What is the remainder (just the number ) when doing this division problem? (15x^(2)+4x-37)-:(3x-4)

The quadratic equations are solved and the value of x are 1 and -7 respectively

A quadratic equation is a second-order polynomial equation in a single variable x , ax² + bx + c=0. with a ≠ 0. Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has at least one solution. The solution may be real or complex.

The roots of the quadratic equations are

x = [ -b ± √ ( b² - 4ac ) ] / ( 2a )

where ( b² - 4ac ) is the discriminant

when ( b² - 4ac ) is positive, we get two real solutions

when discriminant is zero we get just one real solution (both answers are the same)

when discriminant is negative we get a pair of complex solutions

Given data ,

Let the quadratic equation be represented as A

Now , the value of A is

a)

x² + 6x = 7

Adding 9 on both sides of the equation , we get

x² + 6x + 9 = 16

On simplifying the equation , we get

( x + 3 )² = ( 4 )²

Taking square roots on both sides , we get

x + 3 = ±4

Subtracting 3 on both sides , we get

x = 1 and x = -7

Therefore , the value of x are 1 and -7 respectively

Hence , the quadratic equations is solved

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Answer:

1. [tex]75[/tex]

2. [tex]4x^{8}[/tex]

3. [tex]128[/tex]

Step-by-step explanation:

[tex]\frac{3*5^9}{5^7}=\frac{3*5^2*5^7}{5^7}=3*5^2=75[/tex]

[tex]\sqrt{16x^{16}}=4\sqrt{x^{16}} =4x^8[/tex]

[tex]\frac{(-5)(2^8)}{-6+1}/2=\frac{(-5)(2^8)}{(-5)(2)}=\frac{2^8}{2}=2^7=128[/tex]

We can conclude that -

The exponential function is of the form -

f(x) = eˣ

Given is to write the exponential growth and exponential decay equation.

{ 1 } -

The general exponential growth equation is -

[tex]$f(x)=a(1+r)^{x}[/tex]

{ 2 } -

The general exponential decay equation is -

[tex]$\frac {dN}{dt}= -\lambda N[/tex]

Option {A} and option {E} represent the exponential decay. Option {B}, {E} and {D} represent exponential growth.

Therefore, we can conclude that -

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The value of angle x is 134°.

We have:

Angle ABD = 180° (straight line)

Angle ABE = 44° (given)

Angle BCE = 90° (as BC is perpendicular to AB)

Angle AEC = 180° - Angle BCE - Angle BAE = 180° - 90° - 44° = 46° (angle sum of triangle ABE)

Now, we can use the exterior angle property of triangles to find the value of angle x.

Angle AED = Angle AEC + Angle CED = 46° + x (exterior angle property of triangle CED)

Angle AED = Angle ABD = 180° (opposite angles of a cyclic quadrilateral)

Therefore, we have:

46° + x = 180°

x = 180° - 46°

x = 134°

Hence, the value of angle x is 134°.

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Answer:

it means if the given sides are approximately equal then the triangles are equal too

Step-by-step explanation:

if the the sides are equal then the triangles are equal too

A^8 = [\begin{array}{ccc}252&-3&3\\3&252&-3\\-3&3&252\end{array}\right]

To find the eigenvalues and eigenvectors of matrix A, use the characteristic polynomial of A which is given by:
P(λ) = det(A-λI) = λ^3-6λ^2+11λ-6

The roots of the equation are λ1 = 2, λ2 = 3, and λ3 = 1.

The corresponding eigenvectors are:
v1 = [\begin{array}{ccc}-1\\1\\1\end{array}\right]
v2 = [\begin{array}{ccc}1\\-1\\1\end{array}\right]
v3 = [\begin{array}{ccc}1\\1\\1\end{array}\right]

The eigenvalues and eigenvectors of A can be put together in the following matrix:
T = [\begin{array}{ccc}-1&1&1\\1&-1&1\\1&1&1\end{array}\right]

The eigenvalues of A can be put together in the following matrix:
Λ = diag{λ1, λ2, λ3} = [\begin{array}{ccc}2&0&0\\0&3&0\\0&0&1\end{array}\right]

Now, to calculate A^8, you will need to use the eigenvalues and eigenvectors of A. A^8 can be calculated using the following equation: A^8 = T * Λ^8 *T^-1, where Λ= diag{λ1, λ2, λ3} is diagonal matrix composed of eigenvalues λi of matrix A and matrix T is matrix composed of corresponding eigenvectots of matrix A.

