subtract the polynomials (6x^7-x+8)-(x^7+2)

Due to length restrictions, we kindly invite to check the explanation for further detail on the solution of radical equations and existence of extraneous solutions.

In this question we have ten cases of radical equations, whose roots can be found by algebra properties. The solutions to each equation is listed below: (Please notice that a solution is extraneous when an absurdity is found)

Case 1

√(30 - x) = x

30 - x = x²

x² + x - 30 = 0

(x + 6) · (x - 5) = 0

x = - 6

√[30 - (- 6)] = - 6

- √36 = - 6

- 6 = - 6

x = 5

√[30 - 5] = 5

√25 = 5

5 = 5

Case 2

x = √(42 - x)

x² = 42 - x

x² + x - 42 = 0

(x + 7) · (x - 6) = 0

x = - 7

7 = √[42 - (- 7)]

7 = √49

7 = 7

x = 6

6 = √(42 - 6)

6 = √36

6 = 6

Case 3

√(12 - r) = r

12 - r = r²

r² + r - 12 = 0

(r + 4) · (r - 3) = 0

x = - 4

√[12 - (- 4)] = - 4

- √16 = - 4

- 4 = - 4

x = 3

√(12 - 3) = 3

√9 = 3

3 = 3

Case 4

m = √(56 - m)

m² = 56 - m

m² + m - 56 = 0

(m + 8) · (m - 7) = 0

m = - 8

- 8 = √[56 - (- 8)]

- 8 = - 8

m = 7

7 = √(56 - 7)

7 = √49

7 = 7

Case 5

r = √(1 - 2 · r)

r² = 1 - 2 · r

r² + 2 · r + 1 = 0

(r + 1)² = 0

r = - 1

- 1 = √[1 - 2 · (- 1)]

- 1 = √3 (EXTRANEOUS)

Case 6

√(4 · n + 8) = n + 3

4 · n + 8 = (n + 3)²

4 · n + 8 = n² + 6 · n + 9

n² + 2 · n + 1 = 0

(n + 1)² = 0

n = - 1

√[4 · (- 1) + 8] = (- 1) + 3

√4 = 2

2 = 2

Case 7

- n + √(6 · n + 19) = 2

√(6 · n + 19) = n + 2

6 · n + 19 = (n + 2)²

6 · n + 19 = n² + 4 · n + 4

n² - 2 · n - 15 = 0

(n - 5) · (n + 3) = 0

n = 5

- 5 + √(6 · 5 + 19) = 2

- 5 + √49 = 2

- 5 + 7 = 2

2 = 2

n = - 3

- (- 3) + √[6 · (- 3) + 19] = 2

3 + √1 = 2

4 = 2 (EXTRANEOUS)

Case 8

4 + √(- 3 · m + 10) = m

√(10 - 3 · m) = m - 4

10 - 3 · m = (m - 4)²

10 - 3 · m = m² - 8 · m + 16

m² - 5 · m + 6 = 0

(m - 6) · (m + 1) = 0

m = 6

4 + √(- 3 · 6 + 10) = 6

4 + √(- 8) = 6 (EXTRANEOUS)

m = - 1

4 + √[- 3 · (- 1) + 10] = - 1

4 + √13 = - 1 (EXTRANEOUS)

Case 9

x - 5 = √(x + 1)

(x - 5)² = x + 1

x² - 10 · x + 25 = x + 1

x² - 11 · x + 24 = 0

(x - 3) · (x - 8) = 0

x = 3

3 - 5 = √(3 + 1)

- 2 = - 2

x = 8

8 - 5 = √(8 + 1)

3 = √9

3 = 3

Case 10

n - 7 = √(3 · n - 21)

(n - 7)² = 3 · n - 21

n² - 14 · n + 49 = 3 · n - 21

n² - 17 · n + 70 = 0

(n - 7) · (n - 10) = 0

n = 7

7 - 7 = √(3 · 7 - 21)

0 = 0

n = 10

10 - 7 = √(3 · 10 - 21)

3 = 3

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The given algebraic expression (24 - 12w) is equivalent to

6(4 - 2w).

