factor each
x^3 +2x^2 -4x -8 =0

Answer:

Step-by-step explanation:

If the figure is a parallelogram then the angles opposite one another are equal

2x - 30 = x + 40                    Subtract x from both sides.

2x - x - 30 = x - x + 40         Combine

x - 30 = 40                             Add 30 to both sides

x - 30 + 30 = 40 + 30           Combine

x = 70

The coordinate vector of v = 2x² - 5x + 6 relative to the basis S = {1, x - 1, (x - 1)²} is [3, -1, 2].

To find the coordinate vector of vector v = 2x² - 5x + 6 relative to the basis S, we need to express v as a linear combination of the polynomials in S. Let's go step by step:

1. Express v in terms of the basis polynomials P₁, P₂, and P₃:

  v = 2x² - 5x + 6

2. We want to express v in the form:

  v = c₁P₁ + c₂P₂ + c₃P₃

Let's substitute the basis polynomials into this equation:

  2x² - 5x + 6 = c₁(1) + c₂(x - 1) + c₃(x - 1)²

3. Expand the squared term:

  2x² - 5x + 6 = c₁ + c₂(x - 1) + c₃(x² - 2x + 1)

4. Rearrange terms:

  2x² - 5x + 6 = c₃x² + (c₂ - 2c₃)x + (c₁ - c₂ + c₃)

5. Equate the coefficients of corresponding powers of x:

  From the equation above, we have:

  c₃ = 2   (coefficient of x²)

  c₂ - 2c₃ = -5   (coefficient of x)

  c₁ - c₂ + c₃ = 6   (constant term)

6. Solve the system of equations to find the values of c₁, c₂, and c₃:

  From c₃ = 2, we get c₃ = 2.

  Substituting c₃ = 2 into the second equation, we have c₂ - 2(2) = -5.

  Simplifying, we get c₂ - 4 = -5.

  Solving for c₂, we find c₂ = -1.

  Substituting c₃ = 2 and c₂ = -1 into the third equation, we have c₁ - (-1) + 2 = 6.

  Simplifying, we get c₁ + 1 + 2 = 6.

  Solving for c₁, we find c₁ = 3.

7. The coordinate vector of v relative to the basis S is [c₁, c₂, c₃] = [3, -1, 2].

Therefore, the coordinate vector of v = 2x² - 5x + 6 relative to the basis S = {1, x - 1, (x - 1)²} is [3, -1, 2].

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f(y) = (a/3)y + (2/3)by/a - b/3.

To calculate the vertical center of mass of the triangle, we need to first determine the coordinates of its centroid. The triangle has vertices at (0,0), (a,0) and (0,b). The x-coordinate of the centroid, Xc is given by the equation:

Xc = (x1 + x2 + x3)/3

where x1, x2, and x3 are the x-coordinates of the vertices of the triangle. Substituting the values:Xc = (0 + a + 0)/3 = a/3

Similarly, the y-coordinate of the centroid, Yc is given by the equation:Yc = (y1 + y2 + y3)/3

where y1, y2, and y3 are the y-coordinates of the vertices of the triangle. Substituting the values:Yc = (0 + 0 + b)/3 = b/3

Therefore, the centroid of the triangle is located at (a/3, b/3). Now, we need to determine f(y), which is the distance from the line x = a/3 to the top of the triangle at any height y. We can do this by finding the equation of the line joining the centroid to the top vertex of the triangle.

The slope of this line is given by:(y - b/3)/(x - a/3) = -b/a

Solving for y, we get:y = -b(x - a/3)/a + b/3

The top vertex of the triangle is located at (x, y), where x = 0 and y = b.

Therefore, the distance from the line x = a/3 to the top of the triangle at any height y is given by:

f(y) = y - (-b(x - a/3)/a + b/3)

f(y) = y + b(x - a/3)/a - b/3

f(y) = (a/3)y + (2/3)by/a - b/3

Now, we can set up the integral to calculate the vertical center of mass of the triangle. The center of mass, C is given by:C = (1/A) ∫ y dA

where A is the area of the triangle and dA is an element of area. We can express dA in terms of y as:

dA = 2(dy)(y/a)

The factor of 2 is included because we need to integrate over the entire height of the triangle. Substituting the values, we get:dA = 2(dy)(y/a) = 2y/a dy

The limits of integration are from y = 0 to y = b. Therefore,C = (1/A) ∫ y dA = (1/[(1/2)ab]) ∫ [0,b] y(2y/a) dy

C = (2/ab) ∫ [0,b] y2 dy

Integrating, we get:C = (2/ab) [(1/3) b3] = (1/3) b2/a

Therefore, the vertical center of mass of the triangle is located at a distance of b2/(3a) from the side opposite the vertex at (0,0).

f(y) = (a/3)y + (2/3)by/a - b/3.

