The dimensions of the computer screen are modeled by the equation x2 + (x – 4)2 = 202. What is the value of x, the length of the screen?

The equation is:

If x grows then y is going to reduce, and if y gets smaller, then t grows. this means that is an inverse variation

To prove AEB ≅ DEC by ASA (Angle-Side-Angle), the properties that can be used are:

So, the properties to use for proving AEB ≅ DEC by ASA are "Opposite angles are congruent" and "All sides are congruent."

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Answer:

To prove AEB ≅ DEC by ASA (Angle-Side-Angle), the properties that can be used are:

1. Opposite angles are congruent: This property is necessary to establish that ∠AEB ≅ ∠DEC, as both angles are opposite each other in the square ABCD.

2. All sides are congruent: This property is necessary to establish that AE ≅ DE, as both sides are corresponding sides of the square ABCD.

So, the properties to use for proving AEB ≅ DEC by ASA are "Opposite angles are congruent" and "All sides are congruent."

Step-by-step explanation:

Answer: 2.704 2.74 4.2 4.27 4.72

Step-by-step explanation:

To convert the angle -7/6 to degree measure, we can multiply it by 180/π since there are π radians in 180 degrees.

Degree measure = (-7/6) * (180/π) ≈ -210 degrees

The reference angle is the acute angle formed between the terminal side of the angle and the x-axis. To find the reference angle, we take the absolute value of the angle.

Reference angle in degrees = | -210 | = 210 degrees

To convert the reference angle to radians, we can multiply it by π/180 since there are 180 degrees in π radians.

Reference angle in radians = 210 * (π/180) = 7π/6 radians

Therefore, the angle -7/6 is approximately -210 degrees, and its reference angle is 210 degrees or 7π/6 radians.

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We want to find "3/6" of 30.

First of all, let's reduce the fraction (3/6th).

Dividing top and bottom by 3, we have:

3/6

3/3 divided by 6/3

1 divided by 2

This is half.

So, we need half of 30. Which basically means:

Thus,

3/6 of 30

is

Answer:

The solution to the system of equations is (-1/2, 3).

Step-by-step explanation:

To solve this system of equations using substitution method, we first need to solve one of the equations for one of the variables in terms of the other variable. Let's solve the first equation for y:

-2x + y = 4

y = 2x + 4

Now we can substitute 2x + 4 for y in the second equation:

-2x + 2y = 7

-2x + 2(2x + 4) = 7

Simplifying the equation:

-2x + 4x + 8 = 7

2x = -1

x = -1/2

Now we can use this value of x to find the value of y:

y = 2x + 4

y = 2(-1/2) + 4

y = 3

Answer:

In math, order of operations helps you find the correct value for an expression. Order of operations matters in daily life.

Step-by-step explanation:

For example

Engineering

Cooking

Chemistry

Are some explanations of where you may need this skill in real life.

The Euler equation represents the relationship between current-period consumption and future-period consumption in the optimum. It is derived from intertemporal optimization in economics.

In the context of consumption, the Euler equation can be expressed as:

u'(Ct) = β * u'(Ct+1)

where:

- u'(Ct) represents the marginal utility of consumption in the current period,

- Ct represents current-period consumption,

- β is the discount factor representing the individual's time preference,

- u'(Ct+1) represents the marginal utility of consumption in the future period.

This equation states that the marginal utility of consumption in the current period is equal to the discounted marginal utility of consumption in the future period. It implies that individuals make consumption decisions by considering the trade-off between present and future utility.

Note: The Euler equation assumes a constant discount factor and a utility function that is differentiable and strictly concave.

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The coordinate vector of g(t) relative to the basis F is (-2, 1, -2).

We can do this by equating the coefficients of q(t) and the linear combination of p₁(t), p₂(t), and p₃(t) and solving for c₁, c₂, and c₃. Specifically, we want to solve the system of equations:

c₁ + 2c₂ + 2c₃ = -8

c₁ + 0c₂ + 0c₃ = 0

2c₁ - 3c₂ + 2c₃ = -10

The first equation comes from equating the coefficients of t⁰ in q(t) and the linear combination, the second equation from equating the coefficients of t¹, and the third equation from equating the coefficients of t².

