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The complete polynomial is f(x) = 2x³ + 15x² - 6 if n = 3 and a = 15

Given is polynomial f(x) = 2xⁿ + ax² - 6, when divided by (x+3), the remainder is 129,

Calculating the values of a and n :-

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

f(x) = 2xⁿ + ax² - 6 is divided by (x+3), the remainder is 129

This means that,

f(-3) = 129

So, we have

f(-3) = 2(-3)ⁿ + a(-3)² - 6

f(-3) = 2(-3)ⁿ + 9a - 6

2(-3)ⁿ + 9a - 6 = 129

2(-3)ⁿ + 9a = 135

Assume n = 3

So, we have

2(-3)³ + 9a = 135

2/27 + 9a = 135

9a = 135 - 2/27

9a = 3643/27

a = 3643/243

a = 15

Therefore,

n = 3 and a = 15

So, the complete polynomial is f(x) = 2x³ + 15x² - 6

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The hospital needs to replace the cobalt approximately every 2.16 years. Rounded to the nearest whole number, this is 2 years.

The half-life of cobalt-60 is 5.24 years, which means that after 5.24 years, the radioisotope activity will have decreased to 50% of its initial level. Since the hospital needs to replace the cobalt when the radioisotope activity has decreased to 45% of its initial level, this means that the cobalt needs to be replaced after slightly less than one half-life has passed.
To find out how long this is, we can use the formula:
t = (ln(0.45) / ln(0.5)) x 5.24
where t is the time in years since the cobalt was first used.
Using a calculator, we find that:
t ≈ 2.16 years
Therefore, the hospital needs to replace the cobalt approximately every 2.16 years. Rounded to the nearest whole number, this is 2 years.

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The value of the indefinite integral in the context of this problem is given as follows:

B. [tex]\cosh{(e^x + 5)} + C[/tex]

The indefinite integral in the context of this problem is defined as follows:

[tex]\int e^x \sinh{(e^x + 5)} dx[/tex]

We can use substitution to solve the integral, hence:

[tex]u = e^x + 5[/tex]

[tex]du = e^x dx[/tex]

[tex]dx = \frac{du}{e^x}[/tex]

Hence the integral as a function of u is given as follows:

[tex]\int \sinh{u} du[/tex]

The result of the integral is of:

cosh(u) + C.

In which C is the constant of integration.

As a function of x, the integral is given as follows:

[tex]\cosh{(e^x + 5)} + C[/tex]

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The value of f(3) in the function is undefined

The given function are f(x)= x³+18x²+104x+192 for x≤-3

f(x)= 3x-9/x³-2x²-5x+6 for -3< x≤3

f(x)= 3x-9/x³-2x²-5x+6 for -3< x≤3

f(x)=√x²-9

We have to find the value of f(3)

The 3 lies in the interval -3< x≤3

So we use function f(x)= 3x-9/x³-2x²-5x+6 to find f(3)

f(x)= 3(3)-9/(3)³-2(3)²-5(3)+6

=0/27-18-15+6

=undefined

Hence, the value of f(3) in the function is undefined

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The farthest gold dust strike is 76 miles away from the gold vein.

The formula of the distance between two points is P(x₁, y₁) and Q(x₂, y₂) is given by:

d (P, Q) = √ (x₂ – x₁)² + (y₂ – y₁) ²

As per the question, we have to find the distance between the gold vein at (-2, 7) and the farthest gold dust strike at (74, 7).

Substituting the values into the distance formula, we have:

d = √((74 - (-2))² + (7 - 7)²)

d = √(76²)

d = 76

Therefore, the farthest gold dust strike is 76 miles away from the gold vein.

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X is an acute angle x = 5.74 degrees (rounded to the nearest hundredth) would be the appropriate answer for an acute angle satisfying sin(x) = 0.1.

To find the value of x in degrees when sin(x) = 0.1, we can use inverse trigonometric functions. Specifically, we can use the arcsin function to determine the angle whose sine is 0.1.

Using a scientific calculator or a trigonometric table, we can find the arcsin of 0.1. This gives us approximately 5.739 degrees.

