What is the degree of polynomial 5x³ 4x² 7x?

10. a. The sequence is arithmetic as the difference between the next term and the previous term is constant.

b. The 200th term of the sequence is 1382.

c. 100 is not a member of the sequence.

11. a. u₁ is even and d is also even.

b. u₁ is odd and d is even.

An arithmetic sequence is a set of numbers in which every no. next to the previous number has the same common difference

d = aₙ - aₙ₋₁ = aₙ₋₁ - aₙ ₋₂.

In a geometric sequence numbers are written in the same constant ratio(r).

It means every next number is a multiple of a common constant and the previous number.

r = aₙ/aₙ₋₁ = aₙ-₁/aₙ₋₂.

Given, u₁ = - 12 and uₙ₊₁ = uₙ + 7.

So,

u₂ = u₁₊₁ = - 12 + 7 = - 5.

Similarly, u₃ = - 5 + 7 = 2 and u₄ = 9.

So, The terms have a common difference o 7 and hence it is an arithmetic sequence.

We know, uₙ = u₁ + (n - 1)d.

Therefore, u₂₀₀ = u₁ + (200 -1)×7.

u₂₀₀ = - 12 + 199×7.

u₂₀₀ = - 12 + 1393.

u₂₀₀ = 1382.

Now, Determining whether 1000 is a member of the sequence.

Let, 1000 = - 12 + (n - 1)×7.

1012 = 7n - 7.

1019 = 7n, Here is not completely divisible hence 1000 is not a member of the sequence.

11. When all the terms of an AP is even the first term u₁ is even and the common difference would also be even and when all the terms of an AP are odd the first term u₁ would be odd and the common difference d would e even, as odd - odd = even.

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B = (2a + 11)/5 is an expression for b when expressed in terms of a.

What exactly are slopes and lines?

We are aware that lines might have several kinds of equations; the typical form is

The equation of a line in slope-intercept form is Ax + By + c = 0, and

y = mx + b.

m is the slope, and b is the y-intercept.

The y-intercept, or (0,b), is the point where the line crosses the y-axis when x = 0. The slope represents the rate of change of the y-axis relative to the x-axis.

Given:

Coordinates of point Q = (2,3)

Coordinates of point R = (a,b)

The equation of the line is 5x + 2y = 9 ⇒ 2y = - 5x + 9

Therefore, y = (-5/2)x + 9/2.

We know slope m = (y2 - y1) / (x2 - x1)

∴ m = (b - 3)/(a - 2).

∴ (2/5) = (b - 3).(a - 2).

2(a - 2) = 5(b - 3).

2a - 4 = 5b - 15.

2a + 11 = 5b.

b = (2a + 11)/5.

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70% of those who went to the music concert and the play also did so.

A value or ratio that may be stated as a fraction of 100 is referred to in mathematics as a percentage. Divide the number by the total and multiply by 100 to find the percent of a given number. A portion per hundred is what the percentage denotes. Percentage refers to one in a hundred. The word "%" stands in for it.

In addition to being stated as a decimal or a fraction, a percentage is a number that indicates how many out of 100 it is. Three for the price of one! Simply enter the % as the numerator and 100 as the denominator to convert the percentage to a fraction.

We know that 350 people attended the drama play.

50% of 350 = (0.5) · 350 = 175 people attended both the drama play and music concert.

We know that 250 people attended the music concert.

The percentage of the people who attended the music concert even attended the drama play would be 175 ÷ 250 · 100% = 70%

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70% of those who went to the music concert and the play also did so.

Hence, the option A is correct.

In mathematics, a value or ratio that can be expressed as a fraction of 100 is known as a percentage. In order to get the percentage of a given number, divide the number by the total and multiply by 100. The percentage is a chunk out of one hundred. One out of 100 is referred to as a percentage. The symbol for it is "%".

A % is a number that, in addition to being expressed as a decimal or a fraction, also specifies how many out of 100 it is. For the price of one, get three! To convert a percentage to a fraction, just enter the% as the numerator and 100 as the denominator.

We know that 350 people attended the drama play.

50% of 350 = (0.5) · 350 = 175 people attended both the drama play and music concert.

We know that 250 people attended the music concert.

The percentage of the people who attended the music concert even attended the drama play would be 175 ÷ 250 · 100% = 70%

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Therefore, the multiple of the given equations is 10x^2yz + 6xyz^2, 5x^3y^2 + 14x^3y^3, and -10x^5 + 15x^4 - 30x^3 + 40x^2.

