Which of the following is a factor of (x+y)³ - (x³+y³) ?choose the correct answerx²+xy²+2xyx²+y²-xyxy²3xy

The correct option is (2)  [tex]\frac{8}{5}[/tex] and (3)  [tex]\frac{1}{6}[/tex].

The factor of equation  f(x) = 60[tex]x^{4}[/tex] +  86[tex]x^{3}[/tex] – 46[tex]x^{2}[/tex] – 43[tex]x[/tex] + 8 are [tex]\frac{8}{5}[/tex] and [tex]\frac{1}{6}[/tex].

The rational root theorem, also referred to as the rational zero theorem, is a potent mathematical technique used to identify all potential rational roots of polynomial equations of order 3 and above.

For the given polynomial, the roots are given as;

[tex]$$P(x)=a_{n} x^{n}+a_{n-1} x^{n-1}+\cdots+a_{2} x^{2}+a_{1} x+a_{0}$$\\ \\$\pm \frac{\text { factors of } a_{0}}{\text { factors of } a_{n}}$.[/tex]

Factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60 and factors of 8 are 1, 2, 4 and 8.

Out of the given options, only   [tex]\frac{8}{5}[/tex] and [tex]\frac{1}{6}[/tex] can be written in the form:  

[tex]\begin{aligned}&\frac{8}{5}=\frac{\text { a factor of } 8}{\text { a factor of } 60} \\&\frac{1}{6}=\frac{\text { a factor of } 8}{\text { a factor of } 60}\end{aligned}[/tex]

Therefore, the rational roots of polynomial f(x) = 60[tex]x^{4}[/tex] +  86[tex]x^{3}[/tex] – 46[tex]x^{2}[/tex] – 43[tex]x[/tex] + 8 are [tex]\frac{8}{5}[/tex] and [tex]\frac{1}{6}[/tex].

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The complete question is-

Which is a factor of f(x) = 60[tex]x^{4}[/tex] +  86[tex]x^{3}[/tex] – 46[tex]x^{2}[/tex] – 43[tex]x[/tex] + 8? use the rational root theorem to help you find your answer.

Replace x with the value in the table and solve for y

-3:  2(-3)/3 + 4 = -6/3 + 4 = -2+4 = 2

0:  2(0)/3 +4 = 0/3 + 4 = 0+4 = 4

3: 2(3)/3 + 4 = 6/3 + 4 = 2 + 4 = 6

6:  2(6)/3 + 4 = 12/3 + 4 = 4+4 = 8

Answer:

When x = -3:

y = 2(-3)/3 + 4

y = 2

When x = 0:

y = 2(0)/3 + 4

y = 4

When x = 3:

y = 2(3)/3 + 4

y = 6

When x = 6:

y = 2(6)/3 + 4

y = 8

As a percentage, the relative frequency of plastics recycling in New Mexico in 2008 compared to plastics recycled in all three states combined is approximately 11%.

A relative frequency measures the proportion of events that occur within a class out of the total number of observations.

When using relative frequency, the results are usually displayed in percentages, proportions, and fractions.

Year    State                   Recycled Plastics                 Relative

                                       (thousands of tons)            Frequency

2008  New Mexico                   500                        0.111  (500/4,500)

2008  New York                     1,500                        0.333 (1,500/4,500)

2008  Texas                          2,500                        0.566 (2,500/4,500)

Total                                       4,500                        1

Thus, the relative frequency of plastics recycling in New Mexico in 2008 compared to plastics recycled in all three states combined is approximately 11%.

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Answer: 9%

Step-by-step explanation:

just did the question

The correct option is (d) Mutually exclusive events.

Let a and b be the events of the fda approving and rejecting a new drug to treat hypertension, respectively. The events a and b are mutually exclusive events.

Two events are mutually exclusive or disjoint in logic and probability theory if they cannot both occur at the same time. The results of a single coin toss, which can result in either heads or tails but not both, provide a clear illustration.