However, since x is an acute angle, it means that x is between 0 and 90 degrees. The value 5.739 degrees falls within this range.

Therefore, the value of x in degrees, when sin(x) = 0.1 and x is an acute angle, is approximately 5.739 degrees.

Rounded to the nearest hundredth, the value of x would be 5.74 degrees.

It's important to note that the arcsin function has a range from -90 degrees to 90 degrees. In this case, since we are looking for an acute angle, we consider only the positive solution.

So, x = 5.74 degrees (rounded to the nearest hundredth) would be the appropriate answer for an acute angle satisfying sin(x) = 0.1.

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Hello,

150 - 1/3% of 150

= 150 - 33,33% x 150

= 150 - 50

= 100

approximately 100

Example: 33 1/3% = 1/3. 1/3 of $150.00 = $50.00, so discounted price is: $150.00 - $50.00 = $100.00

Answer: v=-19

Step-by-step explanation:

We can multiply by 7 on both sides which cancels out 7 on both sides. He new equation would be v=-19 which is our answer.

Answer:60,000

Step-by-step explanation:

El costo de un terreno es IP al cuadrado de la distancia que lo separa de Lima y DP a su área. Esto se puede expresar como:

Costo = IP^2 * DP / Distancia^2

Sabemos que el costo de un terreno es de 540 mil, por lo que podemos escribir:

540,000 = IP^2 * DP / Distancia^2

Ahora consideremos el segundo terreno, que tiene el doble de área y está a una distancia 3 veces mayor que la del primer terreno. Si llamamos "Distancia anterior" a la distancia del primer terreno, entonces la distancia del segundo terreno es 3 veces la distancia anterior, es decir:

Distancia = 3 * Distancia anterior

Además, sabemos que el segundo terreno tiene el doble de área que el primero, por lo que podemos escribir:

Área = 2 * Área anterior

Reemplazando estas expresiones en la ecuación anterior, obtenemos:

Costo = IP^2 * DP / (3 * Distancia anterior)^2

Simplificando:

Costo = IP^2 * DP / 9 * Distancia anterior^2

Pero sabemos que el costo del segundo terreno es lo que estamos buscando. Llamemos "Precio del segundo terreno" a este valor. Entonces:

Precio del segundo terreno = IP^2 * DP / 9 * Distancia anterior^2

Como el costo del primer terreno es 540 mil, podemos reemplazar los valores conocidos:

540,000 = IP^2 * DP / Distancia anterior^2

Despejando IP^2, tenemos:

IP^2 = 540,000 * Distancia anterior^2 / DP

Reemplazando esta expresión en la ecuación anterior, obtenemos:

Precio del segundo terreno = (540,000 * Distancia anterior^2 / DP) * DP / 9 * Distancia anterior^2

Simplificando:

Precio del segundo terreno = 60,000 / DP * 2

Por lo tanto, el precio del segundo terreno es de 60,000 dividido por dos veces el valor de DP.

Using a system of equations, the investments in each account are as follows:

Maricopa Success invested $80,000 in stocks.

Maricopa Success invested $75,000 in bonds.

Maricopa Success invested $40,000 in CDs.

A system of equations is two or more equations solved simultaneously, concurrently, or at the same time.

The total scholarship fund received = $195,000

The earnings from the investments:

Stocks = 10.1% = 0.101

Bonds = 4.8% = 0.048

CDs = 4.75% = 0.0475

Let the amount invested in CDs = x

Let the amount invested in Bonds = x + 35,000

Let the amount invested in stocks = y

The annual income from the investments = $13,580

x + x + 35,000 + y = 195,000

2x + 35,000 + y = 195,000

2x + y = 160,000 ... Equation 1

0.101y + 0.048x + 1,680 + 0.0475x = 13,580

0.0955x + 0.101y = 11,900 ... Equation 2

Multiply Equation 1 by 0.101:

0.202x + 0.101y = 16,160 ... Equation 3

Subtract Equation 2 from Equation 3:

