Given that -6i is a zero, factor the following polynomial function completely. Use the Conjugate Roots Theorem, if applicable.
f(x)=x^4-15x³ + 90x² - 540x + 1944

Answer:

Step-by-step explanation:

well 2.20 (ronded) pounds is  one kilogram so multiply 258 by 2.20 then divide by two to get 117.03

Answer:

2

Step-by-step explanation:

just did it on end 2022 test quiz

Answer:

Jim would need 3.75 pounds of fruit to make 12 smoothies.

Step-by-step explanation:

Since 1 pound = 16 ounces, 12 smoothies will require:

12 x 5 = 60 ounces of fruit

To convert this to pounds, we divide by 16:

60 / 16 = 3.75 pounds of fruit

Therefore, Jim would need 3.75 pounds of fruit to make 12 smoothies.

Answer:

width = 3x

Step-by-step explanation:

Area of a rectangle = Length × width

Length = 5x + 4

Breadth = y

15x² + 12x = 5x + 4 × y

y = 15x² + 12x

---------------

5x + 4

y = 3x

The height of the plane above the ocean is approximately 15,000 meters to the nearest meter.

The angle of depression is an angle formed between a horizontal line (such as the ground, ocean surface, or any other reference plane) and a line of sight from an observer looking downward towards an object or point of interest that is located below the observer's line of sight.

According to the given information:

The angle of depression is the angle formed between the horizontal line (such as the ocean's surface) and the line of sight from an observer looking downward to an object (such as the island). In this case, the angle of depression is given as 45 degrees.

Given:

Angle of depression = 45 degrees.

Distance from airplane to island = 15,000 meters.

To find the height of the plane, we can use trigonometry. The tangent function is commonly used to relate angles of depression to the height of an object above the horizontal.

In a right triangle, the tangent of an angle is defined as the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle. In this case, the side opposite the angle of depression is the height of the plane, and the side adjacent to the angle is the distance from the airplane to the island.

Using the tangent function:

tan(angle of depression) = height of plane/distance to the island

Plugging in the given values:

tan(45 degrees) = height of plane / 15,000 meters

We can now solve for the height of the plane:

height of plane = tan(45 degrees) * 15,000 meters

Using a calculator, we find:

height of plane = 15000 * tan(45 degrees) ≈ 15000 meters (rounded to the nearest meter)

So, the height of the plane above the ocean is approximately 15,000 meters to the nearest meter.

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If Fred books a certain number of nights, If Fred books 30 nights at either hotel, he will earn 1,661 points.

What are the points?

Let's assume that Fred books "n" nights at the hotel.

For Hotel Elegance, the total number of points that Fred will earn is:

881 + 22n

For Hotel Paradiso, the total number of points that Fred will earn is:

851 + 23n

According to the problem, Fred will earn the same number of points at both hotels if:

881 + 22n = 851 + 23n

Solving for "n", we get:

n = 30

Therefore, if Fred books 30 nights at either hotel, he will earn the same number of points. To find out how many points he will earn, we can substitute "n=30" into either equation:

For Hotel Elegance:

881 + 22n = 881 + 22(30) = 1,661 points

For Hotel Paradiso:

851 + 23n = 851 + 23(30) = 1,621 points

Therefore, if Fred books 30 nights at either hotel, he will earn 1,661 points.

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The length of the arc is approximately 7.5 inches.

What is circle?

A circle is a geometric shape that consists of all points in a plane that are equidistant from a fixed point called the center. It can also be defined as the set of points that are a fixed distance (called the radius) away from the center point.

I'm sorry, but the answer you provided is not correct.

To find the length of the arc, you first need to determine what fraction of the circle the sector represents. The central angle is 36 degrees, which is 36/360 or 1/10 of the full circle.

To find the length of the arc, you can then use the formula:

arc length = (central angle/360) x 2πr

where r is the radius of the circle.

