5. What are the real and complex solutions of the polynomial equation? (1 point)
x-8=0
01+i3, and 1-i√√3
O2,-1+13, and-1-i√√3
O2, 1+2i √√3, and 1-2i √√3
02, 2+2i √√3, and 2-2i

The measure of angle a is 15 degrees and this can be determined by using the properties of the isosceles triangle.

In geometry, interior angles are formed in two ways. One is inside a polygon, and the other is when parallel lines cut by a transversal. Angles are categorized into different types based on their measurements.

Given:

The following steps can be used in order to determine the measure of angle a:

Step 1 - According to the given data, it can be concluded that triangle PQR and triangle PSR are isosceles triangles.

Step 2 - Apply the sum of interior angle property on triangle PQR.

\(\angle\text{Q}+\angle\text{P}+\angle\text{R}=180\)

\(\angle\text{Q}+2\angle\text{R}=180\)

\(2\angle\text{R}=180-60\)

\(\angle\text{R}=60^\circ\)

Step 3 - Now, apply the sum of interior angle property on triangle PSR.

\(\angle\text{P}+\angle\text{S}+\angle\text{R}=180\)

\(\angle\text{S}+2\angle\text{R}=180\)

\(2\angle\text{R}=180-90\)

\(\angle\text{R}=45^\circ\)

Step 4 - Now, the measure of angle a is calculated as:

\(\angle\text{a}=60-45\)

\(\angle\text{a}=15\)

The measure of angle a is 15 degrees.

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Answer:

y=-4/3x

Step-by-step explanation:

Answer:

The angle subtended by an arc at the center is double the angle subtended by it at any  point on the remaining part of the circle.

Step-by-step explanation:

Let us consider the image attached.

Center of circle be O.

Arc AB subtends the angle \(\angle APB\) on the circle and \(\angle AOB\) on the center of the circle.

To prove:

\(\angle AOB = 2 \times \angle APB\)

Proof:

In \(\triangle PAO\): AO and PO are radius of the circles so AO = PO

And angles opposite to equal sides of a triangle are also equal in a triangle.

So, \(\angle PAO = \angle OPA\)

Using external angle property, that external angle is equal to sum of two opposite internal angles of a triangle.

\(\angle AOQ = \angle PAO + \angle OPA=2 \times \angle APO .... (1)\)

Similarly,

In \(\triangle PBO\): BO and PO are radius of the circles so BO = PO

And angles opposite to equal sides of a triangle are also equal in a triangle.

So, \(\angle PBO = \angle OPB\)

Using external angle property, that external angle is equal to sum of two opposite internal angles of a triangle.

\(\angle BOQ = \angle PBO + \angle OPB=2 \times \angle BPO .... (2)\)

Now, we can see that:

\(\angle AOB = \angle AOQ+\angle BOQ\)

Using equations (1) and (2):

\(\angle AOB = 2\angle APO+2\angle BPO\\\angle AOB = 2(\angle APO+\angle BPO)\\\bold{\angle AOB = 2(\angle APB)}\)

Hence, proved.

Hope you could understand.

If you have any query, feel free to ask.

Answer:

138 : 269

Step-by-step explanation:

Last year, the number of bicyclists that showed up was 1345.

This year, there were 690 bicyclists.

The ratio of the number of bicyclists that showed up for the past two years is the ratio of those that showed up this year to those that showed up last year:

690 : 1345

Let us put it in simplest terms:

138 : 269

Answer:

Rate of increase in water pressure is 992

Step-by-step explanation:

Answer:

The tangent of an angle is defined as the ratio of the length of the opposite side to the length of the adjacent side of a right triangle.

1. tan 90 degrees:

In a right triangle with a 90-degree angle, the opposite side of the       angle is the longest side and the adjacent side is 0. Therefore, tan 90 = opposite/adjacent = undefined.

2. tan 45 degrees:

In a right triangle with a 45-degree angle, the opposite side and adjacent side are equal in length. Therefore, tan 45 = opposite/adjacent = 1.

