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The polynomial function with the stated properties is:\(f(x) = -x^2 - 4x + 5\)

To construct a second-degree polynomial function with zeros of -5 and 1, and goes to -∞ as f→-∞, follow these steps:

1. Identify the zeros: -5 and 1

2. Write the factors associated with the zeros: (x + 5) and (x - 1)

3. Multiply the factors to get the polynomial: (x + 5)(x - 1)

4. Expand the polynomial: x^2 + 4x - 5

Since the polynomial goes to -∞ as f→-∞, we need to make sure the leading coefficient is negative. Our current polynomial has a leading coefficient of 1, so we need to multiply the entire polynomial by -1:

\(-1(x^2 + 4x - 5) = -x^2 - 4x + 5\)

The polynomial function with the stated properties is:

\(f(x) = -x^2 - 4x + 5\)

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C personalities are organized and controlled. They take their time completing tasks accurately, like to research things thoroughly, and are always prepared.  Because they put so much time and effort into everything they do, they hate to be criticized. They are perfectionists at heart and take even the smallest complaint personally.  This makes them extremely difficult to confront. The best way to approach it is to focus on parts of the problem largely out of the C personality’s control or aspects of the problem they might not have considered.  Make it clear that you appreciate all of their efforts and that you’re bringing something to their attention because it’s a variable that they need to have in the equation in the future. No matter what, don’t frame the conflict as a personal attack. If you do, the C personality will likely become resentful and go out of their way to avoid future interactions with you.%%%%%%%%%%%%%%%

We know the slope formula

Parallel lines have equal slope so it has m=-2

Answer:

\( \frac{18}{4} \)

Step-by-step

4.5

Step-by-step explanation:

(x+1)^4=x^4+4x^3+6x^2+4x+1

(X+1)^4–x^4=4x^3+6x^2+4x+1

If x=1>>2^4–1^4=4*1^3+6*1^2+4*1+1

x=2>>3^4–2^4=4*2^3+6*2^2+4*2+1

x=3>>4^4–3^4=4*3^3+6*3^2+6*3+1

.

.

X=n>>(n+1)^4-n^4=4n^3+6n^2+4n+1

X=n-1>>n^4-(n-1)^4=4(n-1)^3+6(n-1)^2+4(n-1)+1

Now we add them together

(n+1)^4–1=4(1^3+2^3+3^3+…+n^3)+6(1^2+2^2+3^2+…+n^2)+4(1+2+3+…+n)+(1+1++1+…+n)

(n+1)^4–1=4s(n)+6{n(n+1)(2n+1)/6}+4{n(n+1)/2}+n . So we could multiply this equation by 6

6(n^4+4n^3+6n^2+4n)=24s(n)+6(2n^3+3n^2+n)+12((n^2+n)+6n

24s(n)=6n^4+24n^3+36n^2+24n-12n^3–18n^2–6n-12n^2–12n-6n

24s(n)=6n^4+12n^3+6n^2

S(n)=(n^4+2n^2+1)/4

answer

(n(n+1)/2)^2

Answer:

(n²(n+1)²)/4

Step-by-step explanation:

1³ = 1

1³ + 2³ = 9

1³ + 2³ + 3³ = 36

1³ + 2³ + 3³ + 4³ = 100

Every answer is a perfect square:

1² = 1

3² = 9

6² = 36

10² = 100

Every number to be squared has a similarity:

(1)² = 1² = 1

(1 + 2)² = 3² = 9

(1 + 2 + 3)² = 6² = 36

(1 + 2 + 3 + 4)² = 10² = 100

Therefore we only need to find the formula for 1 + 2 + 3 + ... + n, and square that formula.

For the new series we have:

1 = 1

1 + 2 = 3

1 + 2 + 3 = 6

1 + 2 + 3 + 4 = 10

Let S be the sum of the new series:

S = 1 + 2 + 3 + ... + (n - 1) + n

S can also be re-written as:

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

Adding the two sums of the series we have:

2S = (n + 1) + (n + 1) + (n + 1) + ... + (n + 1) = n(n + 1)

S = n(n + 1)/2

Now we only need to square this formula to get the formula for the original series:

[n(n + 1)/2]²

Applying Laws of Indices we have:

(n²(n + 1)²)/4

Hope this helps!

Answer:

2.4 hours

Step-by-step explanation:

6 3/10 divided by 5 1/4 is 1.2. So 6 3/10 is 1.2 times more than 5 1/4. We then take the 1.2 and multiply it by 2 hours because we need to find what's 1.2 times more than 2 hours. So then you get 2.4 hours.