Plugging in the values you provided, we get:

arc length = (36/360) x 2π(12) = 2.4π inches

Rounding to the nearest tenth gives:

arc length ≈ 7.5 inches

Therefore, the length of the arc is approximately 7.5 inches.

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a. The absolute value of a number is the distance of the number from zero on a number line. It is always a non-negative value, meaning that it is either zero or a positive number. It is denoted by two vertical bars surrounding the number, like |x|.

b. The absolute value of -109 is the distance of -109 from zero on a number line. Since -109 is 109 units away from zero, the absolute value of -109 is 109. Therefore, |-109| = 109.

c. First, we need to evaluate |-7|, which is the absolute value of -7. The distance of -7 from zero on a number line is 7 units, so |-7| = 7. Therefore, the expression |-7| - 2 is equivalent to 7 - 2, which is equal to 5. Therefore, |-7| - 2 = 5.

The volume of the figure is 1795.5 m³.

The volume of the figure can be found as follows:

volume of the figure = base area × height

Therefore, the base of the figure is a trapezium.

Hence,

base area  = 1 / 2 (a + b)h

where

Therefore,

base area  = 1 / 2 (11 + 16)9.5

base area = 1 / 2 (27)9.5

base area = 256.5 / 2

base area = 128.25

Hence,

volume of the figure = 128.25 × 14

volume of the figure = 1795.5 m³

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The probability of success for given number of trials is 0.4751.

What is probability?

Probability can be used to determine the likelihood of an event. The likelihood that an event will happen is the only useful outcome. a scale where 0 indicates impossibility and 1 indicates a specific occurrence.

We know that the probability is given by:

P = nCx * [tex]p^{x}[/tex] * [tex]q^{n-x}[/tex]

P (x ≤ 3) = P(0) + P(1) + P(2) + P(3)

Now,

⇒ P(0) = 7C0 * [tex]0.4^{0}[/tex] * [tex]0.6^{7}[/tex]

⇒ P(0) = 1 * 1 * 0.0279936

⇒ P(0) = 0.02799

Similarly,

⇒ P(1) = 7C1 * [tex]0.4^{1}[/tex] * [tex]0.6^{6}[/tex]

⇒ P(1) = 7 * 0.4 * 0.046656

⇒ P(1) = 0.13064

Similarly,

⇒ P(2) = 7C2 * [tex]0.4^{2}[/tex] * [tex]0.6^{5}[/tex]

⇒ P(2) = 21 * 0.16 * 0.07776

⇒ P(2) = 0.02613

Similarly,

⇒ P(3) = 7C3 * [tex]0.4^{3}[/tex] * [tex]0.6^{4}[/tex]

⇒ P(3) = 35 * 0.064 * 0.1296

⇒ P(3) = 0.2903

So, now we get

⇒ P (x ≤ 3) = P(0) + P(1) + P(2) + P(3)

⇒ P (x ≤ 3) = 0.02799 + 0.13064 + 0.02613 + 0.2903

⇒ P (x ≤ 3) = 0.4751

Hence, the probability of success for given number of trials is 0.4751.

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A linear function representing the number of cards as a function of the number of years, t is y = 50 + 50t.

A linear function is a mathematical or algebraic equation of a straight line in the slope-intercept form.

Linear functions are written as f(x) = mx + b, where m is the slope and b is the y-intercept of the line.

Number of Total Cards in Carlos' Collection

Year             Total Cards

Year 1              50

Year 2            100

Year 3            150

Year 4           200

Slope = Rise/Run = (100 - 50)/(2 - 1)

= 50

Initial value in the first year = 50

Let the number of years involved = t

Let the value in year t = y

y = 50 + 50t

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Answer:

We can start by using the identity 2 sin ϕ cos ϕ = sin 2ϕ to simplify the left-hand side of the equation:

