Solve 5x + 1 = 2x2 + 9x.

Which are steps in the process of completing the square used to solve the equation?

1 = 2(x2 + 2x)
1 = 2x2 + 4x
2 = 2(x2 + 2x + 1)
3 = 2(x + 1)2
2 = 2(x + 1)2

Answer:

yeah I know you are literally perfect for you to be home

By using the expression to approximate the radius of a circle, we want to compare the radius of the two pools. We will find that the radius of the full-sized pool is 2 times larger than the radius of the kiddie pool.

The expression for the radius of a circle is:

R = √(A/3)

Where A is the area of said circle.

The circular kiddie swimming pool has an area of 28ft^2, we just replace that in the above expression to get:

R =  √(28 ft^2/3) = 3 ft

The full-sized pool has an area of 113 ft^2, then its radius is:

R' = √(113 ft^2/3) = 6 ft

To see how much greater is the radius of the full-sized pool than the radius of the kiddie pool, we just take the quotient:

R'/R = 6ft/3ft = 2

Meaning that the radius of the full-sized pool is 2 times larger than the radius of the kiddie pool.

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Answer:

32

Step-by-step explanation:

Answer:

Yes, because all integers without an infinite set of digits (e.g. Pi or Infinity) are rational.

This is an example of interviewer bias where the gender of the interviewer may have impacted the replies of the unmarried males in the poll.

This is an example of interviewer bias, where the gender of the interviewer may have influenced the responses of the unmarried men in the survey. The results may not accurately reflect the true opinions of the participants as their answers could have been affected by their desire to impress or please the interviewer.

This situation is an example of response bias, specifically interviewer bias, which occurs when the respondent's answer is influenced by the gender or characteristics of the interviewer, rather than their true preferences or opinions.

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Given a sample of exam scores with a mean of 83.0 and a standard deviation of 16.2, we need to use Chebychev's rule to determine the lower bound on the percentage of observations that lie within two standard deviations to either side of the mean. We also need to find the value of k to be used in Chebychev's rule.

Chebychev's rule states that for any data set and any real number k greater than 1, at least 100(1 - 1/k^2)% of the observations lie within k standard deviations to either side of the mean. To find the value of k, we need to consider the worst-case scenario where the proportion of observations lying within two standard deviations to either side of the mean is minimized. In this case, we choose k to be the minimum value that satisfies the rule.

By rearranging Chebychev's rule equation, we have:

1 - 1/k^2 = 0.95

Solving for k, we find:

k^2 = 1/0.05

k^2 = 20

k ≈ 4.47

Now, we can use k in Chebychev's rule to find the lower bound on the percentage of observations that lie within two standard deviations to either side of the mean. Since k represents the worst-case scenario, the actual percentage of observations within this range will be higher. Using k = 4.47, the lower bound on the percentage of observations within two standard deviations of the mean is at least 100(1 - 1/4.47^2)% = 88.89%.

Therefore, we can conclude that at least 88.89% of the observations lie within two standard deviations to either side of the mean.

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The probability of both cards being red in one experiment is 180, both cards will be red in 300 simulations of the repeated experiment.

To find the probability of both cards being red in one experiment, we can use the following formula:
Probability = (Number of favorable outcomes) / (Total number of outcomes)
1. Find the probability of drawing a red card for the first draw:
Probability (Red1) = (Number of red cards) / (Total number of cards) = 3/5
2. Since we are replacing the card, the total number of cards remains the same for the second draw. Find the probability of drawing a red card for the second draw:
Probability (Red2) = (Number of red cards) / (Total number of cards) = 3/5
3. To find the probability of both events occurring, multiply the individual probabilities:
Probability (Both Red) = Probability (Red1) * Probability (Red2) = (3/5) * (3/5) = 9/25
4. To find the approximate number of times this event will occur in 300 simulations, multiply the probability by the number of simulations:
Number of occurrences = Probability (Both Red) * Number of simulations = (9/25) * 300
5. Calculate the result:
Number of occurrences ≈ (9 * 300) / 25 ≈ 108
Approximately 108 times, both cards will be red in 300 simulations of the repeated experiment.

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The event B and event C are neither independent nor mutually exclusive.

Hence the correct option is (D).

Given that the probability of occurrence of event B is = P(b) = 0.56

The probability of occurrence of event C is = P(c) = 0.23

The probability of occurrence of event B and C together is = P(b and c) = 0.12

Since P(b and c) is not equal to 0 so the events B and C are not mutually exclusive.

Now, P(b) * P(c) = 0.56 * 0.23 = 0.13 (rounding off to nearest hundredth) is not equal to P(b and c) = 0.12.

So the events B and C are not independent either.

Hence the correct option is (D).

