RATIONAL EXPRESSIONS Adding rational expressions with common Subtract. (19z+6)/(3z)-(4z)/(3z) Simplify your answer as much as possible.

The factored form of the polynomial is (5x^(3))(-x^(3)+3x+4).

To factor the polynomial with a negative coefficient, -5x^(6)+15x^(4)+20x^(3), we can use the content loaded factor method. This method involves factoring out the greatest common factor (GCF) of all the terms in the polynomial.

The GCF of -5x^(6), 15x^(4), and 20x^(3) is 5x^(3). So, we can factor out 5x^(3) from each term:

-5x^(6) = -(5x^(3))(x^(3))
15x^(4) = (5x^(3))(3x)
20x^(3) = (5x^(3))(4)

Now, we can rewrite the polynomial as:

-5x^(6)+15x^(4)+20x^(3) = (5x^(3))(-x^(3)+3x+4)

So, the factored form of the polynomial is (5x^(3))(-x^(3)+3x+4).

In summary, the polynomial -5x^(6)+15x^(4)+20x^(3) can be factored as (5x^(3))(-x^(3)+3x+4) using the content loaded factor method.

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Answer:

Proofs attached to answer

Step-by-step explanation:

Proofs attached to answer

The measure of angle D is \( 125^{\circ} 88^{\prime} 5^{\prime \prime} \).

The interior angles of a quadrilateral are measured as A \( 51^{\circ} 22^{\prime} 30^{\prime \prime} \), B \( 105^{\circ} 38^{\prime} 48^{\prime \prime} \), C \( 78^{\circ} 10^{\prime} 37^{\prime \prime} \), and D \( 124^{\prime} 46^{\prime \prime} \).

To find the measure of angle D, we can use the fact that the sum of the interior angles of a quadrilateral is 360 degrees.

Add the measures of angles A, B, and C:
\( 51^{\circ} 22^{\prime} 30^{\prime \prime} \) + \( 105^{\circ} 38^{\prime} 48^{\prime \prime} \) + \( 78^{\circ} 10^{\prime} 37^{\prime \prime} \) = \( 234^{\circ} 71^{\prime} 55^{\prime \prime} \)

Subtract the sum of angles A, B, and C from 360 degrees to find the measure of angle D:
360^{\circ} - \( 234^{\circ} 71^{\prime} 55^{\prime \prime} \) = \( 125^{\circ} 88^{\prime} 5^{\prime \prime} \)

Therefore, the measure of angle D is \( 125^{\circ} 88^{\prime} 5^{\prime \prime} \).

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The inequalities seen on Cartesian plane are - 2 · x + y > 1 and - (1 / 2) · x + y ≤ 2, respectively.

In this problem we find two graphs by inequalities on Cartesian plane, whose definitions are listed below:

Case 19:

f(x) > y

Case 20:

f(x) ≤ y

Each inequality has a function of the form:

y = m · x + b

Where:

And the slope can be determined by secant line formula:

m = Δy / Δx

Now we proceed to determine each inequality:

Case 1:

Slope

m = 4 / 2

m = 2

Intercept

b = 1

Inequality

y > 2 · x + 1

- 2 · x + y > 1

Case 2:

Slope

m = 1 / 2

Intercept

b = 2

Inequality

y ≤ (1 / 2) · x + 2

- (1 / 2) · x + y ≤ 2

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The height of the fish tank should be approximately 1.981 feet which is also equivalent to 23.772 inches.

As desired capacity of the fish tank is 100 gallons, and 7.48 gallons of water are equivalent to 1 cubic foot, the desired volume of the fish tank is (100 / 7.48) cubic feet, or approximately 13.369 cubic feet.

The desired volume is stated as a number of cubic feet so the known dimensions of the fish tank must be converted from inches to feet.

length = 54 inches = 4.5 feet

width = 18 inches = 1.5 feet

The formula for the volume V of a rectangular prism with length l, width w, and height h is V = lwh. We will substitute the known dimensions into the formula and solve for h.

V = ℓwh

13.369 ≈ 4.5 × 1.5 × h

13.369 ≈ 6.75h

h ≈ 13.369 / 6.75

h ≈ 1.981

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We can state this by responding to the provided question Each friend's equation portion of the tab and the tip is represented by the equation x = 60.