2 sin ϕ cos ϕ + 2 sin ϕ + cos ϕ + 1 = sin 2ϕ + 2 sin ϕ + cos ϕ + 1

Next, we can use another identity, sin^2 ϕ + cos^2 ϕ = 1, to eliminate the cosine term:

sin 2ϕ + 2 sin ϕ + cos ϕ + 1 = sin 2ϕ + 2 sin ϕ + √(1 - sin^2 ϕ) + 1

Now, we can substitute u = sin ϕ to obtain a quadratic equation in u:

sin 2ϕ + 2 sin ϕ + √(1 - sin^2 ϕ) + 1 = sin^2 ϕ + 2 sin ϕ + √(1 - sin^2 ϕ) + 1

sin 2ϕ = sin^2 ϕ

2 sin ϕ cos ϕ = sin^2 ϕ - cos^2 ϕ

2 u √(1 - u^2) = u^2 - (1 - u^2)

2 u √(1 - u^2) = 2 u^2 - 1

4 u^2 (1 - u^2) = (2 u^2 - 1)^2

4 u^4 - 4 u^2 + 1 = 0

This is a quadratic equation in u^2, which can be solved using the quadratic formula:

u^2 = [4 ± √(16 - 16)] / 8 = 1/2 or u^2 = 1

Since 0 < ϕ < 2π, we have 0 < u < 1, so u^2 = 1/2. Therefore, sin ϕ = u = ±√(1/2) and cos ϕ = ±√(1 - u^2) = ±√(1/2).

We can summarize the solutions as follows:

sin ϕ = √(1/2) or sin ϕ = -√(1/2)

cos ϕ = √(1/2) or cos ϕ = -√(1/2)

Therefore

The image coordinates of L′ are L′(-1, 2).

What are Transformation and Reflection?

Single or multiple changes in a geometrical shape or figure are called Geometrical Transformation.

A geometrical transformation in which a geometrical figure changes his position to his mirror image about some point or line or axis is called Reflection.

To reflect the preimage of point L across the line y = -2, we need to find the distance between L and the line y = -2 and then move that same distance above the line to get the image L′.

The distance between point L and the line y = -2 is 4 units (since the y-coordinate of point L is -6 and the y-coordinate of the line y = -2 is -2).

So, to get the image L′, we move 4 units above the line y = -2 starting from the x-coordinate of L, which is -1. This gives us the coordinates (-1, 2).

Therefore, the image coordinates of L′ are L′(-1, 2).

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So, the length of WZ is 24 in kite WXYZ with diagonals WY and XZ.

A triangle is a closed, two-dimensional geometric shape that is formed by three line segments, called sides, that intersect at three points, called vertices. Triangles are one of the most basic shapes in geometry and are studied extensively in mathematics. The properties of triangles depend on the length of their sides and the size of their angles. Triangles can be classified based on the length of their sides as equilateral, isosceles, or scalene, and based on the size of their angles as acute, right, or obtuse. In an equilateral triangle, all three sides are of equal length. In an isosceles triangle, two sides are of equal length, while the third side is of a different length. In a scalene triangle, all three sides are of different lengths.

Here,

Since WXYZ is a kite, we know that its diagonals, WY and XZ, intersect at a right angle and bisect each other. Let M be the point of intersection of the diagonals, so that MW = MY and MX = MZ.

We can use the Pythagorean theorem to find MW and MX, and then use the fact that they are equal to find WZ.

Using the Pythagorean theorem in right triangles WMX and WMY, we have:

MW² = WX² - MX²

= 17² - 5²

= 264

MY² = WY² - MW²

= 13² - 264

= 25

MX² = XZ² - MZ²

= 17² - 13²

= 144

Since MW = MY, we have MW = √(25)

= 5

Therefore, WZ = 2MX

= 2√(144)

= 2*12

= 24

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Boris's gas tank can hold 18 gallons of gas.

Gallons are a unit of volume commonly used to measure liquids, particularly in the United States. One gallon is equivalent to 128 fluid ounces or 3.785 liters. It is often used to measure the amount of gasoline or other fuels used in vehicles, as well as the amount of water in swimming pools or storage tanks.

Let's assume that the tank can hold "x" gallons of gas.