An algebraic expression is a combination of terms both constants and variables. For example -

2x + 3y + z

4x + 5z

Given is the algebraic expression as -

24 - 12w

We can rewrite the expression above as -

24 - 12w

24 - 12w = 6 x 4 - 6 x 2w

24 - 12w = 6(4 - 2w)

Therefore, the given algebraic expression (24 - 12w) is equivalent to

6(4 - 2w).

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The equivalent expression to -24 - 12w is -6 (4 + 2w).

A mathematical operation such as subtraction, addition, multiplication, or division is used to combine terms into an expression. In a mathematical expression, the following terms are used:

An absolute numerical number is referred to as a constant.

Variable: A symbol without a set value is referred to as a variable.

Term: A term can be made up of a single constant, a single variable, or a mix of variables and constants multiplied or divided.

Coefficient: In an expression, a coefficient is a number that is multiplied by a variable.

Given:

We have the Expression as -24 - 12w.

So, Prime factorizing

24 = 2 x 2 x 2 x 3

12 = 2 x 2 x 3

So, -24 - 12w.

= - (2 x 2 x 2 x 3) - (2 x 2 x 3)w

= -2  x 3 ( 2 x 2 + 2w)

= -6 (4 + 2w)

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The equation is  (4.5-0.7)/5 and length of each piece is 0.74

An equation is a  mathematical statement that is made up of two expressions connected by an equal sign.  In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.

here, we have,

He has a piece of wood that is 4.5 feet long.

After cutting five equal pieces of wood from it, he has 0.7 feet of wood left over

an equation that could be used to determine the length of each of the five pieces of wood he cut

legth of each piece is = (4.5-0.7)/5

The total length is 4.5  and the leftover is 0.7, so used wood is total minus left ove

Length of each piece is used woof by number if pieces

(4.5 - 0.7)/5 = 3.7/5 = 0.74

Therefore, the equation is  (4.5-0.7)/5 and legth of each piece is 0.74

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Answer:

pretty sure its "A"

Step-by-step explanation:

Answer:

C

The value of the variables in answer C satisfies both of the equations

Answer:

By using trigonometric relations, we will see that:

AC = 15.6 in

AB = 8.4 in.

How to get the measures of the other two sides of the right triangle?

Here we have the right triangle where:

B = 90°

C = 40°

BC = 10 in.

Notice that is the adjacent cathetus to the angle C, then we can use the two relations:

sin(a) = (adjacent cathetus)/(hypotenuse).

tan(a) = (opposite cathetus)/(adjacent cathetus).

Where:

hypotenuse = AC

opposite cathetus = AB.

Then we will have:

sin(40°) = 10in/AC.

AC = 10in/sin(40°) = 15.6 in

tan(40°) = AB/10in

tan(40°)*10in = AB = 8.4 in.

So we can conclude that for the given right triangle we have:

AC = 15.6 in

AB = 8.4 in.

If you want to learn more about right triangles:

Step-by-step explanation:

The coordinates of the point R: (0, 3.4)

What is the slope?

In mathematics, the slope or gradient of a line is a number that describes both the direction and the steepness of the line

Slope PQ 5–0/ 2–6 = 5 /-4

equation of PQ y =-5/4 x +c ;

this passing through 2,5

5 =-5/4*2 +c ; C = 5 -5/2 =5/2

y =-5x/4+5/2 =-5x+10/4 ; 4y =-5x +10 ;

equation of PQ =5x +4y-10 =0 ;

slope of PR : m1 *m2 =-1 ;m2 = -1/ [-5/4 ] = 4/5

equation of PR y = mx +c this passes through [2,5]

5 = 4/5*2 +C so C = 5- 8/5 =17/5

y =4 x /5 +17/5 so coordinates of R = [0, 3.4]

Hence, the coordinates of the point R: (0, 3.4)

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The area of the shaded region is 73.5 cm square.

Supposing that there is no direct formula available for deriving the area, we can derive the area of that region by dividing it into smaller pieces, whose area can be known directly. Then summing all those pieces' area gives us the area of the main big region.