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Answer:

which principle prevents a brach from abusing  its power

Step-by-step explanation:

which principle prevents a brach from abusing  its power

Answer:

20x - 30 = 250

Step-by-step explanation:

20x - 30 = 250

20x = 280

x = 14

Answer:

28.0001

Step-by-step explanation:

im pretty sure

Answer:

5x + y - 2 + 3 - 1

Step-by-step explanation:

The correct option is (C) 58. In the given figure, since PQRS is a cyclic quadrilateral, the sum of angles P and S is equal to 180 degrees. Therefore, the measure of angle P can be found by subtracting the measure of angle S from 180 degrees: 180 degrees - 102 degrees = 78 degrees.

In triangle LNP, the sum of angles L, N, and P is equal to 180 degrees. We know that the measure of angle P is 78 degrees, so we can substitute this value into the equation: L + N + 78 degrees = 180 degrees. By rearranging the equation, we find that the sum of angles L and N is equal to 180 degrees - 78 degrees = 102 degrees.

Since LQMN is a cyclic quadrilateral, the sum of angles L and N is equal to 180 degrees. Therefore, the measure of the arc LN, denoted as m(LN), is equal to the sum of angles L and N, which is 102 degrees.

Thus, the correct option is (C) 58.

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Answer:

Velocity

Step-by-step explanation:

Velocity is the displacement of an object during a specific unit of time

Answer:

Velocity

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Given

\(\frac{1}{3}\) x - 8 = - 12 ( multiply through by 3 to clear the fraction )

x - 24 = - 36 ( add 24 to both sides )

x = - 12 → A

The horizontal distance from the tower to the fire is 7 feet

The term "angle of depression" describes the angle created by a horizontal line and the line of sight from the observer's eye to a location below their horizontal line of sight. It is often calculated by descending from the horizontal line.

The angle of depression is a term that is frequently used in discussions of observations or measurements involving objects that are below the observer's location in geometry and trigonometry.

We know that;

Tan 3 = x/140

x = 140 Tan 3

x = 7 feet

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Answer:

see explanation

Step-by-step explanation:

A base angle

B leg

C vertex angle

D leg

E base angle

F base

in any isosceles triangle there are 2 congruent legs and 2 congruent base angles.

the base angles are opposite the congruent legs

the remaining side, the base is the 3rd side of the triangle

the vertex angle is formed by the 2 congruent legs

Answer:

l = 194999.45

Step-by-step explanation:

I'm going to assume that you meant 3.14 by 3,14.

336,765 = 3.14 × 0.55 × (l + 0.55)

336,765 ÷ (3.14 × 0.55) = l + 0.55

(336,765 ÷ (3.14 × 0.55)) - 0.55 = l

l = 194999.45

We want to find the x-intercepts of the polynomial

this means, we want to find where this functon crosses the x axis. Recall that the x axis is the line y=0. So we want to solve this equation

if we multiply both sides by -1, we get

on the right, we have a difference of squares, so we can factor it out as

now, as this is a product of numbers, this means that each of the number could be 0. This means we have two different equations, which are

and

on the first one, if we subtract 4 on both sides, we get

and on the second one, if we add 4 on both sides, we get

so the x-intercepts of the polynomial are x=4 and x= -4

ANSWER

True

EXPLANATION

When the order matters, the number of ways to arrange items is determined with a permutation. This way, sets of items with the same items but in different order are counted as different sets. For example, (blue, red, green) is not the same as (green, red, blue).

On the other hand, when order does not matter, the number of ways to arrange items is determined with a combination. This way, sets with the same items are counted as the same set. In the previous example, both sets have the same combination of colors, so they are counted as the same set.

Hence, it is true that when the order does matter, the number of ways to arrange items is determined with a permutation.