0.202x + 0.101y = 16,160

-

0.0955x + 0.101y = 11,900

0.1065x = 4,260

x = 40,000

Substitute x = 40,000 in Equation 1:

2x + y = 160,000

2(40,000) + y = 160,000

80,000 + y = 160,000

y = 80,000

Investment in CDs = $40,000

Investment in Bonds = $75,000 ($40,000 + $35,000)

Investment in Stocks = $80,000

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The quotient function for this problem is given as follows:

(f/g)(x) = (x + 2)/(2x² + 4x - 5)

The functions f(x) and g(x) have the definitions presented as follows:

To obtain the quotient of the two functions, we simply divided the definition of the function f(x) by the definition of the function g(x).

Both functions are defined on the bullet point, hence the quotient function for this problem is given as follows:

(f/g)(x) = (x + 2)/(2x² + 4x - 5)

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Answer: B. (12, 7)

Step-by-step explanation: If we substitute the x values in the equation the answer has to equal the y value of the coordinate. If we substitute 12 for the x we get y = 3. So answer B is the coordinate not represented by the student's graph.

Elisa's savings account has the greater average rate of change between 2005 and 2015.

For Darlene's savings account, the initial amount in 2005 is $500. To calculate the value of the account in 2015, we need to know how many years have passed. Since 2015 is 10 years after 2005, we can substitute t = 10 into the equation given:

f(t) = 500(1 + 0.04t)

f(10) = 500(1 + 0.04(10))

f(10) = 500(1.4)

f(10) = 700

Therefore, the amount in Darlene's savings account in 2015 is $700. The average rate of change between 2005 and 2015 is the slope of the line connecting the points (0, 500) and (10, 700):

slope = (700 - 500) / (10 - 0) = 20

For Elisa's savings account, we are given the values of the function at several points, but we need to determine the slope of the line connecting the points (0, 600) and (10, 977), since this represents the change between 2005 and 2015. The slope is:

slope = (977 - 600) / (10 - 0) = 37.7

Therefore, Elisa's savings account has the greater average rate of change between 2005 and 2015.

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The inequality that best describes the included values of x is x < 8

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

The number line

On the number line, we have the following

The above means that we make use of the less than symbol

This is because the open circle uses < or > while arrows pointing left means <

So, we have

x < 8

Hence, the inequality that best describes the included values of x is x < 8

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The amount more in income tax that Cho pays than Helen each month would be £56.

Here, we have,

First, find Helen's yearly salary :

= 1, 720 x  12

= £ 20, 640

Both Cho's and Helen's annual salaries fall within the Basic rate tax bracket.

Cho 's monthly tax would be:

= (( 24, 000 - 12, 570 ) x 20 % ) / 12

= £ 190. 50

Helen's monthly tax :

= (( 20, 640 - 12, 570 ) x 20 % ) / 12

= £ 134.50

The difference is therefore :

= 190. 50 - 134.50

= £56

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complete question:

You can use these steps to work out the amount of income tax you pay each month.

Work out

monthly salary - 987.5

Work out

answer to Step 1 +5

Step 1

Step 2

Cho has a salary of £24 000 per year.

Helen has a salary of £1720 per month.

How much more income tax does Cho pay than Helen each month?

Answer: 165 ft squared

Step-by-step explanation:

1. First find the area of the bottom face (you don’t need to divide by two because the other triangle makes the one on the bottom a full rectangle.)

10x4.5=45

2. Find area of face facing you. (The lateral one, rectangle face)

10x5=50

3. Find area of left and right lateral faces (its at the back)

6x5=30

8x5=40

4. Add all answers to get total surface area

40+30+50+45=165

5.Add unit and then celebrate because you did it!

165 ft squared

Hope this helps!

Answer:

48.75

Step-by-step explanation:

call highest H and lowest L

H = L + 40.5

sum of them = 138

H + L = 138

(L + 40.5) + L = 138

2L + 40.5 = 138

2L = 138 - 40.5 = 97.5

L = 48.75

When we apply Gauss- Jordon elimination method to solve the system of equation, it becomes;

[tex]\left[\begin{array}{cccc}1&0&0&6\\0&1&0&2\\0&0&1&-6\end{array}\right][/tex]

To solve the augment matrix that represents a system of linear equation using Gauss- Jordon elimination method, we reduce every value to 0's and 1's to get the values in the fourth column.