We are given the dimension of the shaded region.

Length = 15 cm

Breadth = 7 cm

The area of the trapezium is

Area = 1/2(sum of non parallel sides)height

Area = 1/2 (12 + 9) 7

Area = 1/2 x 21 x 7

Area = 73.5

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Answer:

[tex]\frac{1}{8}[/tex] cup pretzels, [tex]\frac{3}{16}[/tex] cup nuts of your choice, [tex]\frac{1}{8}[/tex] cup raisins, [tex]\frac{1}{12}[/tex] cup chocolate chips (optional)

Step-by-step explanation:

A fraction is a fragment of a whole number, used to define parts of a whole. The whole can be a whole object, or many different objects. The number at the top of the line is called the numerator, whereas the bottom is called the denominator.

If we need to multiply the fractions in the recipe by [tex]\frac{1}{4}[/tex], we just need to multiply the denominator by 4.

[tex]\frac{2}{4}[/tex] cups pretzels becomes [tex]\frac{2}{16}[/tex] or [tex]\frac{1}{8}[/tex].

This is because the denominator (4) is multiplied by 4 to get 16. The numerator doesn't change.

[tex]\frac{3}{4}[/tex] cup nuts becomes [tex]\frac{3}{16}[/tex].

This is because the denominator (4) is multiplied by 4 to get 16. The numerator doesn't change.

[tex]\frac{1}{2}[/tex] cup raisins becomes [tex]\frac{1}{8}[/tex].

This is because the denominator (2) is multiplied by 4 to get 8. The numerator doesn't change.

[tex]\frac{1}{3}[/tex] cup chocolate chips becomes [tex]\frac{1}{12}[/tex].

This is because the denominator (3) is multiplied by 4 to get 12. The numerator doesn't change.

Now, the recipe looks like this:

[tex]\frac{1}{8}[/tex] cup pretzels

[tex]\frac{3}{16}[/tex] cup nuts of your choice

[tex]\frac{1}{8}[/tex] cup raisins

[tex]\frac{1}{12}[/tex] cup chocolate chips (optional)

Answer:

C = .25m + 5.45

Step-by-step explanation:

c = (1..05 - .8)m + (16.40 - 10.95)

C = .25m + 5.45

The Luxury car cost  25 cents more per mile and an a higher initial cost of $5.45

Answer:

1110

Step-by-step explanation:

y=100000(0.25)^8 exponential decay​ is 1.526.

The formula represents exponential decay with a decay factor of 0.25 and an initial value of 100,000. To evaluate the formula, you can simply substitute 8 for the variable x (since the formula has y in terms of x) and calculate the result:

y = 100000(0.25)^8

y = 100000(0.00001525878906)

y ≈ 1.526

Therefore, the value of y for x = 8 is approximately 1.526. This means that after 8 units of time, the initial value of 100,000 has decayed to around 1.526.

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The attached graph is provided below .

The slope is determined by dividing the change in price by the variation in the amount of deli meat. The magnitude means that there is a change of 3 units in the cost per each pound of change of deli meat.

A collection of points in the coordinate plane that are all solutions to the equation make up the graph of the linear equation.The equation can be graphed if each variable has a real value by plotting enough points on the graph to discern a pattern, then connecting those points to include all of the points.

The following linear equation represents the cost (x), measured in dollars, as a function of the amount of deli meat (y), measured in pounds:

y = 3x                     ..... (1)

The attached graph is provided below.

The required slope is determined by dividing the change in price by the variation in the amount of deli meat. The magnitude means that there is a change of 3 units in the cost per each pound of change of deli meat.

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Answer:

No. There is a solution.

Step-by-step explanation:

Pages aren't infinite, but lines are! Lines just keep going forever. If the lines aren't parallel, then they will intersect at some point. The point of intersection is the solution to the system. Just because its not on the page doesn't mean it doesn't exist. We just need a bigger page...or maybe, a bigger imagination...or maybe smaller scale on the graph...or maybe a computer graphing utility...or maybe a piece of paper and a pencil to solve the system algebraically!

