what is the solution to the quadratic equation below? x^2-8x+16=11

To find the vertical asymptotes of a rational function, we need to set the denominator equal to zero and solve for x.

To find the vertical asymptotes of a rational function, you need to determine the values of x that make the denominator of the function equal to zero.

Let's check the limit of our example function as x approaches each of the vertical asymptotes:

As x approaches 1 from the left side: f(x) approaches negative infinity

As x approaches 1 from the right side: f(x) approaches positive infinity

Therefore, x = 1 is a valid vertical asymptote.

As x approaches 3 from the left side: f(x) approaches positive infinity

As x approaches 3 from the right side: f(x) approaches negative infinity

Therefore, x = 3 is also a valid vertical asymptote.

The values of x that make the denominator zero are the vertical asymptotes of the function.

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Answer:

Domain:  \(-3\leq x\leq 1\)

Range:  \(-4\leq y\leq 0\)

Step-by-step explanation:

If you find the coordinate of the graph you can get the domain and range

(-3,0), (-2,-4), (-1,-2), (0,0), (1, -4)

Now that we have that find the domain and range

Domain -  x coordinate

Range - y coordinate

Domain: (-3, -2, -1, 0, 1)

Range: (-4, -2, 0)

Since the domain ranges from -3 to 1 you can use the inequality \(-3\leq x\leq 1\) to represent the domain and \(-4\leq y\leq 0\) for the range

Answer: x = 3

Step-by-step explanation: 3 + 3 = 6 ; 30 divided by 6 = 5.

Answer:

x = 3

Step-by-step explanation:

\(\frac{30}{3+x}\) = 5 ( models the statement )

multiply both sides by 3 + x

30 = 5(3 + x)

30 = 15 + 5x ( subtract 15 from both sides )

15 = 5x ( divide both sides by 5 )

3 = x

Given the coordinates:

A(3, -5)

B(10, -8)

C(12, -13)

D(5, -10)

Then, applying the given rule, we have:

A'(3 - 13, -5 + 21) = ( -10, 16)

B'(10 - 13, -8 + 21) = ( -3, 13)

C'(12 - 13, -13 + 21) = ( -1, 8)

D'(5 - 13, -10 + 21) = ( -8, 11)

Answer:

b = 20, c = 160

Step-by-step explanation:

b and 20 degrees are vertical angles, so they are equal.

b (20 degrees) and c are on a line together, so they add up to 180. 180 - 20 = 160 degrees

Efficient convolution of a signal x(n) with a causal filter h(n) can be done using the overlap-add method, where the signal is split into blocks, each block is zero-padded, convolved with the filter, and then added together.

The given scenario describes a technique for efficiently convolving a signal with a causal filter by using the circular convolution property of the discrete Fourier transform. The technique involves breaking up the signal and filter into smaller chunks, performing the circular convolution of these chunks using the Fourier transform, and then reassembling the resulting chunks to obtain the final convolution output.

This approach reduces the computational complexity of the convolution operation and is commonly used in digital signal processing applications.

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Efficient convolution of a signal x(n) with a causal filter h(n) can be done using the overlap-add method, where the signal is split into blocks, each block is zero-padded, convolved with the filter, and then added together.

The given scenario describes a technique for efficiently convolving a signal with a causal filter by using the circular convolution property of the discrete Fourier transform. The technique involves breaking up the signal and filter into smaller chunks, performing the circular convolution of these chunks using the Fourier transform, and then reassembling the resulting chunks to obtain the final convolution output.

This approach reduces the computational complexity of the convolution operation and is commonly used in digital signal processing applications.

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The entering basic value is α and the leaving basic variable is x2.