-5   -3    -4   -12

0    -2    -7    38

0      1     4    -22

    R₁ ÷ -5                                   R₂ ÷ -2

1    3/5     4/5  12/15             1    3/5    4/5   12/15

0    -2    -7    38                   0     1       7/2   -19

0      1     4    -22                  0      1     4    -22          

R₁ - 3/5R₂                                   2R₃

1      0   -13/10   69/5              1      0   -13/10   69/5

0     1      7/2     -19                 0     1      7/2     -19

0     0     1/2      -3                   0     0     1         -6

 R₂ + 13/10R₃                                  R₂ - 7/2R₃

1      0     0     6                             1      0     0     6  

0     1      7/2  -19                          0     1      0      2

0     0     1         -6                         0     0     1      -6

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We need to use the first part of the function, we can see that:

f(-3) = 0

The correct option is the third one.

Here we have a piecewise function. It means that the function behaves differently on different parts of its domain.

Here we want to evalaute the function in x = -3, so we need to find which of the parts of the function we need to use.

We can see that:

f(x) =x + 3 if x ≤ 0

and -3 is smaller than zer, so we need to use this one.

Then:

f(-3) = -3 + 3 = 0

The correct option is the third one.

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Answer:

Step-by-step explanation:

chill

If x > 5, then x - 3 > 0 since x is greater than 3. Therefore, |x - 3| = x - 3.

1. The final velocity is 8.3 m/s and the distance covered is 16.8 m.

2. The acceleration is  34.7  and it would travel  58.9 m.

Acceleration is a physical quantity that describes the rate of change of an object's velocity over time. In other words, it is the rate at which the speed or direction of motion of an object changes.

Using;

v = u + at

v = ?

u = 2.9 m/s

a = 1.8 m/s2

t = 3 s

Then;

v = 2.9 + (1.8 * 3)

v = 8.3 m/s

Also;

[tex]v^2 = u^2 + 2as\\s = v^2 - u^2/2a\\s = (8.3)^2 - (2.9)^2/2 * 1.8[/tex]

s = 68.89 - 8.41/3.6

= 16.8 m

2)

[tex]v^2 = u^2 + 2as\\a = v^2 - u^2/2s\\a = (27)^2 - 0^2/2 * 10.5[/tex]

a = 34.7[tex]m/s^2[/tex]

Using;

[tex]s = ut + 1/2at^2\\ut = 0\\s = 1/2at^2\\s = 0.5 * 34.7 * (2)^2\\s = 69.4 m[/tex]

It would travel; 69.4 - 10.5 = 58.9 m

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The correct order of the functions from least to greatest is g(x), f(x) and h(x).

The given function is f(x)=(x+3)²-2.

g(x) linear graph with y-intercept = c = -3/2 and x-intercept = 3

f (x) = (x + 3)² - 2

For x = -1

f (-1) = (-1 + 3)² - 2

f (-1) = (2)² - 2

f (-1) = 4 - 2

f (-1) = 2

For x = 3

f(3) = (3 + 3)² - 2

f(3) = (6)² - 2

f(3) = 36 - 2

f(3) = 34

AVR = ((34) - (2))/((3) - (- 1))

AVR = 8

For g(x):

linear graph with and intercept of negative 3 over 2 and x intercept of 3

y = mx + b

b = -3/2

For me we have:

0 = m (3) - 3/2

3m = 3/2

m = 1/2

The function g(x) is:

g (x) = (1/2) x - 3/2

For x = -1

g (-1) = (1/2) (- 1) - 3/2

g (-1) = -1/2 - 3/2

g (-1) = -4/2

g (-1) = -2

For x = 3

g (3) = (1/2) (3) - 3/2

g (3) = 3/2 - 3/2

g (3) = 0

AVR = ((0) - (- 2)) / ((3) - (- 1))

AVR = 1/2

For h(x):

Using the table we have:

AVR = ((62) - (14)) / ((3) - (- 1))

AVR = 12

From least to greatest g(x), f(x), h(x)

Therefore, the correct order of the functions from least to greatest is g(x), f(x) and h(x).