According to the problem, Boris's gas tank is initially half full, which means that it contains:

[tex]1/2 * x = x/2[/tex] gallons of gas

After he buys 3 gallons of gas, the tank is 2/3 full, which means it contains:

[tex]2/3 * x = 2x/3[/tex]gallons of gas

We can set up an equation based on the given information:

[tex]x/2 + 3 = 2x/3[/tex]

Multiplying both sides by 6 to eliminate the fractions:

[tex]3x + 18 = 4x[/tex]

Subtracting 3x from both sides:

[tex]18 = x[/tex]

Therefore, Boris's gas tank can hold 18 gallons of gas.

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Boris's gas tank can hold 18 gallons of gas.

What are gallons?

Gallons are a unit of volume commonly used to measure liquids, particularly in the United States. One gallon is equivalent to 128 fluid ounces or 3.785 liters. It is often used to measure the amount of gasoline or other fuels used in vehicles, as well as the amount of water in swimming pools or storage tanks.

Let's call the total capacity of Boris's gas tank "x". We know that when the tank is half full, it contains 1/2x gallons of gas. After Boris buys 3 gallons of gas, the tank is 2/3 full, which means it contains 2/3x gallons of gas. We can set up an equation to solve for x:

1/2x + 3 = 2/3x

To solve for x, we need to isolate it on one side of the equation. We can do this by first subtracting 1/2*x from both sides:

3 = 2/3x - 1/2x

To simplify the right side, we need to find a common denominator. The smallest common denominator of 2 and 3 is 6, so we can rewrite the fractions as:

3 = (4/6)*x - (3/6)*x

Now we can combine the terms on the right side:

3 = (1/6)*x

To solve for x, we can multiply both sides by 6:

x = 18

Therefore, Boris's gas tank can hold 18 gallons of gas.

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The sum of all solutions to the equation 2cos²(x) - 7cos(x) - 4 = 0 for 0 < x < 2π is approximately 9.425 + 2π.

In mathematics, a quadratic is a polynomial expression of the second degree, meaning it contains one or more terms that are squared but no terms that are cubed or higher. Quadratic functions are typically written in the form ax² + bx + c, where a, b, and c are constants and x is the variable.

To find the sum of all solutions to the equation 2cos²(x) - 7cos(x) - 4 = 0 for 0 < x < 2π, we can first use the quadratic formula to solve for cos(x):

cos(x) = [7 ± √(7² - 4(2)(-4))] / (2(2))

cos(x) = [7 ± √89] / 4

The two possible solutions for cos(x) are:

cos(x) = (7 + √89) / 4

cos(x) = (7 - √89) / 4

Note that for 0 < x < 2π, the cosine function has values between -1 and 1. Therefore, the first solution cos(x) = (7 + √89) / 4 is not valid, since it is greater than 1.

The second solution cos(x) = (7 - √89) / 4 is valid, since it is between -1 and 1. Therefore, the sum of all solutions to the equation is:

x = cos⁻¹[(7 - √89) / 4] + 2πn, where n is an integer.

We need to find the sum of all possible values of x for 0 < x < 2π. We can do this by finding the smallest and largest values of n that give valid solutions, and then summing the corresponding values of x.

The smallest value of n that gives a valid solution is n = 0, since cos⁻¹[(7 - √89) / 4] is already between 0 and 2π. The largest value of n that gives a valid solution is n = -1, since adding 2π to cos^(-1)[(7 - √89) / 4] gives a value greater than 2π.

Therefore, the sum of all solutions to the equation is:

89) / 4 - 2π]

x = cos⁻¹[(7 - √89) / 4] + cos⁻¹[(7 - √

x ≈ 6.2832 + 0.8429 + 2π

x ≈ 9.425 + 2π

The sum of all solutions to the equation 2cos²(x) - 7cos(x) - 4 = 0 for 0 < x < 2π is approximately 9.425 + 2π.

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The equation of the circle in standard form with a center at (-6, 5) and passing through the point (-11, 3) is (x + 6)² + (y - 5)² = 29.

