Use the long division method to find the result when 4x^3+13x^2+17x+8 is divided by x+1

A) [tex]$x+y=(1+2 \sqrt{3})+(1-\sqrt{3}) i$[/tex]

B) [tex]$y+z=(\sqrt{3}+1)-(2+\sqrt{3}) i$[/tex]

c) [tex]$y-z=(\sqrt{3}-1)-\sqrt{3} i$[/tex]

are the value of given algebraic expression.

The numbers which can be expressed in the form of [tex]$x+iy[/tex] where, [tex]$x, y$[/tex] are real numbers and 'i' is an imaginary number called "iota".

here [tex]$\mathrm{i}$[/tex] is iota whose value is: [tex]$\mathrm{i}=\sqrt{-1}[/tex]

Given .

[tex]$$\begin{aligned}& x=1+\sqrt{3}+2 i \\& y=\sqrt{3}-(1+\sqrt{3}) i \\& z=1-i\end{aligned}$$[/tex]

upon solving two complex number we solve coefficient of iota together and real number together.

A) to find [tex]$(x+y)$[/tex]

[tex]$$\begin{aligned}& x+y=(1+\sqrt{3}+2 i)+(\sqrt{3}-i-\sqrt{3} i) \\& x+y=(1+2 \sqrt{3})+(2-1-\sqrt{3}) i \\& x+y=(1+2 \sqrt{3})+(1-\sqrt{3}) i\end{aligned}[/tex]

B) [tex]$\mathbf{y}+\mathbf{z}$[/tex]

[tex]$$\begin{aligned}& y+z=(\sqrt{3}-i-\sqrt{3} i)+(1-i) \\& y+z=(\sqrt{3}+1)-(2+\sqrt{3}) i\end{aligned}[/tex]

c) [tex]$\mathbf{y}-\mathbf{z}$[/tex]

[tex]$$\begin{aligned}& y-z=(\sqrt{3}-i-\sqrt{3} i)-(1-i) \\& y-z=(\sqrt{3}-1)-\sqrt{3} i\end{aligned}[/tex]

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Answer:

well, both the domain, and the range can have a positive and/or negative infinity, but as long as the 2nd factor is an opposite symbol then you will have a correct answer, for instance, -infinity, and 2 could work, but if the 2 was negative then there would be a problem

Step-by-step explanation:

Therefore , as a result, x = 53 and y = 10 are the answers to the trigonometry problem that was presented.

Trigonometry is the discipline of mathematics that studies correlations between angles and sides of triangles. Trigonometry is present in all of geometry because every ahead and move form may indeed be resolved to a set of triangles. Amazingly intricate connections exist between geometry and other areas of mathematics, particularly arithmetic, real or abstract, infinite series, arithmetic, and infinite series.

Here,

Sin 30 = Opposing Side/High

1/2 = 5 / y

y = 5 / (1/2)

y = 10

Cos 30 = Adjustment Side/ Hyp

√3/2 = x/y

√3/2 = x/10

x = 10√3 / 2

x = 5√3

In light of this, the given fractional problem's answer is

x = 5√3 and y = 10.

Therefore , as a result, x = 53 and y = 10 are the answers to the trigonometry problem that was presented.

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The new model {A} for the total number of new green tea and fruit juice sales can be written as {A} = 9t^4 + 3t² + 105 .

What is expression ?

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.

Any mathematical statement that includes numbers, variables, and an arithmetic operation between them is known as an expression or algebraic expression. In the phrase 4m + 5, for instance, the terms 4m and 5 are separated from the variable m by the arithmetic sign +.

An algebraic expression is made up of a number of variables, constants, and mathematical operations. We are aware that variables have a wide range of values and no set value. They can be multiplied, divided, added, subtracted, and other mathematical operations since they are numbers. as in 3x Plus 4.

Given is that during a 20-year period, G and I can be modeled by the following equation (where t is the time in years) :

G = 6t^4+ 3t³ – 2t² + 5t + 60

I = 3t^4 - 3t³ + 5t² - 5t + 45

where {G} is the number (in billions) of new green tea sales and {I} be the number in billions of new fruit juice sales.

A new model {A} for the total number of new green tea and fruit juice sales can be written as -

{A} = {G} + {I}

{A} = 6t^4+ 3t³ – 2t² + 5t + 60 + 3t^4 - 3t³ + 5t² - 5t + 45

{A} = 9t^4 + 3t² + 105

Therefore, the new model {A} for the total number of new green tea and fruit juice sales can be written as {A} = 9t^4 + 3t² + 105

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The given quadratic equation has two possible roots as -

{x} = -1/2 and {x} = 1.667.

A quadratic equation is a equation that is of the form -

y = f{x} = ax² + bx + c

Given is the statement as -

"12 x squared minus 14 x equals 10"

The given function can be written as -

f(x) = 12x² - 14x - 10

Refer to the graph attached. The x - intercepts show the solution of the given quadratic equation. So, we can write -

(x + 1/2)(x - 1.667) = 0

(x + 1/2) = 0     and     (x - 1.667) = 0

x = -1/2     and      x = 1.667

Therefore, the given quadratic equation has two possible roots as -

{x} = -1/2 and {x} = 1.667.