Solving this system of equations, we get c₁ = -2, c₂ = 1, and c₃ = -2. Therefore, we can write q(t) as -2p₁(t) + p₂(t) - 2p₃(t). This means that the coordinate vector of q(t) with respect to the basis F is (-2, 1, -2), which is the vector of scalars that we used to form the linear combination of p₁(t), p₂(t), and p₃(t) that equals q(t).

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Answer:35

Step-by-step explanation:

The volume of a cylinder is calculated by multiplying the area of its base by its height. The formula for the volume of a cylinder is V = πr²h, where r is the radius of the base and h is the height.

The volume of a cone is calculated by multiplying the area of its base by its height and then dividing by 3. The formula for the volume of a cone is V = (1/3)πr²h, where r is the radius of the base and h is the height.

Since Sonequa’s two containers have equal radii and equal heights, it can be concluded that the volume of the cylinder is three times the volume of the cone. This means that if Sonequa fills the cone with water and pours it into the cylinder, she will need to repeat this process three times to fill the cylinder completely.

So, the claim that is most likely to be supported using the result of Sonequa’s investigation is: “The volume of a cylinder with the same radius and height as a cone is three times greater than the volume of the cone.”

Answer:

36°

A+B+C+D+E=5C=(5-2)×180°=540°

C=540÷5=108°

since BC=CD

x = CDB = ½(180°-C)=½(180°-108°)=½72°=36°

The equation of the line perpendicular to the tangent to the curve y=x^3-4x+1 at the point (2,1) is y = (-1/8)x + 9/8.

To find the equation of the line perpendicular to the tangent to the curve at (2,1), we need to first find the slope of the tangent line at that point.

The derivative of y=x^3-4x+1 is y'=3x^2-4, so the slope of the tangent line at (2,1) is y'(2) = 3(2)^2-4 = 8.

Since we want the line perpendicular to the tangent, we know that its slope will be the negative reciprocal of the tangent's slope. Therefore, the slope of the line we're looking for is -1/8.

Next, we use the point-slope form of the equation of a line to write the equation of the line with the slope we found and passing through the point (2,1):

y - 1 = (-1/8)(x - 2)

Simplifying and putting the equation in slope-intercept form:

y = (-1/8)x + 9/8

Therefore, the equation of the line perpendicular to the tangent to the curve y=x^3-4x+1 at the point (2,1) is y = (-1/8)x + 9/8.

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Answer:

he descends only 57 feet ,as the mine is 10 feet below the surface befor descending

Answer:

Given:

3 times x plus 4 is greater than or equal to 4 times the sum of x and 1.

To find:

The inequality for the given statement and solution of the inequality.

Solution:

4 times the sum means a distributive property problem.

Now,

3 times x : 3x

3 times x plus 4 : 3x+4

Greater than or equal to : ≥

4 times the sum of x and 1 : 4(x+1)

So, the inequality is

\(3x+4\geq 4(x+1)\)

Using distributive property, we get

\(3x+4\geq 4x+4\)

Isolate variable terms.

\(4-4\geq 4x+3x\)

\(0\geq x\)

It can be written as

\(x\leq 0\)

Therefore, the required inequality is \(3x+4\geq 4(x+1)\) and the solution is \(x\leq 0\).

Answer:

12

Step-by-step explanation:

\( {2}^{2} + 2(2) + 4 = 12\)

(a) The volume V of the box as a function of x is V = 4x^3-60x^2+200x

(b) The domain of V in interval notation is 0<x<5,

(c) The length L , width W, and height H of the resulting box that maximizes the volume is H = 2.113, W = 5.773, L= 15.773

(d) The maximum volume of the box is 192.421 cm^2.

In the given question,

A box is to be made out of a 10 cm by 20 cm piece of cardboard. Squares of side length cm will be cut out of each corner, and then the ends and sides will be folded up to form a box with an open top.

(a) We have to express the volume V of the box as a function of x.

If we cut out the squares, we'll have a length and width of 10-2x, 20-2x respectively and height of x.

So V = x(10-2x) (20-2x)

V = x(10(20-2x)-2x(20-2x))

V = x(200-20x-40x+4x^2)

V = x ( 200 - 60 x + 4x^2)

V = 4x^3-60x^2+200x

(b) Now we have to give the domain of V in interval notation.

