1+1=2

2+2=4

5+5=10

34+35=?

Division of Polynomials is [tex]$$2 x^2-11 x+58-\frac{294}{x+5}$$[/tex] , [tex]$$x^3-5 x^2+17 x-83+\frac{422}{x+5}$$[/tex], [tex]2 x-3+\frac{12}{x^2+2 x-1}[/tex].

What is Polynomials?

A polynomial is a mathematical statement made up of coefficients and indeterminates that uses only the operations addition, subtraction, multiplication, and powers of positive integers of the variables. In an equation such as the quadratic equation, cubic equation, etc., a polynomial function is a function that only uses non-negative integer powers or only positive integer exponents of a variable. For instance, the polynomial 2x+5 has an exponent of 1.

1). [tex]\frac{2 x^3-x^2+3 x-4}{x+5}$$[/tex]

[tex]$$\begin{aligned}& \text { Divide } \frac{2 x^3-x^2+3 x-4}{x+5}: \quad \frac{2 x^3-x^2+3 x-4}{x+5}=2 x^2+\frac{-11 x^2+3 x-4}{x+5} \\& =2 x^2+\frac{-11 x^2+3 x-4}{x+5}\end{aligned}$$[/tex]

[tex]$$\begin{aligned}& \text { Divide } \frac{-11 x^2+3 x-4}{x+5}: \frac{-11 x^2+3 x-4}{x+5}=-11 x+\frac{58 x-4}{x+5} \\& =2 x^2-11 x+\frac{58 x-4}{x+5}\end{aligned}$$[/tex]

Divide [tex]$\frac{58 x-4}{x+5}: \quad \frac{58 x-4}{x+5}=58+\frac{-294}{x+5}$[/tex]

[tex]$$=2 x^2-11 x+58+\frac{-294}{x+5}$$[/tex]

Simplify

[tex]$$=2 x^2-11 x+58-\frac{294}{x+5}$$[/tex]

2.[tex]\frac{x^4-8 x^2+2 x+7}{x+5}$$[/tex]

Divide [tex]$\frac{x^4-8 x^2+2 x+7}{x+5}: \quad \frac{x^4-8 x^2+2 x+7}{x+5}=x^3+\frac{-5 x^3-8 x^2+2 x+7}{x+5}$[/tex]

[tex]=x^3+\frac{-5 x^3-8 x^2+2 x+7}{x+5}$$[/tex]

Divide [tex]$\frac{-5 x^3-8 x^2+2 x+7}{x+5}: \frac{-5 x^3-8 x^2+2 x+7}{x+5}=-5 x^2+\frac{17 x^2+2 x+7}{x+5}$[/tex]

[tex]=x^3-5 x^2+\frac{17 x^2+2 x+7}{x+5}$$[/tex]

Divide [tex]$\frac{17 x^2+2 x+7}{x+5}: \quad \frac{17 x^2+2 x+7}{x+5}=17 x+\frac{-83 x+7}{x+5}$[/tex]

[tex]$$=x^3-5 x^2+17 x+\frac{-83 x+7}{x+5}$$[/tex]

Divide [tex]$\frac{-83 x+7}{x+5}: \quad \frac{-83 x+7}{x+5}=-83+\frac{422}{x+5}$[/tex]

[tex]$$=x^3-5 x^2+17 x-83+\frac{422}{x+5}$$[/tex]

3.

[tex]\begin{aligned}& \frac{2 x^3+x^2-8 x+15}{x^2+2 x-1} \\& \text { Divide } \frac{2 x^3+x^2-8 x+15}{x^2+2 x-1}: \frac{2 x^3+x^2-8 x+15}{x^2+2 x-1}=2 x+\frac{-3 x^2-6 x+15}{x^2+2 x-1} \\& =2 x+\frac{-3 x^2-6 x+15}{x^2+2 x-1} \\& \text { Divide } \frac{-3 x^2-6 x+15}{x^2+2 x-1}: \frac{-3 x^2-6 x+15}{x^2+2 x-1}=-3+\frac{12}{x^2+2 x-1} \\& =2 x-3+\frac{12}{x^2+2 x-1}\end{aligned}[/tex]

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First, identify the variables:

n = amount of nickels

d = amount of dimes

Next, setup the equations based on what you know.  The first equation is:

n + d = 28

For the second equation, we know that a dime is worth 10¢ and a nickel is 5¢, so it should be:

0.05n + 0.10d = 1.95

This a three-step answer:

In one formula (you can use any of them; most people use the simplest one), single out the variable on one side

Apply the first formula into the second formula, and solve it to get the value of one variable

Apply the answer from the second formula into the first formula, and solve it to get the value of the other variable

Answer:

The man made a profit of 63.333% from selling the machine.