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Answer:

Step-by-step explanation:

Its A

Answer: 2.25 grams

Step-by-step explanation:

In this problem, we are given the ratio of grams to weight. Since we are trying to find how many grams to give to a person with a specific weight, we can use proportions to solve.

[tex]\frac{150mg}{5kg} =\frac{x}{75kg}[/tex]               [cross multiply]

[tex]11250=5x[/tex]                  [divide both sides by 5]

[tex]x=2250mg[/tex]

We are almost done with the problem. The problem is asking for grams, not mg, so we can use unit conversions to change that.

[tex]\frac{1000mg}{1g}=\frac{2250mg}{y}[/tex]          [cross multiply]

[tex]1000y=2250[/tex]               [divide both sides by 1000]

[tex]y=2.25[/tex]

Therefore, we need to give 2.25 grams.

The measure of the missing angle is 17 degrees.

Trigonometry is a method that can by used to solve questions involving the application of functions. Some examples of trigonometric functions are: Sine, Cosine, Tangent, Secant, Cotangent etc.

Now considering the given question, we are to find the measure of the missing angle. We have;

cos θ = 0.9563

where θ is the missing angle the value of which is to be determined.

Thus, divide both sides of the expression by cos to have;

cos θ/ cos = 0.9563. cos

θ = cos^-1 0.9563

θ = 17.0 degrees

Therefore, the value of the missing angle is 17 degrees.

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Answer: 2.403 × 10^3 atoms

Step-by-step explanation:

10^13 x 6.02 = 6.02^23 and 6.02^23 x 4 = 2,403 turned into 2.403 x 10^3 atoms.

Answer:

[tex](\frac{5}{3} ;\frac{4}{3} ).[/tex]

Step-by-step explanation:

[tex]\left \{ {{x+y=3} \atop {\frac{y+2}{2} =x}} \right. \ = > \ \left \{ {{x+y=3} \atop {y+2=2x}} \right. \ = > \ \left \{ {{x+y=3} \atop {2x-y=2}} \right. \ = > \ \left \{ {{x=\frac{5}{3} } \atop {y=\frac{4}{3} }} \right.[/tex]

let the third side be b then use the pythagoras theorem

Answer:  19/400

Step-by-step explanation:

4.75% = 4.75/100 (in fractions)

          = 475/10000 (multiply by 100 for both the numerator and denominator)

           = 19 / 400 (divide by 25 for both the numerator and denominator)

How do I know it is 25 for the last step?

Obtain the highest common factor of 475 and 10000. The highest common factor of these two numbers is 25.

The length of ribbon is 48 yards.

The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.

For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.

12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.

As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.

This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.

Given:

Kala got a prepaid debit card with $15.

Price of Ribbon = 24 cents per yard.

After purchase money left $3.48.

So, Price of Ribbon purchased = 15 - 3.48 = $11.52 = 1152 cents

length of ribbon = 1152/ 24

                           = 48 yards

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Answer:

a. A' (-3, -1) B' (3, 2) C' (6, 0); b. A' (-1, -3) B' (1, 6) C' (2, 0); c. A' (-2, -3) B' (2, 6) C' (2, 0)

Step-by-step explanation:

Solutions for graph a, b and c are attached.

a. (x, y) to (3x, y)

A' (-3, -1) B' (3, 2) C' (6, 0)

b. (x, y) to (x, 3y)

A' (-1, -3) B' (1, 6) C' (2, 0)

c. (x, y) to (2x, 3y)

A' (-2, -3) B' (2, 6) C' (2, 0)

REMEMBER: Connect the lines to make the triangles for each graph BEFORE submitting.

Answer:

C.  meters

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

Therefore , the solution of the given problem of angles comes out to be equation :  x+ y =85°.

'

In Euclidean geometry, an angle is a shape that is made up of two rays, known as the tone's flanks, that meet at a midpoint known as such angle's vertex. Two rays may combine to form an angle there in plane where they are positioned. When two planes collide, an angular is also generated. They are referred to as dihedral angles. An angle in plane geometry is the possible configuration of two rays of lines that share a termination. The origin of the English term "angle" is the Latin phrase "angulus," which meaning "horn." The vertex is the point in which the two vectors, also known as that of the faces of the angle, converge.

Here,

Given :

Let two angles be x and y  is

=> x+ y =85°

So, the equation is represented as  x+ y =85°.

Therefore , the solution of the given problem of angle comes out to be equation :  x+ y =85°.