A discrete probability distribution is a statistical distribution that relates to a set of outcomes that can take on a countable number of values, whereas a continuous probability distribution is one that can take on any value within a given range.Therefore, the main difference between the two types of distributions is the type of outcomes that they apply to.

An example of a discrete probability distribution is the probability of getting a particular number when a dice is rolled. The possible outcomes are only the numbers one through six, and each outcome has an equal probability of 1/6. Another example is the probability of getting a certain number of heads when a coin is flipped several times.

On the other hand, an example of a continuous probability distribution is the distribution of heights of students in a school. Here, the range of heights is continuous, and it can take on any value within a given range.

The expected value of a probability distribution measures the central tendency or average of the distribution. In other words, it is the long-term average of the outcome that would be observed if the experiment was repeated many times.

For a discrete probability distribution, the expected value is computed by multiplying each outcome by its probability and then adding the results. In mathematical terms, this can be written as E(x) = Σ(xP(x)), where E(x) is the expected value, x is the possible outcome, and P(x) is the probability of that outcome.

For example, consider the probability distribution of the number of heads when a coin is flipped three times. The possible outcomes are 0, 1, 2, and 3 heads, with probabilities of 1/8, 3/8, 3/8, and 1/8, respectively. The expected value can be computed as E(x) = (0*1/8) + (1*3/8) + (2*3/8) + (3*1/8) = 1.5.

Therefore, the expected value of the distribution is 1.5, which means that if the experiment of flipping a coin three times is repeated many times, the long-term average number of heads observed will be 1.5.

Answer:

The total amount of water Andre brought for the hike was, 3.0 liters.

Step-by-step explanation:

Let the total amount of water Andre brought for the hike be denoted by, x.

It is provided that he drank 1.5 liters of the water during the first part of the hike.

Also, this 1.5 liters of the water is 50% of the water he brought, i.e.

\(1.5\ \text{lt}=50\%\ \text{of}\ x\)

Compute the value of x as follows:

\(1.5\ \text{lt}=50\%\ \text{of}\ x\)

     \(x=\frac{1.5}{50\%}\)

        \(=\frac{1.5}{50}\times 100\\\\=1.5\times 2\\\\=3.0\)

The total amount of water Andre brought for the hike was, 3.0 liters.

\( \leadsto \sf \dfrac{2}{3} \div \dfrac{ - 2}{7} \)

\( \\ \\ \)

\( \leadsto \sf \dfrac{2}{3} \times \dfrac{ - 7}{2} \)

\( \\ \\ \)

\( \leadsto \sf \dfrac{ - 7}{3}\)

Therefore, the number of ways a student can work 7 out of 10 questions on the exam is 120, which corresponds to option (D).

The number of ways a student can work 7 out of 10 questions on an exam can be calculated using the concept of combinations.

The formula for combinations is given by:

C(n, k) = n! / (k!(n - k)!)

Where n is the total number of items and k is the number of items chosen.

In this case, the student is choosing 7 questions out of a total of 10, so we have:

C(10, 7) = 10! / (7!(10 - 7)!) = 10! / (7!3!)

Simplifying:

10! = 10 * 9 * 8 * 7!

3! = 3 * 2 * 1

C(10, 7) = (10 * 9 * 8 * 7!) / (7! * 3 * 2 * 1)

The 7! terms cancel out:

C(10, 7) = (10 * 9 * 8) / (3 * 2 * 1)

C(10, 7) = 120

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Answer:

Your answer is 105km travelled in 7 hours.

Step-by-step explanation:

Divide 150km by 10 to find the amount of km travelled in 1 hour. Then multiply that answer by 7.

Answer:

y=63, x=20, x=47, b=70, c=89, x=133

Step-by-step explanation:

1) y=63- alternate angles are the same

2) 4x+5x=180

9x=180

x=20

3) x=47

4) b=70- angles on a line equal to 180

c=89- angles in a triangle add up to 180

5) x=133- angles that are alternate are the same

The ∆ABC is an isosceles triangle and have the base angles m∠A and m∠C equal to 51° and the angle m∠B is equal to 78°.

An isosceles triangle have the measure of its base angles to be equal, and the sum of the interior angles sum up to 180°.