Thus, A^8 can be calculated as follows:
A^8 = [\begin{array}{ccc}-1&1&1\\1&-1&1\\1&1&1\end{array}\right] * [\begin{array}{ccc}256&0&0\\0&6561&0\\0&0&1\end{array}\right] * [\begin{array}{ccc}-1&1&1\\1&-1&1\\1&1&1\end{array}\right]^-1

= [\begin{array}{ccc}252&-3&3\\3&252&-3\\-3&3&252\end{array}\right]

Therefore, the result of A^8 is: A^8 = [\begin{array}{ccc}252&-3&3\\3&252&-3\\-3&3&252\end{array}\right]

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Answer:

dddiejehehegeheheheh

In trigonometry, temperatures can be converted between different scales, such as Fahrenheit and Celsius, using equations. For example, to convert from Fahrenheit to Celsius, you can use the equation C = (F - 32) * (5/9), where C is the temperature in Celsius and F is the temperature in Fahrenheit.

It seems like there are a lot of typos and irrelevant information in this question, making it difficult to understand what is being asked. However, I will do my best to provide an answer based on the key terms provided.

In trigonometry, temperatures can be converted between different scales, such as Fahrenheit and Celsius, using equations. For example, to convert from Fahrenheit to Celsius, you can use the equation C = (F - 32) * (5/9), where C is the temperature in Celsius and F is the temperature in Fahrenheit.

For the final aubmision, it is important to make sure that your work is accurate and complete before converting it to a PDF. This will ensure that your modified portfolio is professional and easy to understand.

Once you have completed your work, you can download it as a PDF and submit it in your portfolio. This will allow you to keep a record of your work and show your understanding of trigonometry and teffeeratures.

I hope this helps! If you have any further questions, please feel free to ask.

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The seasonally-adjusted forecast for quarter 4 of year 5 is 91.9

The seasonally-adjusted forecast for quarter 4 of year 5 can be calculated by using the following equation:
Seasonally Adjusted Forecast = Trend Equation + Seasonal Factors
= 65 + 6.7X + 0.1
= 65 + 6.7X + 0.1
= 65 + 6.7*4 + 0.1
= 65 + 26.8 + 0.1
= 91.9
Therefore, the seasonally-adjusted forecast for quarter 4 of year 5 is 91.9.

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Y = 4114/5114

3 (a) To solve 2557⋅X=457 for X∈Z57 using Euclid's algorithm, take the GCD of 2557 and 457. That is, the GCD is:

GCD(2557, 457) = GCD(2557 - 457, 457)

                  = GCD(2157, 457)

                  = GCD(757, 457)

                  = GCD(357, 457)

                  = GCD(157, 457)

                  = 457


Therefore, the GCD of 2557 and 457 is 457, and thus the solution to the equation is X = 457/2557.

3 (b) To find all solutions to the equation 50114⋅Y=8114 for Y∈Z114, we need to rewrite the equation in terms of ordinary integers, since the inverse of 50114 does not exist. The equation can be rewritten as Y = 8114/50114 = 8114/(5114⋅2114) = 4114/5114. This equation is the same as the one in part (a), with 25 replaced by 5. Thus, the solution to this equation is Y = 4114/5114, which is the same solution found in part (a). Therefore, there is only one solution to this equation, and this solution is Y = 4114/5114.

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G is linear.

To show that g:V→F defined by g(x)=⟨x,y⟩ for all x∈V is linear, we need to prove that g satisfies the following two properties:

1) g(x+z)=g(x)+g(z) for all x,z∈V
2) g(αx)=αg(x) for all x∈V and α∈F

Proof:

1) Let x,z∈V. Then g(x+z)=⟨x+z,y⟩=⟨x,y⟩+⟨z,y⟩=g(x)+g(z) by the distributive property of the inner product.

2) Let x∈V and α∈F. Then g(αx)=⟨αx,y⟩=α⟨x,y⟩=αg(x) by the scalar multiplication property of the inner product.

Therefore, g is linear.

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Answer:

Below

Step-by-step explanation:

'k' shifts the graph of f(x)   UP   by  ' k'  units     k = 6   ( look how far the y-axis intercepts are shifted UP= 6 units  from -2 to + 4)

The quotient for the associated division is -0.5x^(3)-x^(2)+x+1 and the remainder is -9.

Synthetic division is a method for dividing polynomials by monomials. It is a simplified form of the long division of polynomials, and is useful when the divisor is a monomial. The method involves arranging the coefficients of the dividend in a row, and then dividing each term by the divisor.

To find P(-2) for P(x)=x^(4)+2x^(3)-2x-7, we simply need to substitute -2 for x and evaluate the expression.