Since the lengths must all be positive,

10-2x > 0 ≥ x < 5 and x> 0

So 0 < x < 5

(c) Now we have to find the length L , width W, and height H of the resulting box that maximizes the volume.

We take the derivative of V:

V'(x) = 12x^2-120x+200

Taking V'(x)=0

0 = 4 (3x^2-30x+50)

3x^2-30x+50=0

Now using the quadratic formula:

x=\(\frac{-b\pm\sqrt{b^2-4ac}}{2a}\)

From the equationl a=3, b=-30, c=50

Putting the value

x=\(\frac{30\pm\sqrt{(-30)^2-4\times3\times50}}{2\times3}\)

x= \(\frac{30\pm\sqrt{900-600}}{6}\)

x= \(\frac{30\pm\sqrt{300}}{6}\)

x= \(\frac{30\pm17.321}{6}\)

Since x<5,

So x= \(\frac{30-17.321}{6}\)

x= 2.113

So H = 2.113, W = 5.773, L= 15.773.

d) Now we have to find the maximum volume of the box.

V = HWL

V= 2.113*5.773*15.773

V = 192.421 cm^3

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Answer:

D.  They do not have the same ratio of girls to boys because a straight line cannot be drawn through the points (14, 16), (17, 19), and (0, 0) on a coordinate grid.

Step-by-step explanation:

In order to check if the ratio is the same, convert the ratios to (x, y) points, plot them on a graph and see if you can draw a straight line through them and the origin (0, 0).  If you can, then the ratios are the same.  If not, then the ratios are not the same.

After plotting (14, 16) and (17, 19) and (0, 0) on a graph (attached), you can see that a straight line will only go through any two of the points, but not all three.  Therefore, the ratios are not the same.

Answer:

A is larger.  I know this because I can count the squares in A and B and I can see there are more squares in A (15) verse B ( 12).

Step-by-step explanation:

The length of A (5) is not larger than the length of B (6).

Area of A:

a = lw

a = 5x3

a = 15

15 \(units^{2}\)

Area of B:

a = lw

a = 6 x 2

a = 12

12\(units^{2}\)

Helping in the name of Jesus.

Answer:

morning - 40

afternoon - 85

Step-by-step explanation:

The bus traveled 40 miles in the morning and 85 miles in the afternoon.

The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.

The school bus traveled five miles more on a field trip in the afternoon than it did in the morning. If the journey was 125 kilometers long

Let x the distance traveled by bus in the morning.

As per the given condition, we can get the equation shown below:

⇒ x + 2x + 5 = 125

⇒ 3x + 5 = 125

⇒ 3x = 120

⇒ x = 40

In the afternoon, the bus traveled 2x + 5 miles.

Now substitute the value of x in the equation for the afternoon miles to include:

⇒ 2 × 40 +5 = 85

Therefore, the bus traveled 40 miles in the morning and 85 miles in the afternoon.

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Therefore, Z-scores can be used to identify scores that are unusually high or low compared to the rest of the distribution. This allows researchers to better understand the characteristics of their data and make informed decisions based on their findings.

A researcher calculates standard scores using the population mean and standard deviation. The researcher is calculating the Z-score.Z-scores are defined as the number of standard deviations that a score deviates from the mean of its distribution. They're calculated by subtracting the population mean from the raw score and then dividing the difference by the population standard deviation. The Z-score formula is as follows:

Z = (X - μ) / σ

where Z is the z-score, X is the raw score, μ is the population mean, and σ is the population standard deviation.The purpose of calculating standard scores is to measure the relative position of a score within its distribution. Standard scores can be used to compare scores from different populations or distributions that may have different means and standard deviations. The Z-score has a mean of 0 and a standard deviation of 1, making it useful for comparing scores across different distributions. A Z-score greater than 0 indicates that a score is above the mean, while a Z-score less than 0 indicates that a score is below the mean. Therefore, Z-scores can be used to identify scores that are unusually high or low compared to the rest of the distribution. This allows researchers to better understand the characteristics of their data and make informed decisions based on their findings.

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Answer:

Shen invested $9000.

Step-by-step explanation:

The simple interest formula is i = prt, where p is the principal amuont, r is the annual interest rate as a decimal fraction and t is the time in years.