The solution is out there!

see image

Answer:

Step-by-step explanation:

To find the left-hand derivative of f at x = 4, we need to evaluate:

f′−(4) = limh→0−f(4+h)−f(4)h

Since f(x) = 0 for x ≤ 0 and f(x) = 5 - x for 0 < x < 5, we have:

f(4 + h) = 0 for h < -4

f(4 + h) = 5 - (4 + h) = 1 - h for -4 < h < 1

f(4 + h) = undefined for h > 1

Therefore, we can rewrite the limit as:

f′−(4) = limh→0−f(4+h)−f(4)h = limh→0−(1 - h) - 0h = -1

To find the right-hand derivative of f at x = 4, we need to evaluate:

f′+(4) = limh→0+f(4+h)−f(4)h

Using the same reasoning as before, we can rewrite the limit as:

f′+(4) = limh→0+(5 - (4 + h)) - 0h = -1

Since the left-hand derivative and the right-hand derivative are equal, we can conclude that f'(4) exists and is equal to:

f'(4) = f′−(4) = f′+(4) = -1

Therefore, the derivative of f at x = 4 is -1.

Answer:

Can u make the question more clear?

The first node in set 1 should represent the element.

For each potential value in set 2, create a branch.

Create a new node to represent the following set 1 element at the end of each branch.

Steps 2-4 must be repeated for each additional Set 1 component.

All potential outcomes are represented by the final nodes.

The appropriate line of best fit for the scatter plot is y hat equals 67 hundredths times x plus 4 and 5 hundredths.

The number is a mathematical entity used to represent a computer's magnitude it can be a symbol or a combination of simple you should in order to take quantity such as the two, five, seven, three, or eight numbers are used to verify the context including counting measuring and computing.

This line of best fit indicates that the number of households with cable television will increase by 67 hundredths (or 0.67) each year. This line of best fit is based on the data points on the scatter plot, which suggest that the number of households with cable television has been steadily increasing over the years.

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The best option is Location 2, which you can determine by adding up the points for each site using the information below.

The complete question is:

A supply chain manager faced with choosing among four possible locations has assessed each location according to the following criteria, where the weights reflect the importance of the criteria. Use the information below to calculate total points for each location and choose the best option. Round your answers to two decimal places.

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Answer:

$610.25

Step-by-step explanation:

The simple  interest  at a higher FICO score over the lower FICO score
= 8.9% - 4.2% = 4.7%

4.7% = 4.7/100 = 0.047 in decimal

Therefore at simple interest the amount of money saved for 1 year on a loan of $12,984

= $12,984 x 0.047 = $610.25

Answer:

$611.63

Step-by-step explanation:

To Calculate the amount of interest saved with a higher credit score, we need to find the difference in the amount of interest paid over the course of one year on a loan of $12,984 at each interest rate.

First, we'll calculate the interest paid at 4.2% interest with a FICO score of 776:

Interest rate = 4.2%

Loan amount = $12,984

Simple interest = Interest rate x Loan amount

Simple interest = 4.2% x $12,984

Simple interest = $545.45

Next, we'll calculate the interest paid at 8.9% interest with a FICO score of 495:

Interest rate = 8.9%

Loan amount = $12,984

Simple interest = Interest rate x Loan amount

Simple interest = 8.9% x $12,984

Simple interest = $1,157.08

The difference in interest paid is the amount saved by having the higher credit score:

Interest saved = Interest paid at 8.9% - Interest paid at 4.2%

Interest saved = $1,157.08 - $545.45

Interest saved = $611.63

Therefore, having a higher credit score of 776 would save you $611.63 in simple interest over the course of one year on a loan of $12,984.

Answer:

Step-by-step explanation:

here is a step by step answer:

A. To determine the surface area of the warehouse:

Identify the dimensions of each side of the warehouse. In this case, we know that the sides are 17 ft, 25 ft, and 33 ft in length, and the height is 10 ft.