The solution of the given system of equations is x = -4, y = 5 and z = 2 is the answer.

The system of equations given below:x + 2y + 3z = 11;2x + 4y + 5z = 21;3x + 5y + 6z = 27.

Here, we will solve this system of equations using inverse of the matrix method as follows:

We can write the given system of equations in matrix form as AX = B where, A = [1 2 3; 2 4 5; 3 5 6], X = [x; y; z] and B = [11; 21; 27].

The inverse of matrix A is given by the formula: A-1 = (1/ det(A)) [d11 d12 d13; d21 d22 d23; d31 d32 d33]  where,

d11 = A22A33 – A23A32 = (4 × 6) – (5 × 5) = -1,

d12 = -(A21A33 – A23A31) = -[ (2 × 6) – (5 × 3)] = 3,

d13 = A21A32 – A22A31 = (2 × 5) – (4 × 3) = -2,

d21 = -(A12A33 – A13A32) = -[(2 × 6) – (5 × 3)] = 3,

d22 = A11A33 – A13A31 = (1 × 6) – (3 × 3) = 0,

d23 = -(A11A32 – A12A31) = -[(1 × 5) – (2 × 3)] = 1,

d31 = A12A23 – A13A22 = (2 × 5) – (3 × 4) = -2,

d32 = -(A11A23 – A13A21) = -[(1 × 5) – (3 × 3)] = 4,

d33 = A11A22 – A12A21 = (1 × 4) – (2 × 2) = 0.

We have A-1 = (-1/1) [0 3 -2; 3 0 1; -2 1 0] = [0 -3 2; -3 0 -1; 2 -1 0]

Now, X = A-1 B = [0 -3 2; -3 0 -1; 2 -1 0] [11; 21; 27] = [-4; 5; 2]

Therefore, the solution of the given system of equations is x = -4, y = 5 and z = 2.

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Answer:

(-1, -3), (-2, -5), (-5, -8),(-8, -5), (-9, -3)

Step-by-step explanation:

These are the options of points to pic from. :)

have a good day.

Answer:

RP/QR = OP/NO

Step-by-step explanation:

RP corresponds to OP, QR corresponds to NO. So, RP/QR = OP/ON

Answer:

Step-by-step explanation:

{x,y,z}={−5,−6,1}

Answer:

To verify the relation between the degree measure and the radian measure of an angle

To obtain a relationship between degrees and radians, we can compare the number of degrees in one complete rotation and the number of radians in one complete rotation. The number of degrees in one complete rotation is equal to 360 degrees.

Step-by-step explanation:

Hope it helps! Correct me if I am wrong :>

Answer:

n= 6

Step-by-step explanation:

7^9/7^6 is the same as 7^9 - 7^6/ 7^9-6 but it gives you 7^3

Answer:

No Solution

Step-by-step explanation:

-4x - 9 = 12 - 4x

You add 4x on both sides

-9 ≠ 12

No Solution

The value of the variable expression is  -1/9.

According to the statement

we have to find the value of the given variable expression.

So, For this purpose, we know that the

A variable expression (or) an algebraic expression is a combination of terms by the operations such as addition, subtraction, multiplication, division, etc.

According to the given information:

The variable expression is xyz

And the values of the X = - 5/8, y = - 2/5, Z= - 4/9.

The expression is xyz

Put the values in it then(- 5/8)(- 2/5)(- 4/9)

then the value become is -1/9.

The value of the expression becomes  -1/9.

So, The value of the variable expression is  -1/9.

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Answer:

c

options A  and B

Step-by-step explanation:

the ratio between the lengths of the two legs of a 30-60-90 triangle

General ration of 30-6- 90 degrees triangle is

x : xsqrt(3) : 2x

When x=1 the ratio becomes 1 : 1 sqrt(3)

when x= 2sqrt(3) the ratio becomes

It becomes

Two sides of 30-60-90 triangle cannot be equal

so option c  and option D are not possible

sqrt(2) is also not possible  because we have sqrt(3) in general ratio

Step-by-step explanation:

The more precise estimator ẏ₁ is the most efficient in estimating the average salary. With given values, the confidence interval is calculated to determine whether to accept the claim of a $50,000 mean salary.



In this scenario, we have two estimators for the average salary: ẏ₁, which uses precise data, and ẏ₂, which includes less precise data. The efficiency of the estimators depends on the variance of the data. If we compare the variances, Var(ẏ₁) = 0% and Var(ẏ₂) = o²(1 + 3c). Since Var(ẏ₁) is zero, it implies that ẏ₁ is the most efficient estimator. The answer does not depend on the value of c.