A mathematical equation links two statements and utilises the equals sign (=) to indicate equality. In algebra, an equation is a mathematical assertion that proves the equality of two mathematical expressions. For instance, in the equation 3x + 5 = 14, the equal sign separates the numbers by a gap. A mathematical formula may be used to determine how the two sentences on either side of a letter relate to one another. The logo and the particular piece of software are usually identical. like, for instance, 2x - 4 = 2.

The circumstance, where x is the cost of the groceries, is represented by the equation StartFraction 1 over 8 EndFraction (x + 16) = StartFraction 76 over 8 EndFraction. As the lunch cost and the gratuity were shared equally among the eight companions, this equation accurately depicts the total sum that each of them paid.

The scenario is represented by the equation 8 (x + 16) = 76, where x is the cost of the groceries. This calculation is incorrect since it includes the tip and includes the total amount paid by all 8 friends rather than just the cost of the meal.

Each friend's portion of the tab and the tip is represented by the equation x = 60.

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Using unitary method, we can find out that Alex spent 50 minutes reading.

By using the unitary technique, we can determine both the value of many units from the value of a single unit as well as the value of multiple units from the value of a single unit.

The worth of many things is supplied in the unitary technique, and we must either determine the value of more or fewer items. To do that, we must first determine the value of a single item by division and then determine the value of further or other items by multiplication.

Given in the question,

Alex spent 1 hour 20 minutes less than Lane.

Lane spent 50 minutes less than Pete.

Pete spent 3 hours reading.

Since, Pete spent 3 hours.

So, Lane spent:

= 3 hours or (180 minutes) - 50 minutes

= 2 hours 10 minutes.

Now, Alex spent:

                           = 2 hrs 10 minutes - 1 hour 20 minutes  

                          = 50 minutes

Therefore, Alex spent 50 minutes reading.

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We can rewrite the inequality as:

95 ≤  u ≤  155

Here we have the absolute value inequality:

|125 - u| ≤ 30

Where the variable is u.

The absolute value can be decomposed into two inequalities:

(125 - u) ≤ 30

(125 - u) ≥ -30

Solving these two we will get:

125 - 30  ≤ u

125 + 30  ≥ u

Then the compound inequality is:

95 ≤  u ≤  155

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Answer:

10

Step-by-step explanation:

Answer:

good morning i hope your day is going well so far

Step-by-step explanation:

the answer to your question is 10

i hope this helps!!!

Using the ratio, there are 60 roses  in the floral shop.

To find the number of roses in the floral shop, we can use the ratio given in the question. The ratio of roses to carnations is 1:4, which means that for every 1 rose, there are 4 carnations.

If there are 240 carnations, we can use cross multiplication to find the number of roses.
1/4 = x/240

Cross multiplying gives us:
4x = 240

Solving for x, we get:
x = 240/4
x = 60

In conclusion, if the ratio of roses to carnations in a floral shop is 1:4 and there are 240 carnations, there are 60 roses.

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Answer: 3.25h + 12= 9.25

Step-by-step explanation:

12 is the initial fee which we will just add to our answer

3.25 is the rate per hour, it is being multiplied by the number of hours.

the number of hour it took to reach the same cost is not told so we will just put a variable.

The inflation rate for that decade will be  34.39%. If the inflation rate had been the same for each year in that decade, the annual rate would have been 2.79%.

a) If the annual inflation rate was 3% for 10 years in a row, the inflation rate for that decade would be 34.39%. This is calculated by using the formula (1 + annual inflation rate)^number of years - 1. So in this case, it would be (1 + 0.03)^10 - 1 = 0.3439 or 34.39%.

b) To find the inflation rate for the decade from 1960 to 1970, we need to know the Consumer Price Index (CPI) for both years. The CPI for 1960 was 29.6 and the CPI for 1970 was 38.8.

We can use the formula (CPI in later year/CPI in earlier year)^(1/number of years) - 1 to find the annual inflation rate.

So in this case, it would be (38.8/29.6)^(1/10) - 1 = 0.0279 or 2.79%. Therefore, if the inflation rate had been the same for each year in that decade, the annual rate would have been 2.79%.

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The answer is d

because you're waiting too long.