P(-2)=(-2)^(4)+2(-2)^(3)-2(-2)-7

P(-2)=16+2(-8)-2(-2)-7

P(-2)=16-16+4-7

P(-2)=-3

Therefore, the value of P(-2) is -3.

The associated division would be (x^(4)+2x^(3)-2x-7)/(-2), which can be simplified using polynomial long division. The quotient is -0.5x^(3)-x^(2)+x+1 and the remainder is -9.

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Answer:

the answer is 8

Step-by-step explanation:

subtract 11
67 - 11 = 56

Divide 7 to find the answer

56/7 = 8

F = Fran's income

W = Winston's income

[tex]F+W=80000\hspace{5em}\stackrel{ \textit{one quarter} }{\cfrac{W}{4}}=\stackrel{ \textit{one sixth} }{\cfrac{F}{6}} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{using the 1st equation}}{F+W=80000}\implies F=80000-W \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{\textit{using the 2nd equation}}{\cfrac{W}{4}=\cfrac{F}{6}}\implies \stackrel{\textit{substituting from above}}{\cfrac{W}{4}=\cfrac{80000-W}{6}}\implies 6W=320000-4W \\\\\\ 10W=320000\implies W=\cfrac{320000}{10}\implies \boxed{W=32000}~\hfill \stackrel{ 80000~~ - ~~32000 }{\boxed{F=48000}}[/tex]

x + y = 35  and 2x + 4y = 102 represents the required system of equations.

Two or more expressions with an Equal sign is called as Equation.

Let x be the number of chickens and y be the number of cows.

Each chicken has 2 legs, so x chickens have 2x legs.

Each cow has 4 legs, so y cows have 4y legs.

The total number of animals is 35 and the total number of legs is 102, so we can set up the following system of equations:

x + y = 35 (the total number of animals)

2x + 4y = 102 (the total number of legs)

Hence, x + y = 35  and 2x + 4y = 102 represents the required system of equations.

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The table of values is added below and and the graph is attached

From the question, we have the following parameters that can be used in our computation:

y < |4x + 1| - 3

To create a table of values for y < |4x + 1| - 3, we can choose different values of x and substitute them into the expression to find the corresponding values of y.

Let's choose some values of x: -2, -1, 0, 1, 2.

When x = -2, we have:

y < |4(-2) + 1| - 3

y < 4

When x = -1, we have:

y < |4(-1) + 1| - 3

y < 0

When x = 0, we have:

y < |4(0) + 1| - 3

y < |1| - 3

y < -2

When x = 1, we have:

y < |4(1) + 1| - 3

y < 2

When x = 2, we have:

y < |4(2) + 1| - 3

y < 6

Putting it all together, we have the following table:

x y values

-2 y < 4

-1 y < 0

0 y < -2

1 y < 2

2 y < 6

The graph is attached

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Answer: 5.25

Step-by-step explanation:

     First, a percent divided by 100 is a decimal.

15% / 100 = 0.15

     Next, we are finding 15% of 35. In mathematical terms, "of" usually represents multiplication. We will multiply 0.15 by 35 to find 15% of 35.

0.15 * 35 = 5.25

The work performed on the steam in this compression process per kilogram is -50 kPa*V/kg.\

To find the work performed on the steam in this compression process per kilogram, we need to use the following formula:

W = PΔV

Where W is the work, P is the pressure, and ΔV is the change in volume.Since the process is isothermal, the pressure and volume are inversely proportional.

This means that if the pressure is doubled, the volume will be halved. In this case, the pressure is constant at 100 kPa, and the volume is halved because half of the vapour has condensed.

Therefore, the change in volume is:

ΔV = V/2 - V = -V/2

Substituting this into the formula for work, we get:

W = PΔV = (100 kPa)(-V/2) = -50 kPa*V

To find the work per kilogram, we need to divide the work by the mass of the steam. Since the mass is not given in the question, we can assume it is 1 kilogram. Therefore, the work per kilogram is:

-50 kPa*V/1 kg = -50 kPa*V/kg

So the work performed on the steam in this compression process per kilogram is -50 kPa*V/kg.\

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Javier worked a total of 23 hours over the two weekends (True), Javier earned $184 over the two weekends(True)

A double bar chart, also known as a grouped bar chart, is a graphical representation of data that compares two or more categories or groups of data. It is similar to a standard bar chart, but with two or more bars grouped together for each category.

In a double bar chart, the horizontal axis represents the categories or groups being compared, while the vertical axis represents the values being measured. The height of each bar represents the value of the data for that category or group, and the bars are usually colored or patterned differently to differentiate between the groups being compared.