Calculate the area of each side by multiplying the length and height. For example, the area of the first side is 17 ft x 10 ft = 170 sq ft.

Add up the areas of all the sides to get the total surface area of the warehouse. In this case, the total surface area is 170 + 250 + 330 = 750 sq ft.

B. To determine the area of the surfaces that need siding:

Since all sides of the warehouse need to be covered with siding, the area of the surfaces that need siding is equal to the total surface area of the warehouse. In this case, we calculated the total surface area to be 750 sq ft.

C. To determine how many pieces of siding need to be purchased:

Identify the size of each piece of siding. In this case, we know that each piece of siding is 4 ¾ inches x 24 inches.

Convert the size of each piece of siding to square feet. To do this, we can divide the length and width by 12 to convert to feet, and then multiply the two dimensions to get the area. In this case, 4 ¾ inches is approximately 0.3958 feet, and 24 inches is 2 feet, so the area of each piece of siding is approximately 0.7916 sq ft.

Divide the total surface area of the warehouse by the area of each piece of siding to get the number of pieces needed. In this case, we calculated that the total surface area is 750 sq ft, and each piece of siding covers approximately 0.7916 sq ft. So, the number of pieces needed is 750 sq ft ÷ 0.7916 sq ft/piece = 946.84 pieces. We must round up to the nearest whole number because we can't purchase a fraction of a piece of siding. So, we need to purchase 947 pieces of siding.

D. To determine the approximate cost of siding needed to cover the outside of the warehouse:

Identify the price per piece of siding. In this case, we know that the siding is priced at $22.65 per piece.

Multiply the number of pieces of siding needed by the price per piece to get the total cost of siding. In this case, we calculated that we need 947 pieces of siding, so the total cost of siding is 947 x $22.65 = $21,465.55. So, the approximate cost of siding needed to cover the outside of the warehouse is $21,465.55.

Answer:

Step-by-step explanation:

the answer is

B

and
C

Yes, in ggplot2, mapping refers to the process of connecting variables in a data set to visual elements of a plot, such as points, lines, or other shapes.

Yes, in ggplot2, mapping refers to the process of connecting variables in a data set to visual elements of a plot, such as points, lines, or other shapes. This is done by mapping variables to aesthetic properties of the plot, such as the x and y coordinates, the size, color, or shape of the points, or other visual properties that can be customized.

For example, if we have a data set with two variables, x and y, we can create a scatterplot of the data by mapping the x variable to the x-axis and the y variable to the y-axis, using the aes() function in ggplot2. We can also customize the appearance of the points by mapping other variables to the size, color, or shape of the points, as well as adding other elements to the plot, such as a title or legend.

The mapping process is an important part of data visualization in ggplot2, as it allows us to explore the relationship between different variables and to communicate our findings in a clear and effective way. By mapping variables to visual elements of a plot, we can create informative and visually appealing graphics that can help us understand and communicate complex data sets.

In programming, a variable is a named storage location that can hold a value or a reference to a value. Variables are used to store and manipulate data in a program, and they can take on different values at different times during the execution of the program.

In most programming languages, variables are defined by specifying a name and a data type. The data type determines the kind of data that can be stored in the variable, such as numbers, strings, or Boolean values, and also affects the size and behavior of the variable.

Variables can be assigned a value using the assignment operator, which stores the value in the variable's memory location. Once a value has been assigned to a variable, it can be accessed and manipulated using its name.

In addition to simple data types, programming languages also support more complex types of variables, such as arrays, objects, and pointers, which can store collections of values or references to other variables.

Variables are a fundamental concept in programming, and they are used extensively in all kinds of software applications, from simple scripts to complex systems. Understanding how to use variables effectively is an essential skill for any programmer.

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The domain are the possible input while the range are the possible output of a function.