Given that sides AB ≅ BC, then the triangle ∆ABC has two sides with similar length and base angles so;

angles m∠A and m∠C are the base angles are both equal to 51°

m∠B = 180° - (51 + 51)° {sum of interior angles of a triangle}

m∠B = 180° - 102°

m∠B = 78°

Therefore, the isosceles triangle ∆ABC have the base angles m∠A and m∠C equal to 51° and the angle m∠B is equal to 78°.

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The equation has B. No solution.

An equation is a  mathematical statement that is made up of two expressions connected by an equal sign.

here, given that,

1/4*(-16r-28)= - 4r - 7

-16r - 28 = -16r-28

this statement is not true.

so, The equation has B. No solution.

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If a boat leaves port and follows a course of n77°e at 9 knots for 3 hr and 20 min. then, the boat changes to a new course ofs27°east 12knots for 4hr then the boat is approximately 67.9 nautical miles from the port.

To solve the problem, we can use the law of cosines to find the distance from the boat to the port.

Let A be the position of the boat after the first leg of the trip and B be the position after the second leg. Let x be the distance from A to B. Then, we have:

cos(77°) = (distance from port to A) / x

cos(27°) = (distance from port to B) / x

We can solve for the distances from the port to A and B using the given course and speed information:

(distance from port to A) = 9 knots x 3.33 hours = 29.97 nautical miles

(distance from port to B) = 12 knots x 4 hours = 48 nautical miles

Substituting into the law of cosines, we get:

x^2 = (29.97)^2 + (48)^2 - 2(29.97)(48)cos(130°)

Solving for x gives:

x ≈ 67.9 nautical miles

Therefore, the boat is approximately 67.9 nautical miles from the port.

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20.11 cm3/min is the rate at which the snowball's volume is decreasing.

Given,

The decreasing diameter when the spherical ball is melting = 0.2 cm/min

We have to find the rate in decrease in volume of snowball when diameter is 8 cm.

Here,

Volume of sphere, V = 4/3 π r³ = 4/3 π (D/2)³ = 1/6 π D³

Considering differences according to time,

dV/dt = d/dt (1/6 π D³) = 1/6 π × 3D² dD/dt

dV/dt = 1/2 π D² dD/dt

Substituting

D is 8 cm, and the diameter is changing at a rate of 0.2 cm/min.

dV/dt = 1/2 π D² dD/dt

dV/dt = 1/2 × π × 8² × 0.2 = 20.11 cm³/min

Therefore,

Decreasing snowball volume at a rate of 20.11 cm3/min

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Answer:

√3 cm

or

1.73 cm to the nearest hundredth.

Step-by-step explanation:

Each side must be 2 cm long

Using Heron's formula

Area = √(s(s-a)(s-b)(s-c)  where s = semi-perimeter, a , b and c are the 3 side lengths.

So here s = 6/2 = 3 and all the sides = 2 so

Area  = √(3(3-2)^3

         =  √3 cm.

The value of the given expression is approximately 71.31.

\($$75 - 12(20 ÷ 2.5) ÷ 26$$\)

The Order of Operations states that the sequence of steps in which we carry out the operations of a given problem.

So, we follow the Order of Operations to solve this expression.

Firstly, we will evaluate the parentheses:

\($$20 ÷ 2.5 = 8$$\)

Now, the given expression becomes:

\($$75 - 12 × 8 ÷ 26$$\)

Then, we will evaluate multiplication and division in order from left to right.

12 × 8 = 96

So, the given expression becomes:

\($$75 - 96 ÷ 26$$\)

Evaluating division, we get:

\($$75 - 3.6923$$\)

Now, we will add and subtract from left to right.

\(75 − 3.6923 ≈ 71.31\)

Therefore, the value of the given expression is approximately 71.31.

So, the required  is approximately 71.31.

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(a) There are 20 people in the room.

We can simply use the set theory to find the total number of people in the room by following these steps:

1. Start with the number of math majors, which is 10.

2. Add the number of ECE majors, which is 10. However, 2 of them are math-ECE double majors, so we only add 8 new people (10 - 2 = 8).

3. Add the number of CS majors, which is 3. However, 1 of them is a math-CS double major, so we only add 2 new people (3 - 1 = 2). Now, add the numbers from each step: 10 (math majors) + 8 (ECE majors) + 2 (CS majors) = 20 There are 20 people in the room.

The number of 10-letter binary strings that do not contain the pattern "10" as a substring is 6824.Solution.

( c ) 6824 10-letter binary strings do not contain the pattern "10" as a substring.

