into the formula to find the height.

In order to calculate the distance travelled, the ball must be on the ground, hence f(x) = 0.

-.0033x^2 + 1.19x = 0

x*(-.0033x + 1.19) = 0

x= 1.19/.0033 = 360 .6 meters

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Answer:

Step-by-step explain

You have to solve for 5a

Answer:

Scalene Triangle

Step-by-step explanation:

Right triangles have 90 degree angles. Isosceles triangles have 2 equal sides. While, equilateral triangles have 3 equal sides.

The number √5 + √16 is an irrational number

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

\sqrt{5}+\sqrt{16}

Express properly

So, we have the following representation

√5 + √16

Take the square root of 16

This gives

√5 + 4

Rewrite as

4 + √5

The above expression is an irrational number

This is so because of the radical symbol on 5

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Perimeter of Regular Polygon = 92cm (Number of sides) x (Side length of a polygon) units

The total length of a polygon's boundary is calculated as the polygon's perimeter. Due to the fact that polygons are closed plane shapes, their perimeters likewise reside in a two-dimensional plane. A polygon's perimeter is always measured in linear distances such as metres, centimetres, inches, feet, etc.

Based on the length of its sides, we can classify a polygon as either regular or irregular. The formula for several well-known polygons' perimeter is as follows:

A triangle's perimeter is equal to its three side lengths, a, b, and c.

A rectangle's perimeter equals 2 (length + width).

We first determine whether the given polygon is a regular polygon or an irregular polygon before computing the perimeter of the polygon. The polygon's perimeter is then determined using the proper Formula

Therefore, the formula to find the perimeter of a regular polygon is: Perimeter of regular polygon = (number of sides) × (length of one side)

From the given diagram;

Perimeter of the polygon = AB + BC+ CD + DA

Perimeter of the polygon = 10.5 + 11.5 + 12.5 + 11.5 + 11.5 + 12.5 + 11.5 + 10.5

Perimeter of the polygon = 22 + 24 + 24 + 22

Perimeter of the polygon = 46 + 46

Perimeter of the polygon = 92cm

Hence the Perimeter of the polygon is 92cm

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The number of years that will take for the schools to have the same number of students is given as follows:

11 years.

The number of students in each school is modeled by linear functions in slope-intercept format, as follows:

y = mx + b.

In which:

The functions for this problem are given as follows:

They will have the same number of students when:

Sp(t) = Se(t).

Hence:

1074 + 19t = 1206 + 7t

12t = 132

t = 132/12

t = 11 years.

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Answer: To check if a given value is a root of the equation 8x-4 = 2, we can substitute the value into the equation and see if it makes the equation true.

When we substitute 3 for x in the equation 8x-4=2, we get 8(3)-4=2, which simplifies to 24-4=2, which is not true. So, 3 is not a root of the equation.

To check if a given value is a root of the equation 4y + 5 = y-7, we can substitute the value into the equation and see if it makes the equation true.

When we substitute -4 for y in the equation 4y + 5 = y-7, we get 4(-4) + 5 = -4-7, which simplifies to -16+5=-11=-4-7, which is true. So, -4 is a root of the equation.

Step-by-step explanation:

Answer:

1. y= (x-3)^2+5 vertex form

2. y= 2(x+2)^2+4 vertex form

3. y= 3x^2+18x+20 general form

4. y= x^2+4x+8 general form

The value of the car in the year of 2017 would be of:

$295.

A decaying exponential function is given as follows:

y = a(1 - r)^x.

In which:

The initial value for this problem is of:

a = 16900.

After 8 years, the value was of 1400, hence the decay rate is obtained as follows:

16900(1 - r)^8 = 1400

(1 - r)^8 = 1400/16900

((1 - r)^8)^1/8 = (1400/16900)^1/8

1 - r = 0.73245368177

Hence the function is:

y = 16900(0.73245368177)^x.

2017 is 13 years after 2004, hence the value would be of:

y = 16900(0.73245368177)^13

y = $295.

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the value of function g[h(0)] at x = 0 is 3.

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain.