Given that the formula for the line passing through the points (2, 4, 3) and (4, 2, 4) can be written as (2,4,3)+α[(4,2,4)−(2,4,3)] = (2,4,3)+α(2,−2,1), where 0 ≤ α ≤ 1 for just the line segment between these points. After augmenting with the slack variables x4, x5, x6, x7 for the respective functional constraints, this formula becomes (2,4,3,2,0,0,0) + α(2,−2,1,−2,2,0,0).We have to use this formula directly to answer each of the following questions and relate the algebra and geometry of the simplex method as it goes through one iteration in moving from (2,4,3) to (4,2,4). The questions are:(a) What is the entering basic variable?The entering basic variable is the variable that increases in the formula which in this case is α.(b) What is the leaving basic variable?The leaving basic variable is the variable that makes one of the original basic variables zero and takes its place as a basic variable in the new basic feasible solution. Here, the leaving basic variable is x2.(c) What is the new BF solution?The new basic feasible solution is found by replacing the entering basic variable α for the leaving basic variable x2 and then using Gaussian elimination to solve the linear system. Here is how it is done:At α = 0, we have the point (2,4,3,2,0,0,0).At α = 1, we have the point (4,2,4,0,2,0,0).Let α be the entering basic variable, then we can take x2 to leave the basis. Thus, at α = 0, we have (2,4,3,2,0,0,0) as the BFS and at α = 1, we have (4,2,4,0,2,0,0) as the next BFS.Then we need to use Gaussian elimination to solve the linear system. After Gaussian elimination, we get the new basic feasible solution as (10/3,4/3,0,0,2/3,0,0).Hence, the new BF solution is (10/3,4/3,0,0,2/3,0,0).Thus, the entering basic variable is α, the leaving basic variable is x2, and the new BF solution is (10/3,4/3,0,0,2/3,0,0).

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Answer:

C

Step-by-step explanation:

C because it has sides unequal in length.

Answer: C

Step-by-step explanation:

Isosceles: 2 sides equal

Acute: angles are less than 90 degrees

Scalene: All side lengths are different

Equilateral: All sides are equal

Answer: d. Mean, median and mode are all equal.

Step-by-step explanation:

An inequality that can be written in the form ax + by < c (where a and b are not both zero) is called a linear inequality in two variables.

An inequality that represents a line in a two-dimensional coordinate system is referred to as a linear inequality. The set of points that satisfies the inequality is a half-plane bounded by a line that may be dashed or solid.

In contrast to a linear equation, which represents a line, a linear inequality represents a half-plane. The points on one side of the line, rather than the points on the line, are solutions to the inequality.

The method of shading is used to graph a linear inequality in two variables. First, graph the boundary line, which is usually represented by a solid or dashed line, and then select a test point on one side of the line. Shaded regions of the half-plane containing the test point satisfy the inequality.

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Answer:

It might be 231.

Step-by-step explanation:

Answer:

33

Step-by-step explanation:

3 + jk + k3

substitute j for 2

3 + 2k + k3

substitute k for 6

3 + (2*6) + (6*3)

3 + 12 + 18

33

Answer:

c. the slope of the line

Step-by-step explanation:

because i just know

The direct variation has the same value or expression as that of the slope of a straight line given by - m = y/x.

The general equation of a straight line is -

y = mx + c

where m is slope of line

c is the y - intercept

Given is the direct variation of a quantity.

The direct variation of a quantity in the equation of a straight line is represented by the slope of a straight line. Mathematically, we can write -

y = mx + c

for y - intercept = [c] = 0, we can write -

y = mx

m = y/x

which is the representation of direct variation.

Therefore, the direct variation has the same value or expression as that of the slope of a straight line given by - m = y/x.

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The piece of data that is discrete and which is continuous is given below: a) The number of boys and girls on the team is continuous, and the length of Charlotte's long jump is discrete.

b) The number of hurdles Charlotte can jump is discrete, and the length of her long jump is continuous.

c) The number of hurdles Charlotte can jump is continuous, and the number of boys and girls in the team is discrete.

d) The ranking of the team members is discrete, and the number of boys and girls on the team is continuous.

The correct is option b) The number of hurdles Charlotte can jump is discrete, and the length of her long jump is continuous

The data that can be counted or expressed in integers is known as discrete data. Charlotte's hurdle-jumping ability is the result of a discrete variable since she can only jump a specific number of hurdles. Her hurdle-jumping ability can only take on particular values such as 0, 1, 2, 3, 4, and so on.

The data that can take on any value within a particular range is known as continuous data.