The equation of a circle in standard form with a center at (h, k) and a radius r is:

(x - h)² + (y - k)² = r²

Center: (h, k) = (-6, 5)

Point on circle: (-11, 3)

Substituting these values into the standard form equation:

(x - (-6))² + (y - 5)² = r²

(x + 6)² + (y - 5)² = r²

Now we need to find the value of r, which is the radius of the circle.

The distance between the center (-6, 5) and the point (-11, 3) is equal to the radius of the circle.

Using the distance formula:

r = √((x₂ - x₁)² + (y₂ - y₁)²)

r = √((-11 - (-6))² + (3 - 5)²)

r = √((-5)² + (-2)²)

r = √(25 + 4)

r = √29

r² = 29

The equation of the circle:

(x - h)² + (y - k)² = r²

(x + 6)² + (y - 5)² = 29

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The height of the air plane is obtained as 10503 ft.

We know that we can be able able to use the principles that can apply to the right triangle so as to be able to obtain the height that the triangle has been able to attain.

We know that in working with the right triangle, we have to look out for the ratio that we can be able to use to obtain the height that the problem in this case requires that we should find and as such we have that;

Tan 35 = H/15000

H = height of the airplane

H = 15000 Tan35

H = 10503 ft

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The reflection line  that maps polygon ABCDE to polygon A' B' C' D' E' is the y-axis.

The image is reflected through a line known as a reflection line. A pattern is said to mirror another pattern, and then every point in the pattern is equidistant from every corresponding point in the other pattern. The reflected image must be the same shape and size, but the image is in the opposite direction.

In order to determine the line of reflection that maps  polygon ABCDE to polygon A' B' C' D' E', we must find a symmetrical line  equidistant from each corresponding pair of points. If you project the image across the x-axis, vertex A (-1, -4) is mapped to A' (13, -4) and vertex E (1, -6) is mapped to E'. (11, 6). Therefore, the reflection line must be the x-axis.

If we map the image to the cross x=6, vertex A (-1, -4) would correspond to A' (13, -4) and vertex E (1, -6) would correspond to E' (3, 6). ). Therefore, the reflection line cannot be x=6.

If we project the pattern perpendicular to y=-3, the point A (-1, -4) is opposite to the point A' (-7, -4) and the vertex E (1, -6)  to  the point E . (7, 6). Therefore, the reflection line  cannot be y=-3.

 If you project the image across the y-axis, point A (-1, -4) is mapped to point A' (-13, -4) and  vertex E (1, -6) is mapped to E. (-11 , 6). Therefore, the reflection line  must be the y-axis.

 Therefore, the reflection line  that maps  polygon ABCDE to polygon A' B' C' D' E' is the y-axis.

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The measure of the angle x is 70°, and the measure of its complementary angle is (90 - x) = (90 - 70) = 20°.

When two angles in geometry add up to 90°, they are said to be complimentary.

Right triangles frequently include complementary angles, where one angle is a right angle (measured 90 degrees), while the other two angles are mutually exclusive.

If two angles add up to 90 degrees, they are complimentary.

If one of the angles has a measure of x, then the complementary angle's measure is (90 - x).

We are told that the angle x measures 50° more than its complementary angle, which can be written as:

x = (90 - x) + 50

Simplifying and solving for x, we have:

2x = 140

x = 70

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Answer:

B.

Step-by-step explanation:

x + 3x + 6 = 6 + 4x

4x + 6 = 6 + 4x

4x - 4x = 6 - 6

This means, whatever value we pick in place of x, there will always be a solution therefore, the equation in option B has infinitely many solutions.

Answer:

R = 3

Step-by-step explanation:

V = 4 π r³/3 = 36

Multiply both of the sides by 3

4π · r³ =108 πcm³

Now your going to divide by 4π

r³ = 27cm³

Square off the ³

r = 3

The transformation that took place from shape A to shape B is that there was a 180° turn around at point 0,2 on the graph.