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Answer:

x = 11

Step-by-step explanation:

(11x - 80) and (5x - 14) are congruent angles , then

11x - 80 = 5x - 14 ( subtract 5x from both sides )

6x - 80 = - 14 ( add 80 to both sides )

6x = 66 ( divide both sides by 6 )

x = 11

The correct answer to the given question about mapping quadrilateral ABCD onto quadrilateral HGEF is option D Translation 6 units left and 2 units down

To determine the transformation that maps quadrilateral ABCD onto quadrilateral HGFE, we need to compare the corresponding sides and angles of the two quadrilaterals.

Option 1: Rotation of 180° about the origin

A rotation of 180° about the origin would not map quadrilateral ABCD onto quadrilateral HGFE because the corresponding sides and angles are not congruent. For example, side AB of ABCD would not match side HG of HGFE after the rotation. Therefore, option 1 is incorrect.

Option 2: Reflection across the y-axis

A reflection across the y-axis would not map quadrilateral ABCD onto quadrilateral HGFE because the corresponding sides and angles are not congruent. For example, angle A of ABCD would not match angle H of HGFE after the reflection. Therefore, option 2 is incorrect.

Option 3: Reflection across the x-axis

A reflection across the x-axis would not map quadrilateral ABCD onto quadrilateral HGFE because the corresponding sides and angles are not congruent. For example, side BC of ABCD would not match side GF of HGFE after the reflection. Therefore, option 3 is incorrect.

Option 4: Translation 6 units left and 2 units down

A translation 6 units left and 2 units down would map quadrilateral ABCD onto quadrilateral HGFE because the corresponding sides and angles are congruent. Each point of ABCD would move left by 6 units and down by 2 units to reach its corresponding point in HGFE. Therefore, option 4 is the correct transformation that maps quadrilateral ABCD onto quadrilateral HGFE.

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Answer:

Perimeter = (4x + 12)

Step-by-step explanation:

As given in the question itself,

"Perimeter of a polygon is the sum of measures of all the sides of the polygon."

By this property expression to calculate the perimeter of the given polygon will be,

Perimeter = x + x + x + 2 + 2 + (x + 4) + 2 + 2

                = 3x + 4 + (x + 4) + 4

                = 4x + 12

Hence, Perimeter = (4x + 12)

The Laplace transform of the following functions are:

1. f(t) = 3sinht + 5cosht

To find the Laplace transform of f(t) = 3sinht + 5cosht,

use the following formula:

\($$\mathcal{L}\{f(t)\} = \frac{s}{s^{2} + a^{2}} $$\)

Where a is a constant. Let a = 1.

\($$ \begin{aligned} \mathcal{L}\{f(t)\} &= \mathcal{L}\{3sinht + 5cosht\} \\ &= 3\mathcal{L}\{sinht\} + 5\mathcal{L}\{cosht\} \\ &= 3\left(\frac{1}{s-1} \right) + 5\left(\frac{s}{s^{2} + 1^{2}} \right) \\ &= \frac{3}{s-1} + \frac{5s}{s^{2} + 1} \end{aligned} $$\)

Therefore, the Laplace transform of f(t) = 3sinht + 5cosht is

\($$\mathcal{L}\{f(t)\} = \frac{3}{s-1} + \frac{5s}{s^{2} + 1} $$\)

2. f(t) = 4e-6 + 3sin2t +9 = -6

To find the Laplace transform of f(t) = 4\(e^-6\)+ 3sin2t +9 = -6,

use the following formula:

\($$\mathcal{L}\{f(t)\} = \mathcal{L}\{4e^{-6} + 3sin2t -6 \} $$\)

Taking Laplace transform of each term, we get

\($$ \begin{aligned} \mathcal{L}\{4e^{-6} + 3sin2t -6 \} &= \mathcal{L}\{4e^{-6}\} + \mathcal{L}\{3sin2t\} - \mathcal{L}\{6\} \\ &= 4\mathcal{L}\{e^{-6}\} + 3\mathcal{L}\{sin2t\} - 6\mathcal{L}\{1\} \\ &= 4\left(\frac{1}{s+6}\right) + 3\left(\frac{2}{s^{2} + 2^{2}}\right) - 6\left(\frac{1}{s}\right) \\ &= \frac{4}{s+6} + \frac{6}{s^{2} + 4} - \frac{6}{s} \end{aligned} $$\)

Therefore, the Laplace transform of f(t) = 4\(e^-6\) + 3sin2t +9 = -6 is

\($$\mathcal{L}\{f(t)\} = \frac{4}{s+6} + \frac{6}{s^{2} + 4} - \frac{6}{s} $$\)

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The Laplace Transform of a function f(t) is defined as F(s) = L{f(t)}.

Find the Laplace transform of the following functions below.