Answer:

0.81,74%,5/8,31/50

Step-by-step explanation:

74% means 74/100 which equals to 0.74, and 5/8 is 0.625, and lastly 32/50 is 0.62 so it leaves us with 0.81 as the greatest so we can start ordering them

0.81,74%(0.74),5/8(0.625), 31/50(0.62)

Answer:

359°

Step-by-step explanation:

When an image is rotated by a multiple of 360 degrees, it returns to its original position because it has completed one full revolution. However, if the image is rotated by any angle less than 360 degrees, it will not return to its exact original position.

For example, if an image is rotated by 45 degrees, it will not return to its exact original position, but will instead be in a new and unique position. If the image is then rotated by another 45 degrees, it will again be in a new and unique position, and so on.

Therefore, the highest number of degrees an image can rotate without returning to its exact original position is 359 degrees.

Answer: 359 degrees

Step-by-step explanation:

If you rotate any object exactly 360 degrees, it returns to it's original position. Remember that phrase "360 no-scope?" It involves spinning until you're back where you started; try doing it right now. You'll be back where you were. But this question wants to know how far you can rotate an object without it being back where it was. I would usually say 359.999999999, but it's a whole number answer, so we'll stick with 359. Hope this helps!

The f(g(x)) is equal to 72x^2+48x+9 and g(f(x)) is equal to 3x+22.

To provide an accurate answer, it's important to first understand what the question is asking for. From the given information, it appears that there are several different parts to this question, so I will address each one individually.
1. Finding f-1(x)
To find the inverse of f(x), we can switch the x and y values and solve for y.

\begin{align*}
f(x) &= 2x^2+5 \\
y &= 2x^2+5 \\
x &= 2y^2+5 \\
2y^2 &= x-5 \\
y &= \sqrt{\frac{x-5}{2}} \\
f^{-1}(x) &= \sqrt{\frac{x-5}{2}}
\end{align*}
Therefore, f-1(x) is equal to √((x-5)/2).

2. Determining fx domain and range
The domain of f(x) is all real numbers since there are no restrictions on the input value x. However, the range of f(x) is limited by the fact that 2x^2+5 is always greater than or equal to 5. Therefore, the range of f(x) is [5,∞).

3. Finding f(g(x)) and g(f(x))
To find f(g(x)), we first need to substitute g(x) into f(x) wherever x appears:
\begin{align*}
f(g(x)) &= 2(g(x))^2+5 \\
&= 2(6x+2)^2+5 \\
&= 72x^2+48x+9
\end{align*}
To find g(f(x)), we first need to substitute f(x) into g(x) wherever x appears:
\begin{align*}
g(f(x)) &= 6f(x)-2 \\
&= 6\left(\frac{1}{2}x+4\right)-2 \\
&= 3x+22
\end{align*}
Therefore, f(g(x)) is equal to 72x^2+48x+9 and g(f(x)) is equal to 3x+22.

4. Explaining f(x)=1/(x-9)
The function f(x)=1/(x-9) is a rational function with a vertical asymptote at x=9. This means that as x approaches 9 from either direction, the function values become increasingly large (either positive or negative infinity).
The domain of f(x) is all real numbers except for x=9 (since dividing by zero is undefined). The range of f(x) is all real numbers except for zero (since 1/0 is undefined).I hope this helps! Let me know if you have any further questions.

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The break-even point is 45 tickets.

Algebraic expressions can include one or more variables, which are typically represented by letters, such as x, y, or z. These variables can be used to represent unknown quantities or to express relationships between different quantities in a problem.

Algebraic expressions can also include constants, which are fixed numbers, and coefficients, which are the numbers that multiply the variables in the expression. For example, in the algebraic expression 3x + 2y, the constants are 3 and 2, and the coefficients are 3 and 2, respectively.

To find the break-even point, we need to determine the number of tickets that need to be sold in order to cover the costs of the party.

Let's start by setting up an equation to represent the total cost of the party as a function of the number of tickets sold:

Total Cost = Room Rental + Entertainment + Decorations + Food Cost - Ticket Sales Revenue

Total Cost = 450 + 20n - 25n

where n is the number of tickets sold.

Simplifying this equation, we get:

Total Cost = 450 - 5n + 20n

Total Cost = 15n + 450

Now, we need to set the total cost equal to the revenue from ticket sales:

15n + 450 = 25n

Subtracting 15n from both sides, we get:

450 = 10n

Dividing both sides by 10, we get:

n = 45

Therefore, the break-even point is 45 tickets. If the organizers sell 45 tickets, the revenue from ticket sales will cover the total cost of the party, including the room rental, entertainment, decorations, and food cost.