Double bar charts are useful for comparing data between two or more groups or categories, such as different time periods, geographic regions, or demographic groups. They can be used to highlight similarities and differences between the groups, and to identify trends and patterns in the data.

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The complete question is

To graph a quadratic function, follow the steps explained to obtain the smooth curve of the quadratic function.

Graphing quadratic functions involves plotting the points on a coordinate plane that satisfy the equation of the function. Quadratic functions are typically written in the form:

f(x) = ax^2 + bx + c

where;

To graph a quadratic function, you can follow these steps:

x = -b / 2a

y = f(x)

You can find the x-coordinate of the vertex by using the formula above, and then substitute it into the function to find the corresponding y-coordinate.

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[tex]-\dfrac{3}{4}x-\dfrac{1}{3}+\dfrac{7}{8}x-\dfrac{1}{2} = -\dfrac{3}{4}x+\dfrac{7}{8}x -\dfrac{1}{3}-\dfrac{1}{2} = \\[/tex]

[tex]= -\dfrac{3(2)}{4(2)}x+\dfrac{7}{8}x -\dfrac{1(2)}{3(2)}-\dfrac{1(3)}{2(3)} = -\dfrac{6}{8}x+\dfrac{7}{8}x -\dfrac{2}{6}-\dfrac{3}{6} \\[/tex]

[tex]= \dfrac{-6+7}{8}x -\dfrac{2+3}{6} = \dfrac{1}{8}x -\dfrac{5}{6} \\[/tex]

The two linear functions that have a minimum value but no maximum value are:

f(x) = 10 - 3x over the domain x ≤ 9

f(x) = 5x - 1 over the domain x ≥ -7

From the question, we are to determine the linear function that have minimum value but no maximum value

The decreasing function f(x) = 10 - 3x over the domain x ≤ 9 has a minimum value but no maximum value.

Domain: x ≤ 9

This function is decreasing since the slope is negative.

The minimum value occurs at x = 9, where f(9) = 10 - 3(9) = -17.

Since the slope is negative, the function continues to decrease without bound as x approaches negative infinity.

The decreasing function f(x) = 5x - 1 over the domain x ≥ -7 has a minimum value but no maximum value.

Domain: x ≥ -7

This function is increasing since the slope is positive.

The minimum value occurs at x = -7, where f(-7) = 5(-7) - 1 = -36.

Since the slope is positive, the function continues to increase without bound as x approaches positive infinity.

Hence, the functions are:

f(x) = 10 - 3x over the domain x ≤ 9

f(x) = 5x - 1 over the domain x ≥ -7

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4312 liters of water need to be filled to calculate the volume of water occupying 70% volume of the tank.

What is volume ?

Volume is the amount of space occupied by an object or a substance. It is a measure of the amount of three-dimensional space an object or a substance occupies. The volume of an object or substance is typically measured in cubic units, such as cubic meters (m³), cubic centimeters (cm³), or cubic feet (ft³).

A) To calculate the area of glass for the tank without lid, we need to find the total surface area of the rectangular box.

The front and back sides have dimensions 1.1 m x 7 dm = 1.1 m x 0.7 m = 0.77 m² each.

The top and bottom sides have dimensions 1.1 m x 8 m = 8.8 m² each.

The left and right sides have dimensions 7 dm x 8 m = 0.7 m x 8 m = 5.6 m² each.

Therefore, the total surface area of glass for the tank without lid is:

0.77 m² + 0.77 m² + 8.8 m² + 8.8 m² + 5.6 m² + 5.6 m² = 30.6 m²

B) To calculate the volume of water occupying 70% of the tank, we first need to calculate the volume of the tank.

The volume of a rectangular box is found by multiplying its length, width, and height:

Volume = length x width x height

We have:

length = 1.1 m

width = 8 m

height = 7 dm = 0.7 m

Volume = 1.1 m x 8 m x 0.7 m = 6.16 m³

Next, we need to find 70% of the volume of the tank:

70% of 6.16 m³ = 0.7 x 6.16 m³ = 4.312 m³

Finally, we need to convert cubic meters to liters, using the conversion factor given:

1 m³ = 1000 L

Therefore,

4.312 m³ x 1000 L/m³ = 4312 L

Therefore, 4312 liters of water need to be filled to calculate the volume of water occupying 70% volume of the tank.

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The area of this trapezoid is 66 cm².