A statistical term used to describe events that cannot occur concurrently is "mutually exclusive." It is frequently used to refer to circumstances in which the occurrence of one event takes precedence over the other. For instance, it is impossible for war and peace to exist together. They are therefore opposed to one another.

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Answer:

Step-by-step explanation:

9,328 and you would divide that by 98 and the answer would be 95.18367347 boxes

Answer:

5.46

111

86

367.2

49

467

use labels

Step-by-step explanation:

1. [tex]\frac{39}{2} times . 0.28[/tex]

[tex]\frac{39}{2} times \frac{28}{100} =\frac{1092}{200} \\[/tex]

[tex]\frac{1092}{200} = \frac{273}{50}[/tex]

Answer 273/50 or 5.46 inches

2. [tex]\frac{97}{87} times \frac{100}{1} =\frac{9700}{87}[/tex]

Answer 9700/87= 111%ft

3. [tex]\frac{146}{1} divided \frac{170}{1}[/tex]

[tex]\frac{146}{1}times\frac{1}{170} =\frac{146}{170}[/tex]

Answer=146/170=73/85=

86%tons

4. [tex]\frac{136}{1} times\frac{270}{100} =\frac{36720}{100}[/tex]

Answer=367.2%ft

5 .[tex]\frac{60}{123}[/tex]=49%inches

6.[tex]\frac{56}{1} times\frac{100}{12} =[/tex]467%inches

Mr. Cahn’s total earnings in a year is $18,900.

The total earnings is a function of the annual salary, commission and Christmas bonus.

Total earnings = annual salary + commission + Christmas bonus

Commission = 6% x (160,000 - 20,000)

6% x $140,000

0.06 x 140,000 =  $8,400

Total earnings =  $8,400 + 10,000 + $500 = $18,900

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[tex]\huge\underline{\red{A}\green{n}\blue{s}\purple{w}\pink{e}\orange{r} →}[/tex]

Step-by-step explanation:

5x:9 = 7:3

→ 5x/9 = 7/3

→ x = (7 × 9)/(3 × 5)

→ x = 21/5

Answer:

60 kilograms

Step-by-step explanation:

The distance of the car from the tall building to the nearest meter is 23m.

Given the data in the question;

We use trigonometric ratio since the scenario forms a right angle triangle.

tanθ = opposite / adjacent

tanθ = opposite / adjacent

tan( 35° ) = 16m / x

x = 16m / tan( 35° )

x = 16m / 0.7002

x = 23m

Therefore, the distance of the car from the tall building to the nearest meter is 23m.

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the maximum height is 180ft.

The height of the equation is modeled by:

[tex]y = 60t - 5t^2[/tex]

Notice that this is a quadratic equation with a negative leading coefficient, which means that the maximum is at the vertex, then the maximum is at:

[tex]t = -60/(2*-5) = 6[/tex]

To get the maximum height, we need to evaluate the function in t = 6, we will get:

[tex]y = 60*6 - 5*6^2 = 180[/tex]

This means that the maximum height is 180ft.

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Answer:

[tex]\huge\boxed{\sf \{(-2,1)\}}[/tex]

Step-by-step explanation:

Given equations:

y = x + 3

y = -x - 1

By comparing the above equations, we get:

x + 3 = -x - 1

Add x to both sides

Subtract 3 to both sides

2x = -1 - 3

2x = -4

Divide 2 to both sides

x = -4/2

Substitute x = -2 in first equation.

y = x + 3

y = -2 + 3

So,

[tex]\rule[225]{225}{2}[/tex]

Answer:

[tex]x = - 2 \\ y = 1[/tex]

Step-by-step explanation:

The above are Simultaneous equations.

Simultaneous equations are two or more algebraic equations which share same variables like X,Y or X,Y and Z.

They are called simultaneous equations because they can be solved the same time.