To determine the number of 10-letter binary strings that do not contain the pattern "10" as a substring, we can use the principle of inclusion-exclusion (PIE).How many 10-letter binary strings do not contain the pattern "10" as a substring?The number of 10-letter binary strings that do not contain the pattern "10" as a substring is 6824.Solution:Let A be the set of all 10-letter binary strings, B be the set of all 10-letter binary strings that contain the pattern "10," and C be the set of all 10-letter binary strings that contain the pattern "010." Then, we want to find the cardinality of A \ B, which is the set of all 10-letter binary strings that do not contain the pattern "10" as a substring.By PIE,|B ∪ C| = |B| + |C| - |B ∩ C|We can count the cardinality of each set as follows:|B| = 2^9 (there are 9 places to put the "10," and the other digits can be either 0 or 1)|C| = 2^8 (there are 8 places to put the "010," and the other digits can be either 0 or 1)|B ∩ C| = 2^7 (there are 7 places to put the "10" and "0," and the other digits can be either 0 or 1)Therefore,|B ∪ C| = |B| + |C| - |B ∩ C| = 2^9 + 2^8 - 2^7 = 640A ∩ (B ∪ C)^c = (A ∩ B^c ∩ C^c)^cby De Morgan's laws.So,A \ B = A ∩ B^c = A ∩ (B ∪ C)^cTherefore,|A \ B| = |A ∩ (B ∪ C)^c| = |A| - |B ∪ C||A| = 2^10, so|A \ B| = 2^10 - |B ∪ C| = 2^10 - (2^9 + 2^8 - 2^7) = 6824Therefore, 6824 10-letter binary strings do not contain the pattern "10" as a substring.

(d) The number of 10-letter binary strings that do not contain the pattern "1010" as a sub-string is 5324.

We can use the principle of Inclusion and Exclusion to answer this question: There are 2^10 binary strings of length 10. However, we cannot allow binary strings that contain the pattern "1010".Let X1 denote the number of binary strings of length 10 that contain 1010 as a sub-string. Let X2 denote the number of binary strings of length 10 that contain 2 copies of 1010 as a sub-string. Let X3 denote the number of binary strings of length 10 that contain 3 copies of 1010 as a sub-string. Let X4 denote the number of binary strings of length 10 that contain 4 copies of 1010 as a sub-string. Then, by the principle of Inclusion and Exclusion, the number of 10-letter binary strings that do not contain the pattern "1010" as a sub-string is:2^10 - X1 + X2 - X3 + X4We need to calculate X1, X2, X3, and X4. Let us consider X1. Let us remove the sub-string 1010 from the binary string. Then we are left with a string of length 6, which can be any binary string. Thus, 2^6 binary strings of length 6 contain 1010 as a sub-string. However, each of these can be extended to a 10-letter binary string in 4 ways (there are 4 positions where we can insert the sub-string 1010 back in). Thus, X1 = 4*2^6Similarly, we can calculate X2, X3, and X4.X2: Let us remove 2 copies of 1010 from the binary string. Then we are left with a string of length 2, which can be any binary string. Thus, 2^2 binary strings of length 2 contain 2 copies of 1010 as a sub-string. However, each of these can be extended to a 10-letter binary string in 5 ways. Thus, X2 = 5*2^2.X3: Let us remove 3 copies of 1010 from the binary string. Then we are left with a string of length 14, which can be any binary string. Thus, 2^14 binary strings of length 14 contain 3 copies of 1010 as a sub-string. However, each of these can be extended to a 10-letter binary string in 6 ways. Thus, X3 = 6*2^14.X4: Let us remove 4 copies of 1010 from the binary string. Then we are left with a string of length 18, which can be any binary string. Thus, 2^18 binary strings of length 18 contain 4 copies of 1010 as a sub-string. However, each of these can be extended to a 10-letter binary string in 7 ways. Thus, X4 = 7*2^18.Now, we can substitute these values in our formula:2^10 - X1 + X2 - X3 + X4 = 2^10 - 4*2^6 + 5*2^2 - 6*2^14 + 7*2^18= 1024 - 256 + 20 - 98304 + 7340032= 7254416 Thus, 7254416 10-letter binary strings do not contain the pattern "1010" as a sub-string.

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Step-by-step explanation:

angle of 45° is drawn.

I hope you got it.