The process of multiplying two or more polynomials together is known as polynomial multiplication. Applying the distributive property to the multiplication of polynomials allows us to conduct polynomial multiplication.

Multiplication in mathematics is essentially just adding a number repeatedly in relation to another number. For instance, if we multiply 2 by 3, then implies that 3 gets multiplied by itself twice, meaning 3 + 3 = 6. Children can multiply numbers easily with the help of this method.

1. (5xy+3yz) * 2xz = 10x^2yz + 6xyz^2

2. (6/7x2y) * (35/6xy + 14/3 xy2) = 5x^3y^2 + 14x^3y^3

3. (2x3-3x2+6x-8) * (-5x2) = -10x^5 + 15x^4 - 30x^3 + 40x^2

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The number line is drawn to find the open end point interval is infinity.

Number Line of an Open endpoint to the endpoint of number line =?

Selection of Open endpoint to the endpoint of the number line is  fit for the following intervals as such determined below :

basically the intervals are mentioned as follow

( ), [ ], ( ], [ )  

An open interval is mentioned (a, b), is an interval that does not contain its endpoints. When an interval involves infinity or negative infinity, hence the following rules for whether it is an open or closed interval. (a, and

(-a , a) are open intervals.

For instance [a,∞) doesn't contain all of its endpoints as mentioned . It's a real number where The interval has only one endpoint - a, so it contains all of its endpoints (however it only has one).

Secondly, the definition forgot to add that (−∞,∞) is also open

Take numbers as follows:

Final Answer  as followed  in intervals

(-2, 2)

[-2, 2]

(-∞, 2]

[2, ∞)

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The increase was 250% over the original price.

percentage, a relative value indicating hundredth parts of any quantity.

let 'x' represent the original price, then 'x+0.25x' represents the first increase of 25%

six times greater, converted to a percentage:

(x+0.25x)×2×100 a second increase of six-fold

1.25x×2×100

250

The increase was 250% over the original price.

Hence, the increase was 250% over the original price.

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The number of full test tubes Russel fill with water must be discrete number and not rational. 36 test tubes is the answer.

Volume of a cylinder can be known either by the use of formula (V = πr²h) or by measuring with the volume of a known liquid.

Given that Russel is doing an experiment for a science fair project. He fills a beaker with water three times. He puts 16.5 milliliters of water in each test tube. How many full test tubes can Russel fill with water?

1. Describe one way to estimate the solution to this problem.

By dividing the amount of milliliters of water in the baker by 16.5 ml

2. Russel calculates correctly and says the answer to the problem is 36.36 test tubes. Is Russel's answer reasonable?

No! The reason is based on the fact that the answer must be a whole number and not a decimal number since the question centered on number of full test tubes filled with water.

Therefore, the correct answer should be 36 test tubes.

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Answer:  sqrt(2)

Step-by-step explanation:

Remember that sec x = 1/cos x.

That means that sec 7pi/4 = 1/cos(7pi/4)

cos(7pi/4) = -cos(7pi/4 - pi)

                 = -cos(3pi/4)

cos(3pi/4) is a special angle which evaluates to -sqrt(2)/2.

Hence, -cos(3pi/4) evaluates to simply sqrt(2)/2

Since cos(7pi/4) is equal to -cos(3pi/4),

cos(7pi/4) is equal to sqrt(2)/2.

Lastly, sec 7pi/4 = 1/cos(7pi/4) , which is the reciprocal of sqrt(2)/2, that is 2/sqrt(2).

Rationalizing the answer 2/sqrt(2) gives sqrt(2)

Consequently, it would take polynomials roughly 690,64 years for the disintegrations to disappear.

A polynomial is a mathematical statement made up of coefficients and uncertainty that exclusively uses additions, subtractions, multiplications, and positive integer powers of variables. A single indeterminate x polynomial is represented by the expression x2 4x + 7. A polynomial is an expression in mathematics that consists of variables (sometimes referred to as indeterminates) and coefficients that may be added, subtracted, multiplied, and raised to negative integer powers of non-variables. A polynomial is an algebraic expression made up of coefficients and variables. The only operations that an expression can contain are addition, subtraction, multiplication, and non-negative integer exponents. These expressions are known as polynomials.

The formula for this is Activity = decay constant x atoms.

1238 = 2.64 x 1010 times the decay constant

decay constant is equal to 4.76 x 10-8 min-1.

Currently, the disintegrations are being slowed to 809 disintegrations per minute.