3. f(t) = 3sinht + 5cosht

Using the following Laplace transforms:

L{sinh(at)} = a / \((s^2-a^2)\),

L{cosh(at)} = s / \((s^2-a^2)\), and

L{a cosh(at)} = s / \((s^2-a^2)\)

where a is a constant,

we can find the Laplace transform of the given function f(t) = 3sinht + 5cosht.

L{3sinht + 5cosht} = 3 L{sinh(t)} + 5 L{cosh(t)}

Substituting the Laplace transforms:

\(3 * [a / (s^2-a^2)] + 5 * [s / (s^2-a^2)] = [3a + 5s] / (s^2-a^2)\)

Therefore, the Laplace transform of the function f(t) = 3sinht + 5cosht is F(s) = [3a + 5s] /\((s^2-a^2)\).4.

f(t) = \(4e^{(-6t)\)+ 3sin(2t) + 9

Using the Laplace transform of the unit step function, \(L{e^{-at} u(t)} = 1 / (s+a)\), and

the Laplace transform of sin(at), L{sin(at)} = a / \((s^2 + a^2)\),

we can find the Laplace transform of the given function f(t) =\(4e^{(-6t)\) + 3sin(2t) + 9.

L{\(4e^{(-6t)\) + 3sin(2t) + 9}

= 4L{\(e^{(-6t)\) u(t)} + 3L{sin(2t)} + 9L{1}

Substituting the Laplace transforms:

4 * [1 / (s+6)] + 3 * [2 / (\(s^2\) + 4)] + 9 * [1 / s] = [36\(s^2\) + 78s + 76] / [(s+6)(\(s^2\) + 4)]

Therefore, the Laplace transform of the function f(t) = \(4e^{(-6t)\) + 3sin(2t) + 9 is F(s) = [36\(s^2\) + 78s + 76] / [(s+6)(\(s^2\) + 4)].

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Answer:

a. Indep. = x, and dependent equals f(x)

b. x impacts f(x)

f(-4)= -11

Step-by-step explanation:

hope this helped

The statement "the first step in the sampling design process is to determine the sample size" is false because according to the text, the first step in the sampling design process is to clearly define the target population.

The first step in the sampling design process is typically to define the target population and the research objectives.

This involves specifying the characteristics of the population under study and identifying the specific research questions or objectives that the sampling will address.

Once the target population and research objectives are established, the next steps in the sampling design process typically involve determining the appropriate sampling method (such as random sampling, stratified sampling, or cluster sampling) and selecting the sampling frame (the list or source from which the sample will be drawn).

After these initial steps, researchers can then consider factors such as the desired level of precision, confidence level, and variability in the population to determine the appropriate sample size.

The determination of the sample size usually comes after clarifying the research objectives and selecting the appropriate sampling method.

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Answer:

what ???

Step-by-step explanation:

Answer:

- 2 / 7

Step-by-step explanation:

Let,

x1 = 7

x2 = 14

y1 = 2

y2 = 0

Formula : -

Slope = ( y2 - y1 ) / ( x2 - x1 )

Slope

= ( 0 - 2 ) / ( 14 - 7 )

= - 2 / 7

\(slope \\ = \frac{Δy}{Δx} \\ = \frac{(4 - 2)}{(0 - 7)} \\ = \frac{2}{ - 7} \\ \\ so \: the \: slope \: is \: \frac{2}{ - 7}.\)

This is the answer.

Hope it helps!!

An equation of the line perpendicular to y = -2x is y = (1/2)x.

To find the equation of a line perpendicular to y = -2x, we need to determine the slope of the given line and then find the negative reciprocal to obtain the slope of the perpendicular line.

The equation y = -2x is in slope-intercept form (y = mx + b), where the slope (m) is -2. The negative reciprocal of -2 is 1/2. The negative reciprocal of a slope is found by flipping the fraction and changing the sign.

Now that we have the slope of the perpendicular line, we can use a point-slope form to write the equation. The point-slope form is y - y₁ = m(x - x₁), where (x₁, y₁) is a point on the line and m is the slope.

Since no specific point is provided in the question, we can choose any point. Let's choose the point (0, 0), which lies on both lines.

Using the point-slope form with the slope (m) of 1/2 and the point (0, 0), we get:

y - 0 = (1/2)(x - 0)

y = (1/2)x

Therefore, the equation of the line perpendicular to y = -2x is y = (1/2)x. This line will have a slope of 1/2 and will be perpendicular to the given line.

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The symbols p,x, and s represent sample statistics.

- p (pronounced "p-hat") is the sample proportion. It is used to estimate the population proportion. It is computed as the number of successes in the sample divided by the sample size.

-x (pronounced "x-bar") is the sample mean. It is used to estimate the population mean. It is computed as the sum of all the values in the sample divided by the sample size.

- s is the sample standard deviation. It is used to estimate the population standard deviation. It measures how spread out the data is in the sample. It is computed as the square root of the sum of the squared deviations from the sample mean divided by the sample size minus one.