In the second part, with c = 0, we have Var(Y) = o². Given N = 300, s² = 20,000,000, and ẏ₁ = $48,000, we can use these values to construct a confidence interval. Using a 1% significance level, the critical value is 2.57 (from the standard normal distribution). The confidence interval is given by ẏ₁ ± 2.57 * sqrt(s²/N), which results in $48,000 ± 2.57 * sqrt(20,000,000/300). If this interval contains $50,000, we would accept your friend's claim; otherwise, we would reject it.

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The equation to represent the amount 'R' Natalia and her friends raised after selling 'c' cakes will be;

⇒ R = 4c

What is Equation of line?

The equation of line passing through the points (x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

The friends sold 15 cakes on the first day and 22 cakes on the second day of the bake sale.

On first day, they collect = $60

On second day, they collect = $88

Now,

We have to find the equation as;

⇒ R = mc + b

We need to find the value of m and b.

Since, The first point = (15, 60)

The second point = (22, 88)

Hence, Slope (m) = (88 - 60) / (22 - 15)

m = 28 / 7

m = 4

And, To find b substitute R = 60 , c = 15 and m = 4 in above equation,

⇒ R = mc + b

⇒ 60 = 4 x 15 + b

⇒ b = 0

Thus, Substitute m = 4 and b = 0 in equation (i) we get;

⇒ R = mc + b

⇒ R = 4c + 0

⇒ R = 4c

Therefore, The equation to represent the amount 'R' Natalia and her friends raised after selling 'c' cakes will be;

⇒ R = 4c

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Answer:

b

Step-by-step explanation:

Answer:

T = 540N + 250

Explanation:

The amount saved by Hong after N months is

A = 155N + 250

And the amount saved by his wife after N months is

B = 385N

Then, the total amount saved is the sum of these expressions, so

T = A + B

T = (155N + 250) + (385N)

Simplifying, we get

T = 155N + 250 + 385N

T = 540N + 250

Therefore, the answer is

T = 540N + 250

The equation of the parabola is (x-3)² = -4(y+4)

Given data ,

Let the equation of the parabola be represented as A

Now , the value of A is

The focus of the parabola is F ( 3 , -7 )

Let the directrix is y = -3

And , y = a ( x - h )² + k

where ( h , k ) is the vertex and ( h , k + p ) is the focus

y is the directrix and y = k – p

(x-3)² = -4y - 16

Multiplying both sides by -1/4, we get:

-(1/4)(x-3)² = y + 4

Subtracting 4 from both sides, we get:

-(1/4)(x-3)² - 4 = y

So the equation of the parabola with focus (3,-7) and directrix y=-4 is:

y = -(1/4)(x-3)² - 4, which is equivalent to (x-3)² = -4(y+4)

Hence , the equation is (x-3)² = -4(y+4)

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The inequality relating −2\(e^{(-n/n^2)}\) to 121/\(n^2\) for n ≥ 1 is -2\(e^{(-n/n^2)}\) ≤ 121/\(n^2\).

To derive the inequality, we start by comparing the expressions −2\(e^{(-n/n^2)}\)  and 121/\(n^2\).

Since we want to express the numbers in exact form, we keep them as they are.

The inequality states that −2\(e^{(-n/n^2)}\)  is less than or equal to 121/\(n^2\).

This means that the left-hand side is either less than or equal to the right-hand side.

The exponential function e^x is always positive, so −2\(e^{(-n/n^2)}\)  is negative or zero.

On the other hand, 121/\(n^2\) is positive for n ≥ 1.

Therefore, the inequality −2\(e^{(-n/n^2)}\)  ≤ 121/\(n^2\) holds true for n ≥ 1.

The negative or zero value of −2\(e^{(-n/n^2)}\)  ensures that it will be less than or equal to the positive value of 121/\(n^2\).

In symbolic notation, the inequality can be written as −2\(e^{(-n/n^2)}\)  ≤ 121/\(n^2\) for n ≥ 1.

This representation captures the relationship between the two expressions and establishes the condition that must be satisfied for the inequality to hold.

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Answer:

The cheapest flight from Washington, D.C. to Portland was found 87 days before departure, on average. Book at least 2 weeks before departure in order to get a

Step-by-step explanation:

Answer:

Mila= 420 Nadia= 60

Step-by-step explanation:

Let's call Mila 7x. And x to Nadia. The two of them had a total of 480s.