3. tan 60 degrees:

In a right triangle with a 60-degree angle, the opposite side is √3 times the length of the adjacent side (based on the 30-60-90 triangle rule). Therefore, tan 60 = opposite/adjacent = √3.

4. tan 30 degrees:

In a right triangle with a 30-degree angle, the opposite side is half the length of the hypotenuse and the adjacent side is √3 times smaller than the hypotenuse (based on the 30-60-90 triangle rule). Therefore, tan 30 = opposite/adjacent = 1/√3 = √3/3.

Hope it helped :D

Step-by-step explanation:

The equation of hyperboloid of one sheet: \(\frac{x^{2} }{A^{2} } +\frac{y^{2} }{B^{2} } -\frac{z^{2} }{C^{2} } =1\) which is used to calculate hyperboloid.

The most challenging quadric surface is probably the hyperboloid of a single sheet. For starters, it is puzzling since its equation is quite similar to that of a hyperboloid with two sheets. For information on how to tell them apart, see to the section on the two-sheeted hyperboloid. Its cross portions are also highly intricate equation.

Having said all of that, everyone who has watched The Simpsons, even for the first time, will recognize this form. One-sheet hyperboloids have a striking resemblance to Springfield Nuclear Power Plant cooling towers.

The cross sections of a straightforward one-sheeted hyperboloid with A = B = C = 1.

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The code will have a SyntaxError.

The line cat "Fluffy" = is a syntax error because the variable cat is not defined using the correct Python syntax.

In Python, you must define a variable before you can assign a value to it. The correct way to write this line of code would be:

cat = "Fluffy"

The line dog == "Ducky": print("x is 10") is also a syntax error because the variable dog is not defined. The correct way to write this line of code would be:

dog = "Ducky"

if cat == "Fluffy" and dog == "Ducky":

 print("x is 10")

Therefore, the error of the code is SyntaxError.

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Answer:

9

Step-by-step explanation:

15/100=0.15

0.15x40=6

15-6=9

Answer:   40 percent of 15 is 6. If that is how many he has eaten then subtract that from 15. So 15-6 is 9. That means Tyler has 9 pieces of gum left.

There are many questions and problems for which efficient algorithms exist, but there are also many others for which no efficient algorithm is currently known, and some for which it has been proven that no algorithm can exist.

The field of computer science and mathematics known as computational complexity theory studies which problems can be solved by algorithms and how efficient those algorithms are. The theory classifies problems into different complexity classes based on the resources required to solve them, such as time, space, or the number of processors.

There are certain classes of problems for which efficient algorithms are known to exist. For example, sorting a list of numbers or searching for an item in a database can be done in polynomial time, which means that the time required to solve the problem grows at most as a polynomial function of the size of the input.

On the other hand, there are problems for which no efficient algorithm is currently known. One famous example is the traveling salesman problem, which asks for the shortest possible route that visits a set of cities and returns to the starting point. While algorithms exist to solve this problem, they have an exponential running time, meaning that the time required to solve the problem grows exponentially with the size of the input, making them infeasible for large inputs.

There are also problems for which it has been proven that no algorithm can exist that solves them efficiently. For example, the halting problem asks whether a given program will eventually stop or run forever. It has been proven that there is no algorithm that can solve this problem for all possible programs.

In summary, there are many questions and problems for which efficient algorithms exist, but there are also many others for which no efficient algorithm is currently known, and some for which it has been proven that no algorithm can exist.

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Answer

12

Explanation

2xand 3x

let 3 be 3x

3x=18

X=18/3

X=6

now

2x=2multiply6

12

the number of boys is 12

The 8 consecutive numbers are 12, 13, 14, 15, 16, 17, 18, 19 respectively.

Algebraic expressions are simply described as arithmetic expressions that are made up of arithmetic terms, constants, variables, factors and coefficients.

These expressions are also made up of arithmetic operations which includes;

Based on the information given, we have;

x + x + 1 + x + 2 + x + 3 + x + 4 + x + 5 + x + 6 + x + 7 = 124

Now, collect like terms, we get;

8x + 28 = 124

8x = 124 - 28

Subtract like terms

8x = 96

To determine the value of x, make it the subject by dividing both sides by 8, we have;

8x/8 = 96/8

x = 12

Then,

x = 12

x + 1 = 13

x + 2 = 14

x + 3 = 15

x + 4 = 16

x + 5 = 17

x + 6 = 18

x + 7 = 19

Hence, the values are 12, 13, 14, 15, 16, 17, 18 and 19 respectively.

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Answer:

\(y=\frac{0}{-1} -4\)

Step-by-step explanation:

first, you have to find the slope, and to do that you use this equation \(\frac{y2-y1}{x2-x1}\)

     so, now to insert your points (0,-4), (-1,4)

                                                      (x1,y1)  (x2,y2)

\(\frac{4-4}{-1-0} = \frac{0}{-1}\)

now that you have the slope you can find the y-intercept of the slope-intercept form by looking at your first point (0,-4) and get -4

- if you were to look at this point on a graph it would be on the y-axis therefore, -4 is the y-intercept [if you don't have a point like this one then you can look at a graph with one of your points and make a slope until you are on the y-axis :)]

therefore, the slope-intercept form is y=\(\frac{0}{-1}\) -4

[ps, your slope is a zero slope :)]

Answer:

y = - 8x - 4

Step-by-step explanation:

y = mx + b

"m" is slope, "b" is y-intercept.

( \(x_{1}\) , \(y_{1}\) )

( \(x_{2}\) , \(y_{2}\) )

m = \(\frac{y_{2} -y_{1} }{x_{2} -x_{1} }\)

~~~~~~~~~~~~~~~

(0, - 4) are coordinates of y-intercept.

( - 1, 4)

m = \(\frac{4 + 4}{-1-0}\) = - 8

y = - 8x - 4

Answer:

Step-by-step explanation:

\(5\frac{1}{2}=\frac{11}{2}\\\mathrm{So\:this\:becomes}\\2x-\frac{1}{2}=\frac{11}{2}\\\mathrm{Then,}\\(2x+\frac{-1}{2})+\frac{1}{2}=(\frac{11}{2})+\frac{1}{2}\\2x+\frac{(-1+1)}{2}=(\frac{11}{2})+\frac{1}{2}\\2x+\frac{0}{2}=(\frac{11}{2})+\frac{1}{2}\\\mathrm{Reduce}\\2x+0=(\frac{11}{2})+\frac{1}{2}\\2x=(\frac{11}{2})+\frac{1}{2}\\2x=\frac{(11+1)}{2}\\\mathrm{11+1=12,\:so}\\2x=\frac{12}{2}\\\mathrm{Prime-factorization}\\2x=\frac{(6\times 2)}{(1\times 2)}\)

\(\mathrm{6\times2=12\:and\:1\times2=2\:so\:\frac{12}{2}\:equals\:6,}\\2x=6\\\mathrm{Now,\:divide\:by\:the\:leading\:term,\:2}\\\frac{(2x)}{2}=\frac{6}{2}\\\mathrm{Factorization}\\x=\frac{(3\times 2)}{(1\times 2)}\\\mathrm{3\times2=6\:and\:1\times2=2\:so\:\frac{6}{2}\:equals\:3,}\\x=3\)

Hope this helps.

The solution to the equation 2x - 1/2 = 5 1/2 is x = 3.

Given Equation: 2x - 1/2 = 5 1/2

Step 1: Let's simplify the mixed number 5 1/2 to an improper fraction. 5 1/2 can be written as (11/2).

2x - 1/2 = 11/2

Step 2: To eliminate the fraction, multiply the entire equation by 2 to clear the denominators:

2  (2x - 1/2) = 2 (11/2)

This simplifies to:

4x - 1 = 11

Step 3: Add 1 to both sides of the equation to isolate the variable:

4x - 1 + 1 = 11 + 1

4x = 12

Step 4: Divide both sides of the equation by 4 to solve for x:

(4x)/4 = 12/4

x = 3

Therefore, the solution is x = 3.

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The ratio of sin C in simplest form is 72/97

What is the trigonometric ratio?

Trigonometric ratios are the ratios of a right triangle's sides. The sine (sin), cosine (cos), and tangent (tan) are three often used trigonometric ratios. There are other trigonometric ratios which are reciprocals of these ratios.

Trigonometric ratios can be computed either using the provided acute angle or by calculating the ratios of the right-angled triangle's sides.

The sides of a right-angled triangle are known as the hypotenuse, perpendicular, and base.

Sin C = (Opposite side)/ (hypotenuse )

         =  AB/AC

         =  72/97

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Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles.

rigonometry has numerous practical applications in fields such as engineering, physics, navigation, and astronomy, and is essential in solving problems related to triangles and periodic phenomena.

Some common topics in trigonometry include trigonometric identities, inverse trigonometric functions, and the use of trigonometry in complex numbers and calculus.

sin2 θ (1 + cot2 θ)

Using the identity cot²θ + 1 = csc²θ, we can write:

sin²θ (1 + cot²θ) = sin²θ csc²θ

Next, using the identity csc²θ = 1/sin²θ, we get:

sin²θ csc²θ = sin²θ / sin²θ = 1

Therefore, sin²θ (1 + cot²θ) simplifies to 1.

tan θ/cos θ − sec θ

Using the identity sec θ = 1/cos θ, we can write:

tan θ/cos θ − sec θ = tan θ/cos θ − 1/cos θ

Next, we can combine the two fractions by finding a common denominator:

tan θ/cos θ − 1/cos θ = (tan θ - 1) / cos θ

Therefore, the expression simplifies to (tan θ - 1) / cos θ.

sin 14° cos 46° + cos 14° sin 46°

Using the identity sin(α + β) = sin α cos β + cos α sin β, we can write:

sin 14° cos 46° + cos 14° sin 46° = sin(14° + 46°)

Simplifying the sum inside the sine function, we get:

sin(14° + 46°) = sin 60°

Therefore, the expression simplifies to sin 60°, which is equal to √3/2.

sin(4π/5) cos(7π/5) - cos(4π/5) sin(7π/5)

Using the identity sin(α - β) = sin α cos β - cos α sin β, we can write:

sin(4π/5) cos(7π/5) - cos(4π/5) sin(7π/5) = sin(4π/5 - 7π/5)

Simplifying the difference inside the sine function, we get:

sin(4π/5 - 7π/5) = sin(-3π/5)

Using the identity sin(-θ) = -sin θ, we can write:

sin(-3π/5) = -sin(3π/5)

Using the fact that sin θ = sin(π - θ), we can write:

sin(3π/5) = sin(π - 2π/5) = sin(2π/5)

Using the fact that sin θ = sin(π - θ), we can write:

sin(2π/5) = sin(π - 3π/5) = sin(3π/5)

Therefore,

The expression simplifies to -sin(3π/5), which is equal to -√3/2.

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The required explanation for log of base 10 is described.

The ability of logarithms to solve exponential problems is a large part of their strength. Examples of this include sound (measured in decibels), earthquakes (measured on the Richter scale), starlight brightness, and chemistry (pH balance, a measure of acidity and alkalinity).

The distinction between log and ln is that log is expressed in terms of base 10, while ln is expressed in terms of base e. As an illustration, log of base 2 is denoted by log2 and log of base e by loge = ln (natural log).

The logarithm can be rewritten using the general rule. The common logarithm, which has a base of 10 always, is what you're dealing with when the log has no base.

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Answer:

130.92

Step-by-step explanation:

8.25(12)+3.99(8)

99+31.92

130.92

The correct formula that defines an arithmetic sequence is option d) tn = 5n + 14.

An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms remains constant. In other words, each term can be obtained by adding a fixed value (the common difference) to the previous term.

In option a) tn = 5 + 14, the term does not depend on the value of n and does not exhibit a constant difference between terms. Therefore, it does not represent an arithmetic sequence.

Option b) tn = 5n² + 14 represents a quadratic sequence, where the difference between consecutive terms increases with each term. It does not represent an arithmetic sequence.

Option c) tn = 5n(n+14) represents a sequence with a varying difference, as it depends on the value of n. It does not represent an arithmetic sequence.

Option d) tn = 5n + 14 represents an arithmetic sequence, where each term is obtained by adding a constant value of 5 to the previous term. The common difference between consecutive terms is 5, making it the correct formula for an arithmetic sequence.

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Answer:

the slope is 1/2

Step-by-step explanation:

Answer:

mean- 4.9

median- 4

interquartile range- 7

Step-by-step explanation:

Hope this helps! :)

Answer:

I think ur missing the actual data mate

Step-by-step explanation:

Answer:

Step-by-step explanation:

The probability that, out of a random sample of 10 internet users, 6 are concerned about the privacy of their e-mail can be calculated using the binomial probability formula.

The binomial probability formula allows us to calculate the probability of a specific number of successes (concerned internet users) in a given number of trials (random sample of 10 internet users), given the probability of success in a single trial (95% or 0.95 in this case).

Using the binomial probability formula, we can calculate the probability as follows:

\(P(X = 6) = C(n, x) * p^x * (1 - p)^(n - x)\)

P(X = 6) is the probability of exactly 6 internet users being concerned about privacy,

n is the total number of trials (10 in this case),

x is the number of successful trials (6 in this case),

p is the probability of success in a single trial (0.95 in this case), and

C(n, x) is the number of combinations of n items taken x at a time.

Plugging in the values, we have:

\(P(X = 6) = C(10, 6) * 0.95^6 * (1 - 0.95)^(10 - 6)\)

Calculating this expression will give us the probability that exactly 6 out of the 10 internet users in the random sample are concerned about the privacy of their e-mail.

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Answer:

There's no A so I'm going to assume you meant X

X = 23

Step-by-step explanation:

X is equal to 23, because 23 - 18 = 5

or 5 + 18 = 23

Answer:

2 months and 21 days

Answer:

the answer is (a) a//b

Step-by-step explanation:

perpendicular means that two lines that do not cross over each other.

The difference between the y coordinates  and the difference between the x coordinates then divide them

Gradient is a differential operator used in mathematics to transform a three-dimensional vector-valued function into a vector whose three elements are the partial derivatives of the function with respect to its three variables. The gradient sign is  ∇

As a result, f = ifx + jfy + kfz, where fx, fy, and fz are the first partial derivatives of f and I j, and k are the unit vectors of the vector space, is the gradient of a function, also known as grad f or f. f is the direction of the heat-flow vector in a temperature field, where f is a temperature field in physics that indicates the temperature at every point in a space.

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The minimum and maximum numbers of hours the train will travel at that speed are 1.17 and 1.5

The given parameters are

Speed = 90 miles per hour

Current speed = next 120 miles, plus or minutes 15 miles.

Let the time travelled be x

So, we have the following equation

Speed * Time = Distance

This gives

|90x - 120| =15

Remove absolute bracket

90x - 120 = ±15

Add 120 to both sides

90x = 120 ±15

This gives

90x = (120 - 15, 120 + 15)

Evaluate

90x = (105, 135)

Divide by 90

x = (1.17, 1.5)

Hence, the minimum and maximum numbers of hours the train will travel at that speed are 1.17 and 1.5

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Answer:

Y=5/1x+15

Step-by-step explanation:

I know this is old, but no one answered it so I thought I would

Angle 2 is supplementary to Angle 3 Because it's given that to a supplementary to 3 lines A and B are parallel by the transverse line.

Two Angle whose sum is 180° are called supplementary angles. If a straight line is intersected by a line, then there are two angles form on each of the sides of the considered straight line. Those two-two angles are two pairs of supplementary angles. That means, if supplementary angles are aligned adjacent to each other, their exterior sides will make a straight line.

If ∠ 8 is supplementary to ∠ 9, then line x and y must be parallel lines wheres line s is the transverse line.

∠ 7 = ∠ 4.

Now, ∠ 7 = ∠ 2 and ∠ 4 = ∠ 9.

So, ∠ 2 = ∠ 3 {supplementary angles}

Angle 2 is supplementary to Angle 3 Because it's given that to a supplementary to 3 lines A and B are parallel by the transverse line.

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