These sample statistics are used to make inferences about the corresponding population parameters, which are denoted by Greek letters such as μ (mu) for the population mean and σ (sigma) for the population standard deviation.

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The value that would complete the table to make the relationship between the two quantity proportional is 4.

When two quantities are proportional, their relationship is constant for all values and as one quantity rises, the other rises as well.

A proportional relationship exists between two quantities if they can be written in the general form y = kx, where k is the proportionality constant. In other words, the ratio between these amounts never changes. In other words, no matter which pair of the two numbers you divide, you always obtain the same number k.

The value that would complete the table to make the relationship between the two quantity proportional is 4.

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Hence, the right triangle pyramid has a 15 m³ volume.

The youngster or adolescent should maintain a straight gaze that is parallel to the ground. Measure the kid or adolescent when they are standing with their head, shoulders, hips, and heels on a flat surface (wall).

The following formula can be used to figure out the size of a right triangle pyramid:

V = base area divided by height

Let's start by locating the pyramid's base. The pyramid's base is a right angle with a base height of 3 m and an altitude of 6 m. The formula for a triangle's area is:

A = (1/2) × base × height

Hence, the pyramid's base area is as follows:

B = (1/2) × 3 m × 6 m = 9 m²

We can now enter the data into the algorithm to determine the pyramid's volume:

V = (1/3) × 9 m² × 5 m = 15 m³

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Answer:

a 2:10    1:5

8 4:6    2:3

b3:18    1:6

h 9:15    3:5

C5:25    1:5

i 10:35    2:7

d 30:5    6:1

1 75:10    15:2

e 36:12    3:1

k 72:20    18:5

f 180:20    9:1

1 140:112   5:4

Step-by-step explanation:

Divide each side of the colon by the same number until you cannot divide any more.

The total cost before the sales tax was 19.828 pounds.

For a party, Jordan purchased 3.8 pounds of turkey, 2.2 pounds of cheese, and 3.6 pounds of egg salad.

We have to determine the total cost before sales tax.

As per the question, we have prices as:

cost of turkey = 3.95 per pound

cost of egg cheese = 1.3 per pound

cost of egg salad = 0.89 per pound

The total cost of turkey = 3.8 × 3.95  = 15.01 pounds

The total cost of cheese = 2.2 × 1.3 = 2.86 pounds

The total cost of egg salad = 2.2 × 0.89 = 1.958 pounds

The total cost before sales tax = 15.01 + 1.958 +2.86

Apply the addition operation, and we get

The total cost before sales tax = 19.828 pounds

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The question seems to be incomplete the correct question would be:

Jordan bought 3.8 pounds of turkey, 2.2 pounds of cheese, and 3.6 pounds of egg salad for a party. If prices are 3.95 per pound turkey, 1.3 per pound cheese and 0.89 per pound egg salad What was the total cost before sales tax?

Central tο Malthus' theοrem is the nοtiοn that pοpulatiοn grοws geοmetrically and the fοοd supply οnly increases arithmetically.

Central to Malthus' theorem is the notion that population growth tends to outpace the availability of resources, leading to potential scarcity and societal challenges. Malthus argued that human population has the tendency to increase exponentially, while the production of food and resources grows at a slower rate. This imbalance can result in population pressure, poverty, and other negative consequences.

Malthus' theorem, often referred to as the Malthusian theory, suggests that unless checked by factors such as disease, famine, war, or voluntary restraint, population growth will eventually exceed the capacity of the environment to sustain it. This theory has been influential in the field of demography and has sparked debates about population control, resource management, and sustainable development.

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Answer:

1/4

Step-by-step explanation:

1x4=4

2x4=8

3x4=12

4x4=16

Answer:

The astronomer knows that ACB is a right angle CAB and the angle  could be measured. This is enough information to compute AB   using similar triangles or trigonometry.

Step-by-step explanation:

Answer:

12.5% profit

Step-by-step explanation:

Answer:

g

Step-by-step explanation:

i don't know if this right just trying to help

The line cannot be formed by the intersection with plane and a cylinder.

What is intersection of cylinder and a plane?

A cylindric section is the intersection of a plane with a right circular cylinder.

Why line cannot be formed by the intersection with plane and a cylinder?

The intersection will be parallel lines if the plane is parallel to the cylinder's axis, it is impossible.

Because there are no intersecting lines on a cylinder, the intersection of a plane and a cylinder cannot create intersecting lines.

Hence, the option \(G\) is correct answer.

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     I am not sure what you are asking by the options provided as the formatting has been messed up, but if you simplify the given equation you end up with:

x > 2

Step-by-step explanation:

Given

58 - 10x< 20 + 9x

Add 10x to both sides of the equatoin

58 < 20 + 19x

Subtract 20 from both sides of the equatoin

38 < 19x

2 < x

x > 2