Then we say 7x + x. Their total is 8x. So 480 = 8x. We divide both sides by 8. Here x = 60. Since Mila is 7x, we find Mila as 7.60 = 420, and since Nadia as x, we find Nadia as 1.60 = 60.

If there is any place you don't understand, you can ask.

#Achievements

To calculate the indicated Riemann sum S for the function f(x) = 20 - 2x^2, we need to partition the interval [-1, 9] into five subintervals of equal length and evaluate the sum using the given formula.

The width of each subinterval is determined by dividing the length of the interval by the number of subintervals, which in this case is (9 - (-1)) / 5 = 2.

Using the formula for the midpoint, k = (x_i + x_{i-1}) / 2, we can calculate the midpoint of each subinterval. Let's denote the midpoints as k_1, k_2, k_3, k_4, and k_5 for the five subintervals.

The Riemann sum S is then given by the sum of f(k_i) multiplied by the width of the subinterval for each i.

S = (f(k_1) * 2) + (f(k_2) * 2) + (f(k_3) * 2) + (f(k_4) * 2) + (f(k_5) * 2)

To obtain the specific values of k_i and calculate the sum, we need to find the midpoints of the subintervals and evaluate the function f(x) at those points.

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Answer:

A. Between 3.0 and 3.5 and between 4.0 and 4.5

Step-by-step explanation:

The zeroes of a function occur whenever a value of x returns zero. To predict where the zeroes lie, determine the interval(s) where the function crosses the x-axis. This occurs when either \(f(x)\) goes from a negative value to a positive value or vice versa.

From \(x=3.0\) and \(x=3.5\), the y-values go from 4.0 (positive) to -0.2 (negative), respectively. Therefore, there must be a zero in this interval.

From \(x=4.0\) and \(x=4.5\), the y-values go from -0.8 (negative) to 0.1 (positive), respectively. Therefore, there must also be a zero in this interval.

Thus, the zeros of this function occur between 3.0 and 3.5 and between 4.0 and 4.5, leading to answer choice A.

Answer:

between 3.0 and 3.5 and between 4.0 and 4.5

Step-by-step explanation:

Plato/Edmentum

Bryant Industries uses forecasting to estimate the number of orders that will be placed by their customers. The table below gives the sales figures for the last four months.Month2345Sales92491942004There are different forecasting techniques used by companies like Bryant Industries to predict future sales.

One of the most widely used methods is the time-series method. This method is particularly useful when the demand for a product or service changes over time and when there are no external factors that affect the sales. In this case, we can use a time-series method called the moving average to estimate future sales. The moving average is a time-series method that uses the average of past sales data to estimate future sales. It is particularly useful when there are no external factors that affect the sales. In this case, we can use a 3-month moving average to estimate future sales. The 3-month moving average is calculated as follows: (924 + 919 + 420) / 3 = 754.33. This means that we can expect sales of around 754 units next month. The moving average method is easy to use and is a good way to get a quick estimate of future sales. However, it has some limitations. For example, it does not take into account external factors that may affect sales, such as changes in the economy or in consumer behavior.

In conclusion, Bryant Industries can use the moving average method to estimate future sales. However, they should also consider other factors that may affect sales, such as changes in the economy or in consumer behavior. By doing so, they can make more accurate forecasts and improve their overall performance.

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There are 12 different possibilities for a president. Therefore, there are 11 possibilities for vice-president.

We calculate this combination when we multiply 12 x 11:

12 x 11 = 132

Therefore, there are 132 different ways to make combinations.

Answer:

To solve this problem, we can use a combination formula. We need to distribute 12 identical blackboards among 4 schools, so the total number of possible divisions is:

C(12+4-1, 4-1) = C(15, 3) = 455

However, we need to consider the condition that school a receives at least 2 boards and school b receives at least one board. We can use a complementary counting approach to solve this.

First, let's find the total number of divisions where school a receives less than 2 boards and school b receives less than 1 board. If school a receives 0 or 1 board, that leaves 11 or 10 boards to be divided among the remaining schools. Similarly, if school b receives 0 boards, that leaves 12 boards to be divided among the remaining schools. Using the combination formula, we can find the number of possible divisions:

C(11+3-1, 3-1) * C(12+3-1, 3-1) = C(13, 2) * C(14, 2) = 8190

Now, we can subtract this number from the total number of possible divisions to find the number of divisions that satisfy the conditions:

455 - 8190 = -7735

Wait, that's a negative number! What does it mean? It means that there are no possible divisions that satisfy the conditions. In other words, it's impossible to distribute 12 blackboards among 4 schools such that school a receives at least 2 boards and school b receives at least one board.

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