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280 AND 245 RS  the company GAIN,20% OFF it is 280 rs and 30% off it is 245 rs

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x=125

...............

on solving the equation, we have therefore the value of x from the given equation comes out to be 13.5

An equation is a formula in mathematics that joins two statements with the equal symbol = to represent equality. The definition of an equation in algebra is a mathematical statement proving the equality of two mathematical expressions. In the equation 3x + 5 = 14, for instance, the terms 3x + 5 and 14 are separated by an equal sign. The link between two phrases on either side of a letter is expressed mathematically. There is often only one variable, which is also the symbol. instance: 2x - 4 Equals 2.

equation given is 3(x+2)=7x-48

value of x

[tex]3(x+2)=7x-48\\ 3x+6=7x-48\\7x-48-3x-6=0\\ 4x-54=0\\ 4x=54\\ x=54/4\\ x=13.5\\[/tex]

value of x from the given equation comes out to be 13.5

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=======================================================

Explanation:

I'm assuming your teacher meant to say "same number or letter" instead of "same number of letter" at the very end of the problem.

The best case scenario is that the person selecting the cards is very lucky to select say a king of hearts and king of clubs. This shows that 2 cards is the lowest amount of cards to select here.

----------

Of course, such a scenario is not that likely. That person is likely to get some other card compared to the 1st selection.

Let's assume the person selecting the cards has the worst luck possible. This means they select each card 1,2,3,...,10,J,Q,K exactly once in any order. If this happens, then the person does not have any pairs just yet. The person has selected 13 cards so far with this worst case scenario.

The 14th card is guaranteed to pair up with some other card previously chosen. There simply aren't any other options left once you've exhausted all possibilities. See the pigeonhole principle for more information.

So this is why you would need to select 14 cards to guarantee having at least two pair up together (i.e. you would have 2 or more pairs).

The correct representations of the inequality are

-6x + 15 < 10 - 5x

A number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right.

From the question, we are to determine the correct representations of the inequality

From the given information,

The given inequality is

-3(2x - 5) < 5(2 - x)

To determine the correct representations, we would proceed to solve the inequality

Solving the inequality

-3(2x - 5) < 5(2 - x)

-6x + 15 < 10 - 5x

This is one of the representations of the inequality

Then,

Collect like terms

-6x + 15 < 10 - 5x

-6x + 5x < 10 - 15

-x < -5

Multiply through by -1

x > 5

If the solution is represented on a number line, we would have a number line from negative 3 to 3 with an increments of 1 and an open circle at 5 and a bold line starts at 5 and is pointing to the right.

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Answer: I'm sorry if it's wrong I'm pretty sure it's ≥ if not I'm sorry

Step-by-step explanation:

To calculate the distance between two points:

We apply the following formula:

d = √(x₂ - x₁)² + (y₂ - y₁)²

The points are:

We substitute data and solve:

[tex]\bf{d=\sqrt{(6-(-3))^2+(-8-8(-8))^2 } }\\ \\ \bf{ d=\sqrt{9^2+0^2}=\sqrt{81+0} }\\ \\ \bf{d=\sqrt{81}=9 }[/tex]

The distance between the points (−3,− 8), (6, – 8) is 9.

Answer:

To solve this problem, we can set up the following equation:

2.5 inches = 1,000 feet

We are told that the model is 18 inches high, so we can write the following equation:

18 inches = X feet

To solve for X, we can cross-multiply the equations to get:

(2.5 inches)X = (1,000 feet)(18 inches)

Simplifying this equation, we get:

X = 4,500 feet

Therefore, the height of the volcano is 4,500 feet.

Step-by-step explanation:

Answer: To find the product of two matrices A and B, we must use the matrix multiplication rules.

Matrix A is a 2x2 matrix with values [2 3; 4 5] and matrix B is a 2x2 matrix with values [1 2; 3 4].

The result of matrix multiplication, AB, will also be a 2x2 matrix.

To find each element in the resulting matrix, we take the dot product of the corresponding row in matrix A and column in matrix B.

The first element in the resulting matrix AB, is found by taking the dot product of the first row in matrix A and the first column in matrix B:

(21) + (33) = 2+9 = 11

The second element in the resulting matrix AB, is found by taking the dot product of the first row in matrix A and the second column in matrix B:

(22) + (34) = 4+12 = 16

The third element in the resulting matrix AB, is found by taking the dot product of the second row in matrix A and the first column in matrix B:

(41) + (53) = 4+15 = 19

The forth element in the resulting matrix AB, is found by taking the dot product of the second row in matrix A and the second column in matrix B:

(4*2)

Step-by-step explanation:

Jahnay is making 6.5 cakes from the given ingredients.

The division in mathematics is one kind of operation. In this process, we split the expressions or numbers into the same number of parts.

Given:

Recipe: Makes 1 Cake =  120 g sugar + 130 g butter + 260 g flour + 3 eggs.

Jahnay is following this recipe to make cakes.

Jahnay uses 780 g of butter.

To find the number of cakes:

Use division operation,

780 ÷ 120,

= 780/120

= 78/12

= 6.5

Therefore, Jahnay makes 6.5 cakes.

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Answer:

2.66

Step-by-step explanation:

Answer:

2.66

Step-by-step explanation:

look at first at tenths for the biggest no .if there is a tie proceed to hundredths for biggest no and so on