Step-by-step explanation:

To find the percentage profit, you will need to first calculate the total profit the man made from selling the machine. To do this, you need to subtract the cost of importing the machine and the other costs associated with clearing and shipping it from the selling price.

Here's the calculation:

Total profit = Selling price - (Import cost + Clearing cost + Shipping cost)Substituting the values you provided, we get:Total profit = 1,080,000 - (600,000 + 60,000 + 40,000)

Total profit = 1,080,000 - 700,000Total profit = 380,000

Next, we need to divide the total profit by the import cost, and multiply the result by 100 to express the profit as a percentage. Here's the calculation:

Percentage profit = (Total profit / Import cost) * 100Substituting the values we calculated above, we get:Percentage profit = (380,000 / 600,000) * 100Percentage profit = 63.333%

Therefore, the man made a profit of 63.333% from selling the machine.

Answer:

Step-by-step explanation:

Answer:

  D)  (√13)/2

Step-by-step explanation:

You want to know the cosecant of the angle measured clockwise from the +x axis with point (6, 4) on its terminal side.

The cosecant of the angle is the ratio of the point's distance from the origin to the y-coordinate.

The distance from the origin is found using the Pythagorean theorem:

  d = √(x²+y²) . . . . . . . distance from the origin to (x, y)

  d = √(6² +4²) = √52 = 2√13

Then the desired ratio is ...

  csc(θ) = d/y = (2√13)/4

  csc(θ) = (√13)/2

Using the rules of cryptarithmetics problems and with the provided words and condition for a word, The answer is 9738+2558+1378==13674.

Mathematical puzzles known as cryptarithmetic problems use letters from the alphabet in place of the digits.

A rare version in which a formula is written and the matching cryptarithm's solution is the supplied formula is used to find the solution.

since the digits used are 0 to 9.

first letter can't be zero.

and we can't repeat the same digit for same different alphabets.

Using these rules with the condition that food is multiple of 1279.

The answer is : 9738+2558+1378==13674

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Using the rules of cryptarithmetics problems and with the provided words and condition for a word, The answer is 9738+2558+1378 =13674.

What is a cryptarithmetic problem?

Mathematical puzzles known as cryptarithmetic problems use letters from the alphabet in place of the digits.

What is reverse cryptarithm?

A rare version in which a formula is written and the matching cryptarithm's solution is the supplied formula is used to find the solution.

since the digits used are 0 to 9.

first letter can't be zero.

and we can't repeat the same digit for same different alphabets.

Using these rules with the condition that food is multiple of 1279.

The answer is : 9738+2558+1378 = 13674

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Answer:1/3

Step-by-step theexplanation:1/3 is the probablility of the marbles

7k+42 is the result of adding the first five classroom numbers in a row.

These integers that follow one another in a predictable counting pattern are referred to as consecutive integers. Due to the fact that no numbers are skipped while listing consecutive integers in a sequence, the distance between them is always fixed.

The smallest classroom number on the building's side is k, and there are two spaces between each succeeding odd number.

The first classroom is K.

The second classroom is k + 2.

The third classroom is k + 4.

The third classroom is k + 6.

The fifth classroom is k + 8.

The sixth classroom is k+10.

The seventh classroom is k+12.

The seven classrooms are added together as follows: k + (k + 2) + (k + 4) + (k + 6) + (k + 8)+(k+10)+(k+12)

When we combine terms that are similar,

we obtain,

k + k + k + k + k+ 2 + 4 + 6 + 8+10+12 = 7k+42.

Therefore, 7k+42 is the result of adding the first five classroom numbers in a row.

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Answer:

x = 9

Step-by-step explanation:

since the 3 sides are congruent then the triangle is equilateral with the 3 angles being congruent , all 60° , then

7x - 3 = 60 ( add 3 to both sides )

7x = 63 ( divide both sides by 7 )

x = 9

The statement that is false is A.. all isosceles triangles are similar

An isosceles triangle in geometry is a triangle with two equal-length sides. It can be specified as having exactly two equal-length sides or at least two equal-length sides, with the latter definition including the equilateral triangle as an exception.