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To test with hundreds, thousands, or millions of numbers, MAX_NUM and MAX_COUNT should be adjusted in the code as needed.

The Bubble Sort algorithm is a simple sorting algorithm that repeatedly steps through a given array, comparing elements and swapping them if they are in the wrong order. The sequential Bubble Sort algorithm can be implemented using a for loop that iterates through the array and swaps the elements if they are in the wrong order. The even-odd pass variant of the Sequential Bubble Sort adds two for loops, one for even elements and one for odd elements, which makes it more amenable to a parallel implementation.

Using multiple processes and threads to implement a parallel version of the Bubble Sort algorithm involves using system calls such as fork(), pipe(), pthread_create() and pthread_join(), and shmget(), shmat(), shmdt(), and shmctl() system calls. When implementing this parallel version of the Bubble Sort algorithm, care must be taken to avoid race conditions by properly synchronizing processes and threads.

To test the sequential and even-odd pass variants of the Bubble Sort algorithm, one should use the gettimeofday() function to measure and print the sorting time for different values of N. To test with hundreds, thousands, or millions of numbers, MAX_NUM and MAX_COUNT should be adjusted in the code as needed, and very large output can be redirected to a file using the operator.

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[tex](\stackrel{x_1}{4}~,~\stackrel{y_1}{-16})\qquad (\stackrel{x_2}{8}~,~\stackrel{y_2}{-12}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{-12}-\stackrel{y1}{(-16)}}}{\underset{\textit{\large run}} {\underset{x_2}{8}-\underset{x_1}{4}}} \implies \cfrac{-12 +16}{4} \implies \cfrac{ 4 }{ 4 } \implies 1[/tex]

[tex]\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}{(-16)}=\stackrel{m}{ 1}(x-\stackrel{x_1}{4}) \implies y +16 = 1 ( x -4) \\\\\\ y+16=x-4\implies y=x-20\impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]

The length of ST is 57 unit.

A perimeter is a closed path that covers, surrounds, or outlines a two-dimensional shape or length. The circumference of a circle or an ellipse is its perimeter.

As, we know that the four sides of Rhombus are equal.

So, TR = QR

-x+ 68 = 5x + 2

-x - 5x = 2 - 68

-6x = - 66

x= -66/ (-6)

x= 11

So, the length of ST = 5x+ 2 = -x+ 68 = 57 unit

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f(g(x))=x² + 8x +19 ; g(f(x))=x² + 7 are the value of the asked functions

explanation:-

the given functions are: f(x) = x² + 3 and g(x) = x + 4

f(g(x)) = f(x + 4) = (x + 4)² + 3 = x² + 16 + 8x +3 = x² + 8x +19

g(f(x)) = g(x² + 3) = x ²+ 3 + 4 = x² + 7

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The Finance Charge for the Delgados obtained for an instrument is $1200 to repay the loan in 12 months.

The given data is as follows:

Instrument loan =  $12,000

Loan at APR = 10%

Number of months = 12 Months

The finance charge is calculated by using the formula,

Finance charge = Loan amount x APR x No' of months to repayment / No' of months in a year

Finance charge  = ($12,000 x 10% x 12) / 12

Finance charge = 14400 / 12

Finance charge = $ 1200

Therefore we can conclude that the Finance charge for the Delgados obtained for an instrument is $1200.

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The trinomial [tex]x^(2)+7x-18[/tex] factors into (x+9)(x-2), and the trinomial [tex]x^(2)-7x-18[/tex] factors into (x-9)(x+2). The signs in each binomial are opposite.

In the first trinomial, the signs are positive and negative, while in the second trinomial, the signs are negative and positive. This is because the signs in the binomials are determined by the signs of the constant term and the coefficient of the linear term in the trinomial.

For the first trinomial, the constant term is -18 and the coefficient of the linear term is 7. To factor this trinomial, we need to find two numbers that multiply to -18 and add to 7. The numbers 9 and -2 satisfy this condition, so the trinomial factors into (x+9)(x-2).

For the second trinomial, the constant term is -18 and the coefficient of the linear term is -7. To factor this trinomial, we need to find two numbers that multiply to -18 and add to -7. The numbers -9 and 2 satisfy this condition, so the trinomial factors into (x-9)(x+2).

In both cases, the signs in the binomials are opposite because one of the numbers is positive and the other is negative.

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Answer: 90

Step-by-step explanation:

Answer:

90

Step-by-step explanation:

Given a line and a point, not on the line, there is one and only one line which passes through the given point and is perpendicular to the given line. The correct answer is B.  


A line and a point not on the line are given. We are asked to find the one and only line that passes through the given point and is perpendicular to the given line. The line that passes through the given point and is perpendicular to the given line is known as the perpendicular bisector.

The perpendicular bisector passes through the midpoint of the line segment formed by the two endpoints of the given line. Therefore, the answer is B. There is one and only one line that passes through the given point and is perpendicular to the given line. Therefore the correct answer of this question is option B

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The equation of the red graph is g(x) = x² + 3.

Option C.

The equation of the red graph can be determined by considering upscaling or transformation on the x - axis.

Since the equation focuses on the function g(x) and not on upscaling in the y-axis, any changes should not affect the x-axis. Therefore, we can eliminate (x - 3)² and (x + 3)² from the options given, since they involve modifying the x-axis.

In conclusion, as the transformation involves increasing the y-values along the y-axis, the correct choice is x² + 3 rather than x² - 3.

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A function type that could model the given situation is a linear function.

The rate of change in the truck's worth per year is -1400.

A model that describes this situation is y = -1400x + 43500

In Mathematics, the slope of any straight line can be determined by using this mathematical equation;

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = rise/run

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Substituting the given data points into the slope formula, we have the following;

Slope (m) = (36,500 - 43,500)/(2020 - 2015)

Slope (m) = -7,000/5

Slope (m) = 1,400.

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The fifth term of the expansion of (x − 5)⁶ is found as:  937x².

The Pascal triangle has a lengthy history. It may be traced back to India's Pingala people in the second century BC, who also knew various other binomial formulas at the same time.

Using the binomial series:

(n C r) = n! / (r1(n - r)!

Given equation: (x − 5)⁶

On comparing:

a = x, b = -5 and n = 6

x⁶ + (6C1).x⁶.(-5)¹ + (6C2).x⁴.(-5)² + (6C3)x⁴(-5)³ + (6C4).x²(-5)⁴ + (6C5).x¹.(-5)⁵ + (-5)

Using binomial calculator to solve the expression as;

x⁶ - 30x⁵ + 375x⁴ - 2500x³ + 937x² - 1870x + 15625

Thus, the fifth term of the expansion of (x − 5)⁶ is found as:  937x².

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Answer:
3:14
for every 3 women, there is 14 men

Step-by-step explanation:

The two functions are not equivalent.

The given functions f(x,y) = x^2 + 3y^2 and f′(x,y) = x^2 + 4xy + 7y^2 are not equivalent.

To determine if two functions are equivalent, we can compare their equations and see if they are the same. In this case, the equations of the two functions are different. The first function, f(x,y), has a term of 3y^2, while the second function, f′(x,y), has a term of 4xy and a term of 7y^2.

Therefore, the two functions are not equivalent.

It is important to note that two functions can have different equations but still be equivalent if they produce the same output for any given input. However, in this case, the two functions will produce different outputs for the same input, so they are not equivalent.

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The area of the parallelogram is ∇19.

To determine the area of the parallelogram, we will use the formula: Area = ||u x v||, where u and v are vectors representing two sides of the parallelogram.

First, we need to find the vectors u and v. We can do this by subtracting the coordinates of two adjacent vertices:
u = (−4,9,5) - (−7,7,6) = (3,2,-1)
v = (−10,6,6) - (−7,7,6) = (-3,-1,0)

Next, we need to find the cross product of u and v:
u x v = [(2)(0) - (-1)(-1), (-1)(-3) - (3)(0), (3)(-1) - (2)(-3)] = [-1, 3, -3]

Finally, we need to find the magnitude of the cross product, which will give us the area of the parallelogram:
Area = ||u x v|| = ∇((-1)^2 + (3)^2 + (-3)^2) = ∇(1 + 9 + 9) = ∇19

Therefore, the area of the parallelogram is ∇19.

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