Ln(809) = Ln(2.64 x 1010) - Ln(4.76 x 10-8 x t)

t=3.63x108min = 690.64y

Consequently, it would take roughly 690,64 years for the disintegrations to disappear.

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2 equations that could be used to solve for missing lengths are:

[tex]\frac{AD}{A'D'} = \frac{BC}{B'C'}[/tex]

Now, According to the question:

Two quadrilaterals are similar if their corresponding angles are equal and also their corresponding sides must be proportional.

Quadrilateral ABCD is similar to quadrilateral A'B'C'D'.

ABCD ~ A'B'C'D'

So,

[tex]\frac{AB}{A'B'} = \frac{BC}{B'C'}\\ \\ \frac{CD}{C'D'} = \frac{AD}{A'D'}[/tex]

Hence,  2 equations that could be used to solve for missing lengths are:

[tex]\frac{AD}{A'D'} = \frac{BC}{B'C'}[/tex]

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Oscar Wilde creates a hilarious tone by using puns, situational irony, dramatic irony, satire, and epigrams.

Oscar Fingal O'Flahertie Wills, an Irish poet, and playwright, lived from 16 October 1854 to 30 November 1900.

He wrote in a variety of genres throughout the 1880s before becoming one of London's most well-known playwrights in the early 1890s.

The Picture of Dorian Gray, his plays and epigrams, as well as the circumstances surrounding his meningitis-related early death at age 46 and criminal conviction for gross indecency for consensual homosexual activities in "one of the earliest celebrity trials," is what people will remember him for most.

Using puns, situational irony, dramatic irony, satire, and epigrams, Oscar Wilde establishes a humorous tone.

Therefore, Oscar Wilde creates a hilarious tone by using puns, situational irony, dramatic irony, satire, and epigrams.

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The equation that is modeled to the situation is x - 2y + 2 = 0 and the slope of the line is 1/2.

A line's steepness and direction are measured by the line's slope. Without actually using a compass, determining the slope of lines in a coordinate plane can assist in determining if the lines are parallel, perpendicular, or none at all.      

The slope intercept form of a line is y = mx + c              

Where, c - y-intercept and m - the slope of the line

Given that

The cost of using the internet at an internet cafe is equal to a fee plus a certain rate per minute.

4 minutes of internet costs $ 3

8 minutes of internet costs $ 4  

[ We can represent the given situation as given below ]      

And the coordinates formed are (4, 3) and (8, 4)

The slope of the line formed = (4 - 3)/(8 - 4) = 1/4

Let y = mx + c be the equation to the model situation

=> y = (1/2)x + c

=> 2y = x + c ---- (1)

As we know (1) will pass through (4, 3)

=> 2(3) = 4 + c

=> 6 = 4 + c

=> c = 6 - 4

=> c = 2

=> 2y = x + 2

=> x - 2y + 2 = 0

Therefore,

The equation that is modeled to the situation is x - 2y + 2 = 0 and the slope of the line is 1/2.

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Nate's car was filled with 16 gallons of gas.

The concept is used in this is equations. An equation is a mathematical statement with an 'equal to' symbol between two expressions that have equal values. An equation is the set of variables, constants, and mathematical operations like addition, subtraction, multiplication, or division balanced by an equal sign. For example, 3x + 5 = 15. There are different types of equations like linear, quadratic, cubic, etc.

As gas is $2. 09 per gallon at the gas station.

$2. 09 → per gallon

and Nate filled up his car and spent $33. 44.

$33. 44 for fully filled → how many gallons ?

So,

33.44 / 2.09 = 16 gallons.

Therefore, Nate filled 16 gallons gas in his car.

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A grocer makes a display of cans in which there are 10 rows.

The top row has one can and each lower row has two more cans than the row above it.

We can write it as sequence:

1, 3, 5, 7, . . .

We can observe that it's an arithmetic sequence: 1, 3, 5, 7, . . . , 2n-1

We know that the formula for the sum of n-terms of arithmetic sequence:

S(n) = (n/2)(1 + 2n-1)

Here, Sn = 100

So, (n/2)[1 + 2n-1] = 100

n(1 + 2n + 1)

n(2n) = 200

2n^2 = 200

n^2 = 100

n = 10

Hence, the number of rows = 10

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The difference between the polynomials 9x² + 8x and 2x² + 3x is 7x² + 5x.

A polynomial is formed mathematically by combining one or more algebraic terms (monomials). The roots of "polynomial" are poly- (many) and -nomial (terms). A polynomial can have exponents (powers), constants (numbers), and variables (letters), but not negative exponents or variable division.