An isosceles triangle has two of its three sides with equal lengths, and its two base angles are also equal. Although two isosceles triangles can have two sides that are equal on their own, they may not be similar because their sides may be of a different measurement.

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The number of points that Carlos score based on the information is 19 points.

An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side. It demonstrates the equality of the relationship between the expressions written on the left and right sides. We have LHS = RHS (left hand side = right hand side) in every mathematical equation.

In this.case, Fabio and Carlos play on a basketball team together. In the last game, Fabio had 7 points less than 2 times as many points as Carlos.

Let Carlos point = x

Fabio point will be = 2x - 7

The equation will be:

2x - 7 = 31

2x = 31 + 7.

2x = 38

Divide

x = 19

Carlos had 19 points

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Answer:

x=21

Step-by-step explanation:

rs= 6(x-9)

rt=2(2x-6)

rs=rt

6(x-9)=2(2x-6)

6x-54=4x-12

2x=42

x=21

The diagonals of rectangle are congruent.

We should know that a rectangle is a plane shape with four sides, four vertices and four angles.

Using a rectangle with the lettering ABCD

The diagonal AC divide the rectangle into two right angled triangles

<ADC = 90⁰

In the rectangle, AD=BC and AB=CD

Also, The same diagonal AC has another right angled triangle ABC with <ABC=90⁰

Similarly, diagonal BD divides the rectangle into two right angled triangles of ΔBAD and ΔBCD with a common hypothenuse of  BD

Hence AB=CD and AD= BC

Therefore, the two diagonals are congruent

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The reasonable estimate of the probability that Todd runs 5/13.

We know that,

Experimental probability = Number of favorable outcomes/total number  of outcomes.

Experimental probability, also called empirical probability, is based on real experiments and rational records of what happened. A series of real-world experiments are conducted to determine the occurrence of events. Experiments with undetermined results are called random experiments. The results of such experiments are uncertain. Repeat the random experiment several times to determine its probability. Experiments are repeated a specified number of times, and each repetition is called a trial. Mathematically, the formula for experimental probability is defined as:

Probability of event P(E) =

frequency of occurrence of event / total number of trials.

According to the question:

The number of favorable outcomes are 5.

The total number of outcomes are 2 + 3 + 3 + 5 = 13.

Therefore, the reasonable estimate of the probability that Todd runs is 5/13.

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Answer:

Landon would have -$43.53 in his checking account after the check is cashed and the bank handles his overdraft.

Step-by-step explanation:

All of the following are examples of performance measures that should be considered when designing a queue.

There are several performance measures that should be considered when designing a queue, including:

a. Probability that the waiting time exceeds t minutes (e.g. t can be 10 minutes): This measure can be used to assess the likelihood that customers will have to wait longer than a certain amount of time before being served. A high probability of long waiting times may indicate that the queue is not functioning effectively or that there are not enough servers to handle the demand.

b. Probability that servers are busy more than t minutes (e.g. t can be 10 minutes): This measure can be used to assess the likelihood that servers will be occupied for longer than a certain amount of time. A high probability of busy servers may indicate that the queue is not functioning effectively or that there are not enough servers to handle the demand.

c. Average waiting time: This measure can be used to assess the average amount of time that customers spend waiting in the queue before being served. A high average waiting time may indicate that the queue is not functioning effectively or that there are not enough servers to handle the demand.

Other performance measures that may be considered when designing a queue include the average number of customers in the queue, the average time that servers spend serving customers, and the probability that customers will leave the queue without being served.

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Answer:

1.4142135623730951i

Step-by-step explanation:

Did it help pls make me the brainliest and you can round your answer to how you want it and if not that's you answer thank you.

Step-by-step explanation:

please refer to the attached sketch for the answer.

Answer:

see below.

Step-by-step explanation:

[tex]a^{2}[/tex] + [tex]b^{2}[/tex] = [tex]c^{2}[/tex]

[tex]8^{2}[/tex] + [tex]15^{2}[/tex] = [tex]c^{2}[/tex]

64 + 225 = [tex]c^{2}[/tex]

289 = [tex]c^{2}[/tex]

[tex]\sqrt{289}[/tex] = [tex]\sqrt{c^{2} }[/tex]

17 = c

The simplest form of an expression is x³-13x². Therefore, option D is the correct answer.