The length of Charlotte's long jump is continuous data because it can take on any value between the minimum (0 feet) and maximum (infinity feet) possible length of the jump. The length of her jump can be 5.0 feet, 5.2 feet, 5.2256897 feet, or any other value within that range.

Therefore, it is concluded that the number of hurdles Charlotte can jump is discrete, and the length of her long jump is continuous.

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The operation that Amjed should perform to determine the relative frequency of a person over 30 years old who prefers to ride a mountain bike is given as follows:

2) Divide 25 by 462.

The parameters that are needed to calculate a probability are listed as follows:

Then the probability is calculated as the division of the number of desired outcomes by the number of total outcomes, hence it is the same as a relative frequency.

The total number of people is given as follows:

58 + 164 + 215 + 25 = 462.

Out of these people, 25 prefer mountain bike, hence the relative frequency is given as follows:

25/462.

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Answer:

donknow

Step-by-step explanation:

Approximately 109 grams of protein would be consumed on a 2500 kcal daily diet, with 35% of the calories coming from proteins.

Protein intake is an important aspect of a healthy diet, as it plays a vital role in various bodily functions. To calculate the grams of protein consumed, we start by determining the total calorie intake and then find the proportion of calories that come from proteins. In this case, the daily diet consists of 2500 kcal. To find the protein calories, we multiply this by the percentage of calories from proteins, which is 35%. This gives us 0.35 * 2500 = 875 kcal from proteins.

Next, we need to convert these calories into grams of protein. Each gram of protein provides approximately 4 calories. Therefore, we divide the protein calories (875 kcal) by 4 to get the grams of protein consumed, which is 875 / 4 ≈ 218.75 grams. Rounding this to the nearest gram, the individual would consume approximately 219 grams of protein on a 2500 kcal daily diet with 35% of the calories coming from proteins.

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The equation of the exponential function in the form h(x) = a - b^x that passes through the points (-2, 7/16) and (3, 14) is h(x) = 14 - 7/16^x.

To find the equation of an exponential function that passes through a given set of points, you can use the point-slope form of a linear equation. The point-slope form is given by y - y1 = m(x - x1), where (x1, y1) is a point on the line, m is the slope of the line, and (x, y) are the coordinates of any other point on the line.

In the case of an exponential function, the slope is equal to the difference between the y-values of the two points divided by the difference between the x-values of the two points, and the point-slope form becomes y - y1 = (y2 - y1)/(x2 - x1)(x - x1). To find the equation of the exponential function, you can substitute the coordinates of the two given points into this equation and solve for the variables a and b. In this case, the equation of the exponential function is h(x) = 14 - 7/16^x.

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To shoot a 20-cm-long arrow parallel to the axle and through the wheel without hitting any spokes, the arrow should be aimed at a point on the circumference of the wheel that is 4 cm away from any spoke.

The diameter of the wheel is 60 cm (2 x radius), so the circumference is 188.5 cm (π x diameter). Since the arrow is 20 cm long, it must pass through the wheel at a point that is at least 20 cm away from any spoke. To find this point, divide the circumference of the wheel by the number of spokes (which is not given in the problem).

Since the spokes are equally spaced, this will give the minimum distance between any two spokes. For example, if there are 6 spokes, the distance between each spoke is 31.4 cm (188.5 / 6). Therefore, the arrow should be aimed at a point on the circumference of the wheel that is 4 cm (20 / 5) away from any spoke.

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Answer: you answer is A hope that helped

Step-by-step explanation:

Hey there! :)

Answer:

V = 3408 units³

Step-by-step explanation:

Given:

r = 12

h = 71

Volume of a cone: V = 1/3 (bh) where b = πr²

Calculate the area of the base:

A = 12²π

A = 144π units²

Plug this into the formula for the volume of a cone:

V = 1/3 (144π · 71)

V = 1/3 (10224)

V = 3408 units³

Answer:

B . 3408 π  units^3

Step-by-step explanation:

\(h = 71\\r = 12\\V =?\\V = \frac{1}{3} \pi r^2 h\\V = \frac{1}{3} \pi \times 12^2 \times 71\\V = \frac{1}{3} \pi \times 144 \times 71\\V = 3408 \pi -units^3\)

Answer:

14

Step-by-step explanation:

|-14|=14

The given expression \(m^6p^{-3}v^{10} .\ m^2p^5v^2\) for all values of m, p, and v is equivalent to \(m^{8}p^{2}v^{12}\). Therefore, option D is the right choice for this question.