From the question,

[tex]y = x + 3 - - - - - - (1) \\ y = - x - 1 - - - - - - (2) \\ Substitute \: equation \: (2)into \: (1) \\ - x - 1 = x + 3 \\ Collect \: liketerms \\ - x - x = 3 + 1 \\ - 2x = 4 \\ Divide \: bothsides \: by \: - 2 \\ \frac{ - 2x}{ - 2} = \frac{4}{ - 2} \\ x = - 2 \\ Substitute \: the \: value \: of \: x \: into \: equation \: (1) \\ y = x + 3 \\ y = - 2 + 3 \\ y = 1 \\ Therefore \: x = - 2 \: \: and \: y = 1[/tex]

The ratio comes out to be 1:4.

What is ratio?

A ratio in mathematics shows how many times one number is contained in another. For instance, if a mixture of milk and water contains eight liters of water and six liters of milk, the ratio of water to milk is eight to six. Similarly, the ratio of water to the overall amount of mixture is 8:14, while the ratio of milk to water is 6:8.

Calculating the Ratio of the Solution:

Let us assume that x is the quantity of 30% of the solution and y be that of 5% solution, then,

30% of x + 5% of y = 10% of (x + y)

0.3x + 0.05y = 0.1 (x + y)

0.3x + 0.05y = 0.1x + 0.1y

0.3x - 0.1x = 0.1y - 0.05y

0.2x = 0.05y

Thus, the required ratio is,

0.2x / 0.05y = 1

x / y = 0.05 / 0.2

x / y = 5 / 20

x:y = 1 : 4

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The equivalent expressions indicated are;

1) 1/a^6b^4

2) a^6/b^6

3) a^6/b^5

4) b^6/a^6

5) a^5b^3

We have to note that when we talk about the equivalent expressions, we mean the expressions that we have to get from each other when we carry out a little computational work on the original expression.

Thus, the equivalent expression has shown that the expression that is in the bracket is the same as the original expression by the use of the laws of exponents.

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Using a system of equations, it is found that Oscar bought 6 markers, 6 notebooks and 15 packs of sticky notes.

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

In this problem, the variables are:

He bought the same number of markers as notebooks, hence:

x = y.

He bought three more packs of sticky notes than markers and notebooks combined, hence:

z = 3 + x + y

z = 3 + 2x.

He paid $1.05 for each marker, $2.25 for each notebook, and the packs of sticky notes were $1.95. He spent $49.05 in total, hence:

1.05x + 2.25y + 1.95z = 49.05.

Then:

1.05x + 2.25x + 1.95(3 + 2x) = 49.05.

7.2x = 43.2

x = 43.2/7.2

x = 6.

The amounts are as follows:

He bought 6 markers, 6 notebooks and 15 packs of sticky notes.

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Answer:

1800(5/6)^t

Step-by-step explanation:

I don't see any answer choices, but this would be another form if it is listed. The negative exponent means that you get the reciprocal of the fraction (in this case 1.2). This turns 1.2 into (1/1.2), which is equivalent to 5/6.

The probability that the schools in Los Angeles will be closed for four days next year is 0.1680.

In order to comprehend separate events that happen at a steady pace over the course of a specified amount of time, Poisson's distributions are frequently utilized.

Formula for Poisson's distribution:

f(x) = ((λ^x)/x!).(e^(-λ))

x = Event to be calculated for

λ = Expected number of occurrences

P(X = x) = ((λ^x)/x!).(e^(-λ))

Here λ = 3 and x = 4

P(X = 4) = (81 / 4!).(e^(-3))

P(X = 4) = (81 * e^(-3))/24

P(X = 4) = (81 * 0.049)/24

P(X = 4) = 0.1680

Hence, the probability that schools in Los Angeles will be closed for four days next year is 0.1680.

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OPTION A is the correct answer

The bronze-casting process that depends on a modelled original form is:  lost-wax casting.