Expressions are rewritten in a compact and unlike terms-free manner when they are simplified. Expressions are simplified by combining like phrases, resolving any provided brackets, and only leaving unlike terms that cannot be further reduced in the final simplified expression.

The given expression is -(2x³+x²)+3(x³-4x²)

Simplify the given expression as follows

-2x³-x²+3x³-12x²

= x³-13x²

The simplest form of an expression is x³-13x². Therefore, option D is the correct answer.

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Answer:

Step-by-step explanation:

so we know 3w = L + 5

and then we know that 2w + 2L = 194

so those are our two equations

since we have L by itself in the first equation, we are going to move the 5

L = 3w - 5

so now we can plug that in as L in the second equation

2w + 2(3w - 5) = 194

so now we distribute that 2

2w + 6w - 10 = 194

then simplify

8w - 10 = 194

then add the 10 to the other side

8w = 204

then we divide the 8

we get w = 25.5

so now we take that and go all the way back and plug that into the othr equation (ik this is a lot)

L = 3w - 5

so we plug in what we got for w

L = 3(25.5) -5

then multiply

L = 76.5 - 5

L = 71.5

so we end up with

w = 25.5 and L = 71.5

have a great day!! <3

The unknown angle in the intersecting lines is as follows:

m∠2 = 20 degrees

In the figure m∠ABD is 100 degrees and m∠1 is four times m∠2. Therefore, let's find the angle m∠2.

From the diagram, the sum of angle ABC and angle CBD is equals to angle ABD.

Therefore,

m∠ABD = 100 degrees

m∠ABC = m∠2

m∠CBD = m∠1

Therefore,

let

x = m∠2

m∠1 = 4x

Hence,

100 = 4x + x

5x = 100

divide both sides by 5

x = 100 / 5

x = 20 degrees

Therefore,

m∠2 = 20 degrees

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The point at which  =the curve xy = 25 is the tangent line parallel to 5x + y = 0 is y = ± 5√5 so, option A is correct.

A simple line in Euclidean geometry. A line, according to Euclid, is the distance between two points and can stretch forever in either direction. While Euclid's initial definition is now regarded as a line segment, such an extension in both directions is now thought of as a line.

Given:

the curve xy = 25 and the equation of the line is 5x + y = 0,

The equation of line  parallel to line 5x + y = 0 will be,

y = mx + c

y = -5x + c   (y = -5x)

The line will be in the curve as it is tangent, so,

xy = 25 and y = -5x + c line have a solution,

Solve the above equation as  shown below,

y = ± 5√5

Thus, the point y = ± 5√5 the line is tangent to the curve.

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Answer: 66 1/24

Step-by-step explanation:

Answer:

EL/EF

OS/OJ

Step-by-step explanation:

Tangent is equal to opposite/adjacent

The required solution of the given inequality is given as x > 4, and the answer for the blanks is to Divide both sides by -8 and change the inequality sign.

Inequality can be defined as the relation of the equation containing the symbol of ( ≤, ≥, <, >) instead of the equal sign in an equation.

Here,
Given inequality,
-8x < 32
Divide both sides by -8
x > 4

The sign of the inequality change because multiplication with the negative value changes the inequality sign and the higher negative value is the least value.

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The sum of the lengths of two sides is equal to the length of the third side is 45°.

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The Co-ordinates of the point C that divides the line in the ratio of 3:4 is (-20/7, -17/7)

What is Section Formula?

The Section formula is used in coordinate geometry to compute the ratio of a line segment split by a point, either internally or externally. It determines the centroid, incenter, and excenters of a triangle. It is used in physics to determine the centre of mass of systems, equilibrium locations, and so on.

Solution:

A(-8, 1) and B(4, -7)

Ratio is 3:4

Section Formula is (mx2 + nx1/ m + n), (my2 + ny1/ m + n)

m = 3 and n = 4

Co-ordinates of C are (3*4 + 4*(-8)/ 3+4), (3*(-7) + 4*1 / 3+4)

= (12 - 32 / 7), (-21 + 4 / 7)

= (-20/7, -17/7)

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Answer:

me either

Step-by-step explanation: