The one at the bottom

The zeros of the polynomial function f(x) = x^2 - 9x - 70 can be found by factoring or using the quadratic formula. The zeros are -5 and 14.

To find the zeros of the polynomial function f(x) = x^2 - 9x - 70, we can factor the expression or use the quadratic formula. Let's factor the expression:

f(x) = x^2 - 9x - 70

= (x - 14)(x + 5)

Setting each factor equal to zero, we get:

x - 14 = 0 --> x = 14

x + 5 = 0 --> x = -5

Therefore, the zeros of the polynomial function are x = -5 and x = 14. These values represent the x-coordinates where the function intersects the x-axis, indicating the points where the function equals zero.

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The equation for the cosine function is given as;cos(x) = 3 cos(π/2 x) + 5

A cosine function is defined as follows;cos(x) = a cos(b(x - h)) + kwhere a is the amplitude, period is 2π/b, and k is the midline. The amplitude, period, and midline of a cosine function can be used to find its equation.In this case,

we have a cosine function that has a midline of y=5, an amplitude of 3 and a period of 4/π. Thus, the amplitude of the function is given as 3, the midline is given as 5, and the period is 4/π.

The amplitude is the vertical distance from the midline to the highest point on the curve and also to the lowest point on the curve. The period is the distance over which the cosine function completes one full oscillation, or cycle.

In this case, we have a period of 4/π, so we can find b by the formula b = 2π/period = 2π/(4/π) = π/2.To find the phase shift, h, we use the formula h = x₀ - (π/b), where x₀ is the x-coordinate of the maximum or minimum value of the cosine function.

Since the midline is y=5, the maximum value of the cosine function occurs when y=8 and the minimum value occurs when y=2. The maximum and minimum values occur when cos(b(x - h)) = 1 and cos(b(x - h)) = -1, respectively.

Therefore, we have;8 = 5 + 3, cos(b(x - h)) = 1when x - h = 0, so x₀ = h2 = 5 - 3, cos(b(x - h)) = -1when x - h = π/b

Thus, h = 0 for the maximum value, and h = π/2 for the minimum value. We choose the value of h that corresponds to the maximum value of the cosine function, so h = 0.

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Answer:

y€ R : y greater than or equal to 1

Answer:

132 dollars I think

Step-by-step explanation:

a)  Bryan is 1,168 meters away from the base of the watchtower

b) The nearest meter, Bryan and Lily are 315

a) To the nearest meter, Bryan is 1,168 meters away from the base of the watchtower.

Let AB be the watchtower. From B, the angle of elevation to the top of the tower is 20°.

We have to find BC.

BC/AB = tan 20°

BC = AB tan 20°

BC = 90 tan 20°

BC = 32.3

Therefore, BC = 32 meters

Now we have to find AC. AC is the distance between the foot of the watchtower and Bryan's position.

To do that, let BD = h be the height of the tower and AD = x be the distance between A and D.

From the information given, we know that tan 85° = h/x.

Rearranging the formula, x = h/tan 85°

x = 90/tan 85°

x = 418.55 meters

Therefore, AC = x + BC

AC = 418.55 + 32.3

AC = 450.85 meters

So, to the nearest meter, Bryan is 1,168 meters away from the base of the watchtower.

b) To the nearest meter, Bryan and Lily are 315 meters apart.

Let E be the position of Lily and AD be the distance from the foot of the watchtower to the position of Bryan. We have already found that AD = 418.55 meters.

Bryan and Lily are along the same horizontal line.

So, BE is the distance between them. We have to find BE.

From triangle AEB, tan 20° = h/AE.

Rearranging the formula, AE = h/tan 20°

AE = 90/tan 20°

AE = 267.9 meters

From triangle DEC, tan 85° = h/DE.

Rearranging the formula, DE = h/tan 85°

DE = 90/tan 85°

DE = 3,442.97 meters

Therefore, EC = DE - DC = 3,442.97 - 350 = 3,092.97 meters

Now, BE = AC - EC

BE = 450.85 - 3,092.97

BE = -2,642.12 meters (negative value means Bryan is to the left of Lily)So, to the nearest meter,

Bryan and Lily are 315 meters apart. Answer: (a) 1168m and (b) 315m

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Answer:

Option 4

Step-by-step explanation:

The smaller sides must add up to be greater than the largest side so:

1) 6 + 8 < 15

1) No

2) 6 + 9 = 15

2) No

3) 9 + 6 < 16

3) No

4) 9 + 8 > 16

4) Yes

Answer:

I NEED HELP ON THE SAME QUESTION

Step-by-step explanation:

NO ONE INDERSTANDS JT FOR SOME REASON AND NEITHER DO I

a) The solution to the given problem isL(F) = f(t) = 0 + (-(10 + 7C)/6)[tex]e^{-2t}[/tex]) + C[tex]e^{-3t}[/tex]+ D[tex]e^{-3t}[/tex]

b) The solution to the given problem isL(F) = [tex]e^{-2t}[/tex] [sin t + cos t](c)

c) The solution to the given problem is L(F) = 1/9 [[tex]e^{2t}[/tex] sin 9t - 3[tex]e^{2t}[/tex]) cos 9t]

(a)The inverse Laplace transform of F(s) = 10/s(s + 2)(s + 3)² can be found as follows:

L(F) = L{10/[s(s + 2)(s + 3)²]}

= 10 ∫∞₀[tex]e^{-st}[/tex]) /[s(s + 2)(s + 3)²] dt

L{F} = L⁻¹{10/[s(s + 2)(s + 3)²]}

By using partial fractions, we can simplify the equation and get it in a form that can be integrated easily.

L(F) = 10 ∫∞₀ {1/s - 2/(s + 2) + 3/(s + 3) - 2/(s + 3)² + 1/(s + 2)(s + 3)} [tex]e^{-st}[/tex]dt

L{F} = L⁻¹{1/s} - 2L⁻¹{1/(s + 2)} + 3L⁻¹{1/(s + 3)} - 2L⁻¹{d/ds[1/(s + 3)]} + L⁻¹{1/(s + 2)}

As the inverse Laplace transform of L{F} is given by L(F)

= L⁻¹{1/s} - 2L⁻¹{1/(s + 2)} + 3L⁻¹{1/(s + 3)} - 2L⁻¹{d/ds[1/(s + 3)]} + L⁻¹{1/(s + 2)}

Thus, the solution to the given problem isL(F) = f(t) = 0 + (-(10 + 7C)/6)[tex]e^{-2t}[/tex]) + C[tex]e^{-3t}[/tex]+ D[tex]e^{-3t}[/tex]

(b)

The inverse Laplace transform of F(s) = s/[s² + 4s + 5] can be found as follows:

L(F) = L{s/[s² + 4s + 5]}

= ∫∞₀ s e^(–st) / (s² + 4s + 5) dt

L{F} = L⁻¹{s/[s² + 4s + 5]}

By using partial fractions, we can simplify the equation and get it in a form that can be integrated easily. L(F) = ∫∞₀ [s/(s² + 4s + 5)] [tex]e^{-st}[/tex]) dt

L{F} = L⁻¹{s/(s² + 4s + 5)}

The solution to the given problem isL(F) = [tex]e^{-2t}[/tex] [sin t + cos t](c)

c) The inverse Laplace transform of F(s) = ([tex]e^{-3s}[/tex]) s/[(s - 2)² + 81] can be found as follows:

L(F) = L{([tex]e^{-3s}[/tex]) s/[(s - 2)² + 81]}= ∫∞₀ ([tex]e^{-st}[/tex]) s/[(s - 2)² + 81] dt

L{F} = L⁻¹{([tex]e^{-3s}[/tex])) s/[(s - 2)² + 81]}

So, The solution to the given problem is L(F) = 1/9 [([tex]e^{2t}[/tex]) sin 9t - 3([tex]e^{2t}[/tex]) cos 9t]

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Answer:

hi

Step-by-step explanation:

(a) The probability that a single randomly selected value is greater than 19.4. P(X> 19.4) = 0.6965.

(b) The probability that a sample of size n = 20 is randomly selected with a mean greater than 19.4. P(M> 19.4) =  0.9883.

To solve these probability questions, we can utilize the properties of the standard normal distribution since we know the mean and standard deviation of the population.

(a) Find the probability that a single randomly selected value is greater than 19.4.

To calculate this probability, we need to standardize the value 19.4 using the formula: z = (x - μ) / σ, where x is the value, μ is the mean, and σ is the standard deviation.

z = (19.4 - 42.3) / 44.6 = -22.9 / 44.6 ≈ -0.51498

Using the standard normal distribution table or a calculator, we can find the corresponding probability for z > -0.51498, which is approximately 0.6965.

Therefore, P(X > 19.4) ≈ 0.6965.

(b) Find the probability that a sample of size n = 20 is randomly selected with a mean greater than 19.4.

For this question, we need to consider the sampling distribution of the sample mean. The mean of the sampling distribution is equal to the population mean (μ = 42.3), and the standard deviation of the sampling distribution, also known as the standard error, is equal to σ / √n, where σ is the population standard deviation and n is the sample size.

Standard error = 44.6 / √20 ≈ 9.9766

To find the probability that the sample mean is greater than 19.4, we need to standardize the sample mean using the formula: z = (x - μ) / (σ / √n), where x is the value (19.4 in this case), μ is the mean, σ is the standard deviation, and n is the sample size.

z = (19.4 - 42.3) / (44.6 / √20) ≈ -22.9 / 9.9766 ≈ -2.2972

Using the standard normal distribution table or a calculator, we can find the corresponding probability for z > -2.2972, which is approximately 0.9883.

Therefore, P(M > 19.4) ≈ 0.9883.

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The correct option to the statements "1st statement: In an experimental study we can examine the association between the independent and dependent variable, and 2nd statement: In an experimental study we can examine the temporal relationship between the independent and dependent variable" is: a. Both statements are true.

An experimental study can be used to determine the relationship between two variables. It is also used to determine whether there is a cause-and-effect connection between two variables.

In an experimental study, two groups are compared. One group receives the independent variable, and the other group receives the dependent variable.

In an experimental study, the following two statements are true:

In an experimental study, we can examine the association between the independent and dependent variable. It is the correlation or connection between the two variables we are interested in exploring

In an experimental study, we can examine the temporal relationship between the independent and dependent variable. It refers to the timing or sequence of events that occurs between the two variables in question.

The study must include a time element that describes the order in which the dependent and independent variables were introduced to the subjects.

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To find the arc of circle WTV, you need the arc length or central angle. Use formulas: Arc Length = (Arc Angle / 360) × (2πr) or Arc Length = (Central Angle / 360) × (2πr).

To find the arc of a circle, WTV, you would need to know either the length of the arc or the measure of the central angle subtended by the arc. If you have the length of the arc, you can use the formula:

Arc Length = (Arc Angle / 360 degrees) × (2πr),

where r is the radius of the circle. Rearranging the formula, you can solve for the Arc Angle:

Arc Angle = (Arc Length / (2πr)) × 360 degrees.

If you know the measure of the central angle, you can calculate the arc length using a similar formula:

Arc Length = (Central Angle / 360 degrees) × (2πr).

To find the radius, you would need additional information such as the diameter or circumference of the circle. Once you have the radius, you can substitute the values into the appropriate formula to find either the arc length or the central angle of the circle.

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the linear approximation at z = 0 to sin(42) is A + Bz, where A = sin(42) and B is the coefficient of z, which is cos(42).

The linear approximation of a function f(x) at a point x = a is given by the equation f(x) ≈ f(a) + f'(a)(x - a). In this case, we want to approximate sin(42) at z = 0.

The derivative of the sine function is cos(x), so the derivative of sin(42) with respect to z is cos(42). Evaluating the derivative at z = 0, we have cos(42).

To find A in the linear approximation A + Bz, we substitute z = 0 into the original function sin(42) and obtain A = sin(42).

Therefore, the linear approximation at z = 0 to sin(42) is A + Bz, where A = sin(42) and B is the coefficient of z, which is cos(42).

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Answer:

How many siblings do you have?

Answer:

∠R = 38°

Step-by-step explanation:

∠R = 1/2(arc PE - arc SQ)

∠R = 1/2(140 - 64) = 1/2(76) = 38°

Answer:

the cost of the replacement window will be $1501.44.

Step-by-step explanation:

area of an equilateral triangle:

[tex]A = \frac{\sqrt{3}}{4} a^{2}[/tex]

A = (√3)/4 * (17)^2

A = 125.12 in^2

125.12 * 12 = $1501.44

C ≈ 62.83cm is the answer!

Hope this helps!

Answer:

One pair of socks is $370.

Step-by-step explanation:

Sean bought three pairs of the same socks and a shoe polish for $1450. If the

polish cost $340, how much is the cost of one pair of socks.

6x - 340 = 1450

6x = 1450 -340

6x = 1110

2x = 1110 / 3

2x = 370

Answer:

80

Step-by-step explanation:

The number that has no composite factors is (c) 77

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

Number = 21

The factors of 21 are 3 and 7

These factors are composite numbers because they are prime numbers

using the above as a guide, we have the following:

The number 77 has no composite factors

This is so because

77 = 7 * 11

These factors are composite numbers because they are prime numbers

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Answer:

A.

Step-by-step explanation:

Answer:

A. 4,000,000 + 600,000 + 10,000 + 2,000 + 200 + 50 + 8 + 9

Step-by-step explanation:

Answer:

2 6/7 units

Step-by-step explanation:

You substitute 5/7 in for x

4(5/7) = 20/7 = 2 6/7 units

You can also add 5/7 + 5/7 + 5/7 + 5/7 to check your work

Answer:

18 in

Step-by-step explanation:

len = y

width= y - 6

the area of rectangle is len x width

(Y) x (Y-6) = 216

Y^2 - 6Y = 216, Y^2 - 6y -216 = 0

y = (36 /2) or (-24 /2)

len couldn't be negative so 18

The sum of the mean and the median of the given dataset, which consists of the scores 7, 4, 9, 6, 10, 9, 5, and 4, is 13.25.

To find the sum of the mean and the median, we first need to calculate the mean and median of the given dataset.

The dataset is: 7, 4, 9, 6, 10, 9, 5, 4

To find the mean, we sum up all the numbers in the dataset and divide by the total number of data points:

Mean = (7 + 4 + 9 + 6 + 10 + 9 + 5 + 4) / 8 = 54 / 8 = 6.75

To find the median, we arrange the numbers in ascending order:

4, 4, 5, 6, 7, 9, 9, 10

Since we have 8 data points, the median will be the average of the two middle numbers:

Median = (6 + 7) / 2 = 6.5

Now we can find the sum of the mean and the median:

Sum of mean and median = 6.75 + 6.5 = 13.25

Therefore, the sum of the mean and the median of the given dataset is 13.25.

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Answer:

23

Step-by-step explanation:

please mark me as brainliest

The equation c₁ · a · c · x / b₁ · d · iₙ can have a solution for x if and only if the matrices a, b, and c are compatible and satisfy certain conditions.

Further information about the matrices and their properties is required to determine the specific solution.

To determine if the equation c₁ · a · c · x / b₁ · d · iₙ has a solution, we need to consider the compatibility and properties of the matrices involved.

Let's break down the equation:

c₁: The first column of matrix c.

a: Matrix a.

c: Matrix c.

x: The solution vector.

b₁: The first row of matrix b.

d: Matrix d.

iₙ: The identity matrix of size n.

For the equation to have a solution, the matrices a, b, and c need to be compatible, meaning their dimensions align appropriately for matrix multiplication. Specifically, the number of columns in matrix a should match the number of rows in matrix c.

Additionally, certain conditions or properties of the matrices may be required to ensure a solution exists. Without additional information about the specific matrices a, b, c, and d, it is not possible to determine the solution for x.

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