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Answer:

82 in^2

Step-by-step explanation:

Total Surface Area (TSA) = 2 × Base Area + Base Perimeter × Height

TSA = 2× (7×2) + (7+7+2+2) ×3

= 2 × 14 + 18 × 3

= 82 in^2

Answer:

2?

Step-by-step explanation:

a) The equation of the plane is 2y + z - 2 = 0.

b) The equation of the plane Π1 that is parallel to Π and passes through (2,2,2) is 2y + z - 6 = 0.

c) The distance between the planes Π and Π1 is 4 / √6.

Given data ,

The given line has the parametric equations:

x = 1 + 2t

y = -1 + 3t

z = 4 + t

By comparing the coefficients of t, we can identify a point on the line, which is (1, -1, 4) when t = 0.

To find the normal vector to the plane Π, we use the fact that it is parallel to the vector ⟨0, 2, 1⟩. Since the normal vector is perpendicular to the plane, any vector parallel to the plane can serve as the normal vector. Therefore, we can take the vector ⟨0, 2, 1⟩ as the normal vector.

Now we have a point (1, -1, 4) on the plane Π and a normal vector ⟨0, 2, 1⟩.

The equation of the plane Π can be written as:

0(x - 1) + 2(y + 1) + 1(z - 4) = 0

Simplifying the equation gives:

2y + z - 2 = 0

So, the equation of the plane Π is 2y + z - 2 = 0.

(2)

To find the equation of the plane Π1 that is parallel to Π and passes through (2, 2, 2), we can use the same normal vector ⟨0, 2, 1⟩.

The equation of the plane Π1 can be written as:

0(x - 2) + 2(y - 2) + 1(z - 2) = 0

Simplifying the equation gives:

2y + z - 6 = 0

So, the equation of the plane Π1 is 2y + z - 6 = 0.

(3)

We can take the point (1, -1, 4) on the plane Π and find the perpendicular distance from this point to the plane Π1 using the equation of Π1.

The distance between the two planes is given by the formula:

Distance = |Ax₀ + By₀ + Cz₀ + D| / √(A² + B² + C²)

Using the point (1, -1, 4) and the equation of Π1: 2y + z - 6 = 0, we can substitute the values into the formula:

Distance = |(2)(-1) + (1)(4) - 6| / √(2² + 1² + 1²)

= |(-2) + 4 - 6| / √(4 + 1 + 1)

= |-4| / √6

= 4 / √6

Hence , the distance between the planes Π and Π1 is 4 / √6.

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Answer:

Step-by-step explanation:

You want the left sum and the right sum of the four subinterval areas under the curve f(x) = √(x+3) on the interval [-1, 1].

The Riemann sum is the sum of the subinterval areas. The area of each subinterval is the height of the rectangular area, multiplied by its width. Here, the interval width is (1 -(-1))/4 = 0.5.

The heights of the intervals of interest will be the function values f(-1 +0.5n) for f(x) = √(x+3) and n = 0 .. 3 for the left sum and 1 .. 4 for the right sum.

The attached calculator display shows the function values for n=0 .. 4. The expression Total(Most( )) adds the first four function values; while the expression Total(Rest( )) adds the last four function values of these five. Multiplying by the interval width (1/2) gives the left- and right-Riemann sums, respectively.

__

Additional comment

The actual integral value is about 3.44772.

<95141404393>

The simplification of the given expression above would be = x⁵

The exponential laws in mathematics states that to multiply two exponential functions with the same base, we simply add the exponents.

The second law states that to divide two exponential functions with the same base, we subtract the exponents.

From the expression given above;

x⁷/x² = X(7-2) = x⁵

Therefore, in conclusion, the simplification of the given expression above while following the guide of the exponential laws would be = x⁵

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