On the graph, the shape A is the same size as the shape B but with different angles of transformation.

For shape A,

The width at x-axis = -4,-2

length at y-axis = 1,4

For shape B;

The width at x-axis = 2,4

length at y-axis = 0,3

Therefore, transformation that took place from shape A to shape B is that there was a 180° turn around at point 0,2 on the graph.

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The average velocity is given by the displacement during the time thus,[3, 4]: Average Velocity = 40 m/s. [3, 3.5]: Average Velocity = 40 m/s. [3, 3.1]: Average Velocity = 40 m/s. [3,3.01]: Average Velocity = 40 m/s.

Unaffected by direction, speed is a scalar quantity that describes how quickly an object is travelling. The speed and direction of an object's motion are both described by its velocity, which is a vector quantity. In other terms, velocity is the rate of positional change of an object in a specific direction. Therefore, if two objects are travelling in separate directions or if one is accelerating while the other is not, they can have the same speed but distinct velocities.

The average velocity is given by the displacement during the time, thus we have:

Displacement = h(t2) - h(t1) = (40t2 - 0.8312) - (40t1 - 0.8312) = 40(t2 - t1)

Now, the average velocity between t2 - t1 is:

Average Velocity = Displacement / Duration = 40(t2 - t1) / (t2 - t1) = 40 m/s

Using the different values of t2 and t1 we see that:

[3, 4]:

Average Velocity = 40 m/s

[3, 3.5]:

Average Velocity = 40 m/s

[3, 3.1]:

Average Velocity = 40 m/s

[3,3.01]:

Average Velocity = 40 m/s

[3, 3.001]:

Average Velocity = 40 m/s

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The function N for d days of both rumors are N(d) = 2 + 5d and N(d) = 2(3)^d

Here, the number of students are the students that start the rumor i.e. Susanna and Liz

So, we have

For the Justin Beiber rumor, the rumor spreads at a linear rate of 5 per day

So, we have

JB day 2 = 2 + 5(2) = 7

For the Rihanna rumor, the rumor spreads at an exponential rate of 3

So, we have

Rihanna day 2 = 2 * (3)^2 = 18

Using the functions, we have

JB

2 + 5x = 32 students

5x = 30

x = 6 days

Rihanna

2(3)^x = 162 students

3^x = 81

x = ln(81)/ln(3)

x = 4 days

JB

N(d) = 2 + 5d

Rihanna

N(d) = 2(3)^d

So, we have

d          JB          Rihanna

0           2           2

1           7           6

2          12           18

3           17           54

4           22           162

5           27           486          

6           32           1458

7           37           4374

8           42           13122

9           47           39366

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Note that all values of y > 0 at x = (0, 1, 2, 3, 4)

As seen from the graph attached in answer area as well, The graph is above  x-axis (i.e. y value of equation) only when x has values {0, 1, 2, 3, 4}.

At x = 0:

y = - | 0-2| + 2
⇒ - 2+ 2

y = 0

At x = 1:

y = - | 0-1| + 2
⇒ 0+ 2

y = 1

At x = 2:

y = - | 2-2| + 2
⇒ - 1+ 2

y = 1

At x = 3:

y = - | 3-2| + 2
⇒ - 1+ 2

y = 1

At x = 4:

y = - | 4-2| + 2
⇒ - 2+ 2

y = 0

Thus,  all values of y > 0 at x = (0, 1, 2, 3, 4)

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Answer:

Step-by-step explanation:

I can cover this, so a math book is a rectangle, I hope you knew that, there is the front, back, and sides of a math book, given 2 faces and 4 sides of a book, there will be 6 faces, now for the vertices, there are 6 faces, so the edges will make 8 vertices, a vertex is where 2 or more edges meet, so now we will count the edges, given the 6 faces, we can count all of the edges and end up with 8 edges, I hope this helped you

Answer:

One possible pair of numbers whose product is -10 is 2 and -5. Another possible pair of numbers whose product is -10 is -2 and 5.