Polynomials are typically expressed in standard form. Furthermore, because there are no similar terms among the exponents, they are arranged in descending order (largest to smallest).

To find the difference between

(9x² + 8x) - (2x² + 3x)

We do calculation

= 9x² + 8x - 2x² - 3x

= 9x² - 2x² + 8x - 3x

= 7x² + 5x

Thus, the difference between the polynomials is 7x² + 5x.

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Answer: 7

Step-by-step explanation:

Distance (d) = √(4 - -3)2 + (5 - 5)2

= √(7)2 + (0)2

= √49

= 7

ΔX = 4 – -3 = 7

ΔY = 5 – 5 = 0

y = 0x + 5

When x=0, y = 5

Answer:

Step-by-step explanation:

D = SQRT(x 2 - x 1) 2 + (y 2 - y 1) 2

X2 Y2

(-3,5)

X1 Y1

(4,5)

D= SQRT (-3-4)^2 + (5-5)^2

D= SQRT 49

D=7

Avogadro's number is a unitless object. It represents a number.

What is unit?

The mass of a particular piece of metal or the length of a particular rod are examples of quantities (specific properties) of objects that have historically been used to define measurement units. An object that has no units is known as unitless.

The proportionality factor that connects the number of constituent particles (often molecules, atoms, or ions) in a sample with the amount of material in that sample is called the Avogadro constant, also known as NA or L. It has a precise value of  6.02214076 × 10²³ reciprocal moles and serves as a SI defining constant.

The value of Avogadro's number is 6.02214076 × 10²³.

One mole of the chemical compound consists of 6.02214076 × 10²³ atoms.

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Answer:

Step-by-step explanation:

Let the number be x then,

1) 4 * x + 11

2) 8 * (x + 7)

3) 2x - 1

4) x+ 3x

5) 5x + 12

6) 16 + 1 + x = 17 + x

7) 20 - ( x - 5) = 20 - x + 5 = 25 - x

8) x - 6 + 15 = x +9

The height of an acute triangle can be calculated using the Pythagorean Theorem. The formula for this theorem is a2 + b2 = c2, where a and b are the two legs of a right triangle and c is the hypotenuse.

To find the height of an acute triangle, we must first identify the two legs of the triangle. The length of the two legs can be determined by measuring the lengths of the three sides of the triangle. Once we have the lengths of the two legs, we can apply the Pythagorean Theorem to calculate the length of the hypotenuse.

Once the length of the hypotenuse is determined, we can use the formula h2 = c2 - a2 - b2 to calculate the height of the triangle. This formula states that the square of the height of the triangle is equal to the square of the hypotenuse minus the square of the two legs. So, to find the height of an acute triangle, we first measure the lengths of the three sides, then use the Pythagorean Theorem to calculate the hypotenuse, and finally use the formula h2 = c2 - a2 - b2 to calculate the height of the triangle.The height of an acute triangle can be calculated using the Pythagorean Theorem. The formula for this theorem is a2 + b2 = c2, where a and b are the two legs of a right triangle and c is the hypotenuse. To find the height of an acute triangle, we must first identify the two legs of the triangle. The length of the two legs can be determined by measuring the lengths of the three sides of the triangle. Once we have the lengths of the two legs, we can apply the Pythagorean Theorem to calculate the length of the hypotenuse.

Once the length of the hypotenuse is determined, we can use the formula h2 = c2 - a2 - b2 to calculate the height of the triangle. This formula states that the square of the height of the triangle is equal to the square of the hypotenuse minus the square of the two legs. So, to find the height of an acute triangle, we first measure the lengths of the three sides, then use the Pythagorean Theorem to calculate the hypotenuse, and finally use the formula h2 = c2 - a2 - b2 to calculate the height of the triangle.

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The 3 linear equations are

1. y = mx + b

2. ax + by = c

3. x/a + y/b = 1

1. y = mx + b is a linear equation in two variables, x and y. The equation is in the slope-intercept form, where m is the slope of the line and b is the y-intercept.

2. ax + by = c is a linear equation in two variables, x and y. The equation is in the standard form, where a and b are constants and c is the result of the equation.

3. x/a + y/b = 1 is a linear equation in two variables, x and y. The equation is in the general form, where a and b are constants and 1 is the result of the equation.

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Answer:

Step-by-step explanation:

55 times 25, making Angel attempt 1375 free throws

Answer:

Step-by-step explanation:

David's deposit of $220 compounded continuously at a rate of 1.7% will become $260 after 10 years.

Here we have been given that David invested $220.

The interest rate was 1.7%

Since the amount was compounded continuously, there is no fixed date of when it was compounded, the whole process is taken as an exponential distribution.

There were no withdrawals or additional deposits to this, so our Principal is constant. Hence we can write the formula

Amount = Principal X eᵃˣ

where a = rate of interest/100

x = time

Therefore, we can say that

Ampunt after 10 years = 220 X e¹⁰ ˣ ⁰°⁰¹⁷

= $260.76707

rounding off to the nearest 10 dollars we get

= $260

Hence David's deposit of $220 compounded continuously at a rate of 1.7% will become $260 after 10 years.

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Answer: Zasha spent $6 on packages of gum, which means that she bought 6 / $1.20 = 5 packages of gum.

If she has a $20 bill, she has $20 - $6 = $14 left to spend on gum.

Zasha can buy an additional 14 / $1.20 = 11.6666666666666666666666667 packages of gum with this money.

Rounded down, Zasha can buy an additional 11 packages of gum.

Therefore, Zasha can buy a total of 5 + 11 = 16 packages of gum.

Step-by-step explanation:

Coordinate (0,1) of y-intercept implies that a line or curve cross the Y axis

at 1.

The location of a point on the cartesian coordinate plane where a straight line or curve line as well as a plane crosses the Y axis is called Y-intercept. The coordinate of y-intercept is expressed as (0, y). This y value is y-intercept. The X coordinate of y intercept is zero.

In case of an equation of line while writing in slope-intercept form it is denoted by b such as y = mx+ b

in the above equation, b is y-intercept and m is the slope.

The y -intercept given by coordinate (0, 1) defines that a straight-line or curve line cross the Y axis at 1. The x coordinate of y -intercept is always zero because over the Y axis there is no value of X.

The y-intercept can have negative or positive value.

Suppose we have an equation of line 4x + 8y + 10 = 0

                                we will write it in a slope-intercept form

                                     8y = -4x - 10

                                     y = - 4x/8 - 10/8

                                    y = -1/2x - 5/4

In the above equation - 5/4 or -1.25 is the y-intercept that means the line crosses the Y-axis at -1.25

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Answer:

the one that is not equivalent to the others would be 116-34

Step-by-step explanation:

because its 116 and the others dont have anything to do with 116 :)

Answer: The statement that is not equivalent should be D. |16-34

Therefore , the solution of gross pay problem is 62% is this of her gross wage.

Hannah's take home pay of percentage 785 is 62.8% of her gross wage of 1250. This can be calculated by dividing 785 by 1250 and multiplying the answer by 100.

Here,

62.8% is the same as 0.628.

This can be calculated by dividing 785 by 1250.

To get the answer to the nearest whole percentage, we round up 0.628 to 0.63 which is 63%.

This means that Hannah's take home pay of 785 is 63% of her gross wage of 1250.

63% is the answer to the question: what percentage is Hannah's take home pay of her gross wage? This is correct to the nearest whole percentage.

To summarise, Hannah's take home pay of 785 is 63% of her gross wage of 1250, correct to the nearest whole percentage.

Hannah's take-home pay is 62.8% of her gross wage. This percentage is the result of taxes and other deductions taken by her employer.

Knowing this percentage can help Hannah better understand how much money she is taking home each week and how much money is being withheld from her paychecks.

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The area of the parking lot is  2,025 .81 meter2.

In essence, it is equal to 1/2 of the height times the base, or A = 1/2 b h. Therefore, we need to know the triangular polygon's base (b) and height (h) in order to calculate its area.

A triangular parking lot has sides measuring 90 meters, 54 meters, and 128 meters.

Triangle Height Determination Using Area

Now that you are aware of the triangle's area, you may use the triangle formula A=1/2bh to get the triangle's height.

s   = a + b+ c /2

90 + 54 + 128 / 2 = 136

A = [tex]\sqrt{s (s-a) (s-b) (s-c)}[/tex]

A = [tex]\sqrt{136(136-90)(136-54)(136-128}[/tex])

A = 2,025 .81

The area of the parking lot is  2,025 .81 meter2.

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Answer:

m = 2

Step-by-step explanation:

Slope = rise/run or (y2 - y1) / (x2 - x1)

We see the y increase by 4 and the x increase by 2, so the slope is

m = 4/2 = 2

So, m = 2