Monomials are algebraic expressions with single terms. They can be said to be specialized cases of polynomials.

We are given the algebraic expression - \(m^6p^{-3}v^{10}\) . \(m^2p^5v^2\)

To simplify it we will use the rules of the indices as follows -

\(a^{m}.\ a^{n} = a^{m+n}\)

Now,

\(m^6p^{-3}v^{10}\) . \(m^2p^5v^2\)

Segregating the like variables, we get,

= \((m^6.\ m^2) .\ (p^{-3}.\ p^{5}) .\ (v^{10}.\ v^{2})\)

by using the rules of indices, we will get,

= \((m^{6+2}) .\ (p^{-3+5}) .\ (v^{10+2})\)

= \((m^{8}) .\ (p^{2}) .\ (v^{12})\)

= \(m^{8}p^{2}v^{12}\)

Hence, the given expression \(m^6p^{-3}v^{10} .\ m^2p^5v^2\) is equivalent to \(m^{8}p^{2}v^{12}\).

Therefore, option D is the right choice for this question.

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Answer:

Natalie will have \(1\frac{43}{56}\) jars of coins all together after receiving John's coins.

Step-by-step explanation:

Given that:

Coins Natalie have = \(1\frac{1}{8}\) jars of coins

Coins John have = \(\frac{9}{14}\) jars of coins

When John will give all his coins to Natalie.

Total coins Natalie have = Her coins + John's coins

Total coins Natalie have = \(1\frac{1}{8}+\frac{9}{14}\)

Total coins = \(\frac{9}{8}+\frac{9}{14}\)

Total coins =\(\frac{63+36}{56}=\frac{99}{56}\)

Total coins = \(1\frac{43}{56}\)

Hence,

Natalie will have \(1\frac{43}{56}\) jars of coins all together after receiving John's coins.

Answer:

no.

Step-by-step explanation:

nigerians are cool

Answer:

D

Step-by-step explanation:

in this case, because it is being dilated by a factor of 2 this means that figure A´B´C´ will be double the size of its pre-image ABC.

each side will now be its double which means:

side A´C´= 10

side B´C´= 6

and side A´B´= 8

since the figure is only increasing its sides the angles of the right triangle remain the same.

<A= 37 degrees

The length of A'B' is, 8 units and the measure of angle A' is, 37 degree.

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

ΔABC is dilated by a factor of 2 to produce ΔA'B'C'.

Now, When the triangle undergoes dilation, the length of its sides gets multiplied by 2 (dilation factor) but the angles remain the same ( since, the shape has to remain same).

Thus, The length of A'B' is,

= 4 x 2

= 8

And, the measure of angle A' is, 37 degree.

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Answer:

Six apples.

Step-by-step explanation:

18 apples divided by 3 minutes equals 6 apples.

Answer:

Step-by-step explanation:

The inequality that represents all the solutions of 10(3x + 2) > 7(2x − 4) is 10(3x + 2) > 7(2x − 4). To solve this inequality, first we must combine like terms on each side of the inequality. On the left side, 10(3x + 2) becomes 30x + 20. On the right side, 7(2x − 4) becomes 14x − 28. After combining the like terms, the inequality becomes 30x + 20 > 14x − 28. Next, we must subtract 14x from both sides of the inequality. On the left side, 30x + 20 becomes 16x + 20. On the right side, 14x − 28 becomes −28. After subtracting 14x from both sides, the inequality becomes 16x + 20 > −28. Finally, we must subtract 20 from both sides of the inequality. On the left side, 16x + 20 becomes 16x. On the right side, −28 becomes −48. After subtracting 20 from both sides, the inequality becomes 16x > −48. To solve the inequality, we must divide both sides of the inequality by 16. On the left side, 16x becomes x. On the right side, −48 becomes −3. Therefore, the solution to the inequality is x > −3.