Lost-wax casting is a bronze-casting process which is also referred to as the cire-perdue. In this type of metal casting, a wax model is created when a molten metal is usually poured into a mold. The wax model is then melted and drained.

In summary, the name for this bronze-casting process that relies on this wax model is called: lost-wax casting.

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The correct answer is 2.930 × [tex]10^{23}[/tex]

What is Avogadro's number?

Avogadro's number, which is equal to 6.02214076 1023, is the quantity of units in one mole of any material (defined as its molecular weight in grams). Depending on the substance and the nature of the reaction, the units may be electrons, atoms, ions, or molecules (if any).

You have two numbers here. While number 2.0550 is stated with five significant figures, Avogadro's number is supplied with four. This implies that you must provide four significant figures with your result.

(6.022 × [tex]10^{23}[/tex]) / 2.0550 = 2.930 × [tex]10^{23}[/tex]

Therefore, the correct answer is 2.930 ×[tex]10^{23}[/tex] .

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The graph and inverse of a function are reflections of each other along the line y = x.

A relation made up of ordered pairs (x, y) has as its inverse the set of all ordered pairs (y, x).

When a point is mirrored over the line y = x, the x- and y-coordinates swap places. Similarly, when a point is mirrored over the line y = -x, the x- and y-coordinates swap places and become negated.

Therefore,

The point (x, y)'s reflection over the line y = x is (y, x).

The point (x, y)'s reflection over the line y = - x is (-y, -x).

Thus, the graph and inverse of a function are reflections of each other along the line y = x.

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Answer:

2.0

Step-by-step explanation:

Answer:

$1,800

Step-by-step explanation:

If the Smiths agree to the installment plan and pay $150 every month for 12 months, it will add up to $1,800 at the end of the year.

Answer:

1.

x=-10

x=-6

2.

x=10

x=-3

Step-by-step explanation:

to find the zeros of a function you need to set it equal to zero:

x^2+16x+60=0

then you factor

(x+10)(x+6)=0

then you have to finish factoring/simplifying

x+10=0

  -10

x=-10

x+6=0

 -6

x=-6

and the same thing for number 2

x^2-7x-30=0

(x-10)(x-3)=0

x=10, x=3

Answer:

1.) x = -10, x = - 6

2.) x = 10, x = -3

Step-by-step explanation:

1.) factorize and set the equation to zero by multiplying a and c and finding factors of it that will result in b once added/subtracted

[tex]x^2+16x+60\\(x+10)(x+6)\\(x+10)(x+6)=0\\x=-10, x=-6[/tex]

2.) do the same for number 2:

[tex]x^2-7x-30\\(x-10)(x+3)\\(x-10)(x+3)=0\\x = 10, x = -3[/tex]

i hope this helped!

Answer:

1.5, -1.5

Step-by-step explanation:

Using the quadratic formula, you should have a plus, and minus solution. These should be your answers.

Based on the fact that Jessica and her best friend split the money and were able to get $16.32, the total amount that they found was $32.64

The fact that they split the money evenly means that they split it in half which each person getting the same amount.

This means that the total amount they found was twice the amount that Jessica and her best friend got.

The total amount found is therefore:

= Jessica's share + Best friend's share

= 16.32 + 16.32

= $32.64

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Answer:

  D.  π/30 + n(π/15)

Step-by-step explanation:

The given equation can be solved by isolating the cosine function and using the inverse function to find the angles.

  30cos(30x) +14 = -16

  30cos(30x) = -30 . . . . . . subtract 14

  cos(30x) = -1

This is an extreme value of the cosine function that first occurs where the argument is π, and repeats every 2π after that:

  30x = π +2nπ

  x = π/30 +n(π/15) . . . . . odd multiples of π/30

__

Additional comment

The answer choices other than D include all multiples of π/30, or only even multiples of π/30. Either way, they are not part of the correct answer.

Step-by-step explanation:

3 - 11x

x is "a number".

so, the request is to multiply it by 11 and subtract the result from 3.