(a) The domain = [-√2, √2], the range = [0, 2]

(b) The domain = [-1, 1], the range = [0, 1]

(c) The domain = [-1, 1], the range = [0, -1]

(d) The domain = [0, 2], the range = [0, 1]

(e) The domain = [-(2 + √2), (√2 - 2)], the range = [0, 2]

Reasons:

The given functions can be expressed by the equation; (-x + 1)·(x + 1) = -x² + 1

Therefore, we have;

(a) y = f(x) + 1 = -x² + 1 + 1 = -x² + 2

The x-intercept of the above function are, x = √2, and x = -√2

Which gives;

The domain = [-√2, √2]

The range = [0, 2]

(b) y = 3·f(x) = 3 × (-x² + 1) = -3·x² + 3

At the x–intercepts, we have;

-3·x² + 3 = 0

x = ±1

The domain = [-1, 1]

The maximum value of y is given at x = 0, therefore;

= -3 × 0² + 3 = 3

The range = [0, 1]

(c) y = -f(x) = -(-x² + 1) = x² - 1

At the x–intercepts, x² - 1 = 0

x = ± 1

The domain = [-1, 1]

The minimum value of y is given at x = 0, which is y = -1

The range = [0, -1]

(d) y = f(x - 1) = -(x - 1)² + 1 = -x² + 2·x

At the x–intercepts, we have;  -x² + 2·x = 0, which gives;

(-x + 2)·x = 0

Which gives, x = 0, or x = 2

The domain = [0, 2]

The maximum value of y is given when x = -b/(2·a) = -2/(2×(-1)) = 1

y = f(1) =  -1² + 2×1 = 1

Therefore;

The range = [0, 1]

(e) y = f(x + 2) + 1 = (-(x + 2)² + 1) + 1 = -x² - 4·x - 2

At the x–intercepts, we have;  -x² - 4·x - 2 = 0, which gives;

x = -(2 + √2) or x = x = √2 - 2

The domain = [-(2 + √2), (√2 - 2)]

The maximum value of y is given when x = -4/(2)) = -2

Which gives;

-(-2)² - 4·(-2) - 2 = 2

The range = [0, 2]

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Answer: 6 3/4 I hope this helps

Step-by-step explanation:

27/4

Convert the improper fraction into a mixed number

6 3/4

Mixed number-A number written as a whole number and a fraction.

The system of inequalities that can be used to find the possible original prices of a laptop, x, and of a printer, y is: x + y ≥ 1050 and 0.8x + 0.9y > 860

Let x be the original price of the laptop and y be the original price of the printer.

So, the discounted price of the laptop is 0.8x and the discounted price of the printer is 0.9y

If the two are purchased together, the total discounted price is:

0.8x + 0.9y

This exceeds $860

0.8x + 0.9y > 860

The original prices of the two together is at least $1,050.

This can be written as:

x + y ≥ 1050

So, we have

x + y ≥ 1050 and 0.8x + 0.9y > 860

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The option is (B) The entire solution region is viable is correct when both the inequalities are solved.

What is an inequality?

In Algebra, an inequality is a mathematical statement that uses the inequality symbol to illustrate the relationship between two expressions. An inequality symbol has non-equal expressions on both sides. It indicates that the phrase on the left should be bigger or smaller than the expression on the right, or vice versa.

Let's first translate the given information into mathematical inequalities -

The perimeter of the tabletop to be no more than 28 feet -

Perimeter = 2(length + width) ≤ 28

The length of the tabletop to be greater than or equal to the square of 2 feet less than its width -

Length ≥ (Width - 2)²

We can combine these two inequalities to form the system -

2(length + width) ≤ 28

Length ≥ (Width - 2)²

Now, let's solve for y in terms of x (so that we can graph the solution region) -

2(y + x) ≤ 28

y ≥ (x - 2)²

Simplifying the first inequality -

y ≤ -x + 14

Now graph both the inequalities -

The viable solutions are the points that satisfy both inequalities, which lie in the shaded region above.

Therefore, there is no part of the solution region that includes negative length or negative width.

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The solution is,

the function is increasing at (-5,-2)

the function is decreasing at (6,2)

the function is constant at (-8,5)

Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable.

here, we have,

from the given graph we get,

the function is increasing at (-5,-2)

the function is decreasing at (6,2)

the function is constant at (-8,5)

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