Given that,the functions f(x) = 3x, g(x) = x + 4 , and h(x) = x² − 1

Since,

G(h(x)) = x² - 1 +4

G(h(x)) =  x² + 3

Thus at x = 0

G(h(0)) =  0² + 3

G(h(0)) =  3

therefore, the value of function g[h(0)] at x = 0 is 3.

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Symmetry is a way of measuring the shape of a data set. It is defined as the similarity between the upper and lower halves of a distribution.

A symmetric distribution is one where the data is equally distributed around a central point. To calculate this, you need to subtract the mean (the average of the values) from each data point and then divide by the standard deviation (the measure of how much the data is spread out). The formula for symmetry is: (x-mean)/standard deviation. An example of a symmetric distribution would be the scores of a group of students on an easy test. If the mean score was 70 and the standard deviation was 10, then any score between 60 and 80 would be considered symmetric.

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There is more variability on glasses of doctor B's dataset than the glasses of doctor A's dataset

Now, According to the question:

The doctors' mean absolute deviation on glasses

The dataset of doctor A is given as:

643 634 670 658 636 624 641 655 649 629

The dataset of doctor B is given as:

651 625 622 624 631 621 653 647 646 646

Using a statistical calculator, we have:

Doctor A

Doctor A: Mean Absolute Deviation (MAD) = 11.28

Doctor B: Mean Absolute Deviation (MAD) = 12

Hence, the mean absolute deviation is 11.28 for Doctor A’s and 12 for Doctor B’s data set on glasses

The variation of the two data

In a dataset, the larger the mean absolute deviations value, the larger the variation.

By comparison, 12 is greater than 11.28

Hence, there is more variability on glasses of doctor B's dataset than the glasses of doctor A's dataset

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The given question is incomplete, complete question is:

What is the mean absolute deviation for Doctor A’s data set on glasses? What is the mean absolute deviation for Doctor B’s data set on glasses? Write a sentence comparing the variation of the two data sets using their mean absolute deviations.

Doctor A Doctor B

Corrective Lenses Glasses Contacts Corrective Lenses Glasses Contacts

745 643 102 763 651 112

726 634 92 736 625 111

769 670 99 735 622 113

765 658 107 759 624 135

756 636 120 748 631 117

742 624 118 756 621 135

757 641 116 765 653 112

748 655 93 761 647 114

770 649 121 768 646 122

738 629 109 761 646 115

Let A be the point (-2, 9, 10) and n be the normal vector of the plane. The direction vector of the line is <1, 3, -3>, and since the plane is perpendicular to the line, n is orthogonal to the direction vector.

So, n is a vector that satisfies:

n . <1, 3, -3> = 0

The equation of the plane can be written in the form:

n . (x - A) = 0

Where x = (x, y, z) is any point in the plane.

We can find n by taking the cross product of two non-parallel vectors in the plane, such as <1, 0, 0> and <0, 1, 0>. Then,

n = (1, 0, 0) x (0, 1, 0) = (0, 0, 1)

Substituting the values of A and n into the equation of the plane, we get:

0 . (x - (-2, 9, 10)) = 0

0 . (x + 2, y - 9, z - 10) = 0

z - 10 = 0

z = 10

So the equation of the plane is:

z = 10

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Answer:

a) The two variables are the number of years and the height of the tree in feet

b) It is a positive linear relationship.

c) Put a point at (0,3) and one at (3,7), and connect the dots.

The function that can be used to get the height of the helicopter above the ground is: H=280m−1,500

A function is a statement, rule, or law in mathematics that establishes the link between an independent variable and a dependent variable (the dependent variable).

How to solve for the function

The value 280 is the constant rate that the helicopter is said to be descending.

The altitude from which it is coming down is given as 1500 feet

The function would be written as H=280m−1,500

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Answer:

[tex] \sf \: x = 5[/tex]

Step-by-step explanation:

Now we have to,

→ Find the required value of x.

The equation is,

→ 15 - x = 10

Then the value of x will be,

→ 15 - x = 10

→ -x = 10 - 15

→ -x = -5

→ [ x = 5 ]

Hence, the value of x is 5.

The percent markup for the scooter that costs a retailer $75 but sells for $125 at the local store is 66.67%.