To find the area of a trapezoid, we use the formula:

Area = (a + b) x h / 2

Where:

a and b are the lengths of the parallel sides of the trapezoid

h is the height

If we assume that the 22 cm and 11 cm sides are parallel sides, that is

a = 22

b = 11

and h = 4 cm

Now we can use the formula to find the area:

Area = (22 cm + 11 cm) x 4 / 2

Area = 66 cm²

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1) a. 6     b. 5 - i     c. 1 + 4i    d.  -0.5 + 2.5i

2) x^3 - (7 - 3i)x^2 + (14 - 6i)x - (8 - 24i).

(1)
(a) 2 + 3i + 4 - 3i = 6 + 0i = 6

(b) (3 + 2i)(1 - i) = 3 + 2i - 3i - 2i^2 = 3 - i + 2 = 5 - i

(c) 2 + 3i - (1 - i) = 2 + 3i - 1 + i = 1 + 4i

(d) 2+3i / 1-i = (2+3i)(1+i) / (1-i)(1+i) = (2+2i+3i+3i^2) / (1-i+i-i^2) = (2+5i-3) / (1+1) = (-1+5i) / 2 = -0.5 + 2.5i

(2)

If x = 1 – 3i, x = 2, and x = 4 are roots of f(x),

then we can write f(x) as:
f(x) = (x - (1 - 3i))(x - 2)(x - 4)

Multiplying these factors out, we get:

f(x) = (x^2 - (1 - 3i)x - 2x + 2(1 - 3i))(x - 4)
f(x) = (x^2 - (3 - 3i)x + 2 - 6i)(x - 4)
f(x) = x^3 - (7 - 3i)x^2 + (14 - 6i)x - (8 - 24i)
So, the polynomial f(x) is x^3 - (7 - 3i)x^2 + (14 - 6i)x - (8 - 24i).

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Based on the figure, the measure of the angle GPY is 118 degrees.

Alternate angles are a pair of angles that are formed by a transversal intersecting two parallel lines.

When a transversal intersects a parallel line, it creates four angles.

Alternate angles are the pairs of angles that are on opposite sides of the transversal and on opposite sides of the parallel lines.

The key property of alternate angles is that they are congruent, meaning they have the same measure.

Here angle GPY is alternate to angle RPK.

Thus;

8p + 94 = 5p + 103

8p - 5p = 103 - 94

3p = 9

Divide both sides by 3;

p = 3

The measure of angle GPY becomes ;

= 5(3) + 103= 15 + 103= 118 degrees.

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The possible rational zeros of [tex]f(x) = 5x^(4) - 9x^(3) - 7x^(2) + 9x - 2[/tex] are [tex]±1, ±2, ±1/5, and ±2/5.[/tex]

According to the Rational Zeros Theorem, the possible rational zeros of a polynomial function are the ratios of the factors of the constant term to the factors of the leading coefficient. In this case, the constant term is -2 and the leading coefficient is 5.

The factors of -2 are ±1 and ±2. The factors of 5 are ±1 and ±5. So, the possible rational zeros are:

[tex]±1/1, ±2/1, ±1/5, ±2/5[/tex]

Simplifying these gives us the following list of possible rational zeros:

[tex]±1, ±2, ±1/5, ±2/5[/tex]

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a. The minimum-cost healthy purchase snack problem can be formulated as a linear optimization problem with the objective to minimize cost. The decision variables are x_b for the number of brownies purchased and x_c for the number of mini-cheesecakes purchased. The constraints are as follows:

The linear optimization problem can be solved using the linprog routine from the scipy.optimize library.

b. The Lagrangian for this problem can be written as follows:


L = 50x_b + 80x_c + λ_1(3x_b + 0x_c - 6) + λ_2(2x_b + 4x_c - 10) + λ_3(2x_b + 5x_c - 8),


where λ_1, λ_2 and λ_3 are the Lagrange multipliers associated with the constraints.


The optimality conditions for this problem are:

c. The values of the Lagrange multipliers can be computed by solving the system of equations given by the optimality conditions. Their physical interpretation in this problem is that they are proportional to the amount by which the constraints are violated. Positive values of the Lagrange multipliers indicate that the corresponding constraints are active, while negative values indicate that the constraints are inactive. The values of the Lagrange multipliers will depend on the optimal solution.

d. The problem can be converted to canonical form by rewriting the inequality constraints as:

The canonical form of the problem is used internally in the solution.

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The depth of water is fount to be 2.0 fathom when its was 12 feet.

Given:

Conversion unit:

1 foot = 0.167 fathom

Then,

12 feet = 0.167*12 fathom

12 feet = 2.004 fathom

12 feet = 2.0 fathom

Thus, the depth of the water is fount to be 2.0 fathom when its was 12 feet.

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