The markup is the additional price added to the cost of an item for retail sales.

Markups are usually expressed in percentages.

To express the markup in percent determine the difference between the retail price and the cost price.  Then divide the difference by the cost price and multiply by 100.

The cost price of the scooter = $75

The selling price of the scooter = $125

The markup in dollars = $50 ($125 - $75)

The markup percent = 66.67% ($50/$75 x 100)

Thus, the scooter was marked-up at 66.67%.

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The 14th term of the arithmetic sequence is 109 whose common difference is d = 8 and whose first term is a(1)=5.

The value of 14th term of an AP is 109.

In the given question

The common difference = 8

The value of first term=5

And we have to find the value of 14th term of Arithmetic progression

We utilize the method for locating the nth term to locate a specific term in an arithmetic series. An arithmetic sequence's nth term is determined by an = a + (n - 1)d in step 1.

Putting the given value in formula:

an = a + (n - 1)d

a 14th=5+(14-1)8

a 14th=5+13*8

a 14th=5+104

a 14th=109

So the value of 14th term of an AP is 109.

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The relation between the number of hours spent using electronic devices is 2 times the number of hours spent playing sports. ​

The term called relation is defined as the relationship between sets of values of ordered pairs and the set of elements in the first set are called domain which is related to the set of the element in another set, which is called range.

Here we have know that the number of hours spent using electronic devices is 30 and the number of hours spent playing sports 15.

As per the definition of relation, in order to find the relation we need to do the division operation on then we get,

=> 30/15

=> 2

Which means that the first one is 2 times of the second one.

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Answer:

165/34

Step-by-step explanation:

245=80+(25+9)w We subtract 80 from each side and simplify

165=(34)w Divide each side by 34

165/34 = w

The required number in which when subtracted from both 17 and 12 , the product will be 1.04  is  x = 11.8 or 17.2.

ax^2 + bx + c = 0 is a quadratic equation, which is a second-order polynomial equation in a single variable. a 0. It has at least one solution because it is a second-order polynomial equation, which is guaranteed by the algebraic fundamental theorem.

Let the number is x, then

(17 - x)(12 - x) = 1.04

204 - 17x - 12x + x² = 1.04

x² - 29x + 204 = 1.04

x² - 29x + 202.96 = 0

On solving for x, we get

x = 11.8 or 17.2

Thus, the number can be x = 11.8 or 17.2.

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The needed value is either x = 11.8 or 17.2, which when deducted from both 17 and 12 will result in a product of 1.04.

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Answer:
Smallest to Largest =
5.899, 15.2, 50.57, and 150

Step-by-step explanation:

I hope this helps you out :D

The standard form of the equation 9y^2+72y=72=6x-x^2 will be x-3)^2/81 + (y+4)^2/9=1.

The given equation is :

[tex]x^{2} + 9y^{2} -6x +72 y = 72[/tex]

[tex]x (x-6) +9y (y+6) = 72[/tex] +1 +36

x(x-6) / 109 + 9y(y+6) / 109 = 1

Thus, by simplifying above equation

(x-3)^2/81 + (y+4)^2/9=1

In this case, Option C is correct.

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Answer:

C) (x-3)^2/81 + (y+4)^2/9=1

Step-by-step explanation:

That regression model is described as overfitting. The model has identified specific data points in the data that are not universal.

A regression model, which provides a function, describes the relationship between one or more independent variables and a response, dependent, or target variable. To explain the relationship between height and weight, for instance, a linear regression model might be utilized.

Regression analysis is the foundation for many forecasts and evaluations of the effects on target variables. Regression models are widely employed in research to support claims about fuel economy, the causes of pollution, or the effects of screen time on learning.

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By algebra properties, the value of variable c for linear equation 3 · (x - 1) = 2 · x + c such that x = 3 is equal to 0.

In this problem we need to find the value of a variable c such that the following system of linear equations exists:

3 · (x - 1) = 2 · x + c

x = 3

First, substitute x in the first equation:

3 · (3 - 1) = 2 · 3 + c

Second, simplify and clear the resulting expression:

3 · 2 = 6 + c

6 = 6 + c

c + 6 = 6

c = 0

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