Here, $2160 = P*0.06*(4 yrs), so:

         $2160

P = ----------------- = $9000

            0.24

A. The 95% confidence interval for the mean weight of all fridges is (97.01 kg, 102.99 kg).

B. The confidence interval means that we can be 95% confident that the true population mean weight of all fridges falls within this range. This means that if we were to collect multiple samples and calculate their confidence intervals, approximately 95% of those intervals would contain the true population mean. In this case, it means that we are 95% confident that the true average weight of all fridges is between 97.01 kg and 102.99 kg.

C. Without calculating another confidence interval, we can say that a 90% confidence interval would be less precise than the 95% confidence interval created in part a). This is because a higher confidence level requires a wider interval to capture the true population mean with a higher degree of certainty. Since a 90% confidence interval is less confident than a 95% confidence interval, it would need to be narrower. Therefore, a 90% confidence interval would be less precise, as it would provide a smaller range of values for the population mean.

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A parallelogram is a quadrilateral with opposite sides that are parallel. In order to determine if the given points form a parallelogram, None of the given options clearly demonstrate that the four points are the vertices of a parallelogram.

A parallelogram is a quadrilateral with opposite sides that are parallel. In order to determine if the given points form a parallelogram, we need to examine the relationships between the sides and diagonals.

Option A, which states that DA = AB = BC = CD, does not provide enough information about the relationship between opposite sides or diagonals. Similarly, Option B, which states that AB = CD = and DA = BC =, does not provide sufficient information.

Option C, which states that DB = and AC =, also does not provide enough information to establish the parallelism of opposite sides.

Option D, which is not provided, cannot be evaluated as it is missing the necessary information.

In conclusion, none of the given options demonstrate the properties required to establish that the four points are the vertices of a parallelogram. Additional information, such as the slopes or lengths of the sides, is needed to determine if the given points form a parallelogram.

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It should be noted that mathematics is multicultural. This implies that mathematics applies to different cultures.

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The solution is, after paying the agent commission, Brian will get 155.605265 pounds.

And, the percentage increase in the price 7.9%

the car travel in 2 hours 45 minutes is 291.5 km.

Currency conversion can be stated as the process of converting one currency into another currency. This is usually done in order to make transactions or investments in another country or to keep track of the value of assets held in different currencies.

here, we have,

we know.

The value of one currency is generally expressed in terms of another currency using exchange rates, which means  the value of one currency in terms of another currency at a specific point in time.

We know that, exchange rate can fluctuate over time, and currency conversion can be done manually or through various financial services or tools.

we have,

To calculate that how many pounds Brian will get for R2 100,

At first we need to calculate the amount of commission he will have to pay to the agent.

Commission = 1.5% of R2 100

Commission = 0.015 x R2 100

Commission = R31.50

Now we can calculate how much money Brian will have left after paying the commission:

Amount left after commission = R2 100 - R31.50

Amount left after commission = R2 068.50

Next, we can use the exchange rate given to convert Rands to Pounds:

1 Rand = 0.075199 Pounds

Therefore, to find out how many Pounds Brian will get for R2 068.50, we can multiply R2 068.50 by the exchange rate:

2 068.50 x 0.075199 = 155.605265 pounds

Next Part:

The price of petrol is increased from R12, 58 per litre to R13, 28 per litre.

i.e. increase of price = 100

so, the percentage increase in the price = 100 * 100/1258

                                                                   =7.9%

Next Part:

A motor car drives at an average speed of 106 km/h.

the car travel in 2 hours 45 minutes = 106* 165 / 60

                                                           =291.5 km

So The solution is, after paying the agent commission, Brian will get 155.605265 pounds.

And, the percentage increase in the price 7.9%

the car travel in 2 hours 45 minutes is 291.5 km.

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Answer:

there will be 8 rows

the number of photographs in each row is 8

Answer:

x = - 4

Step-by-step explanation:

-79 = 7x + 3(4x - 1)

-79 = 7x + 12x - 3                      Distribute 3 to the paranthesis

-79 = 19x - 3                              Add like terms

-76 = 19x                                   Add 3 to both sides

- 4 = x                                          Divide 19 to both sides

The solution of the equation is n=1/6.

The following steps solve the equation given:

\(\frac{1}{2n}+3=6\)

Subtracting 3 on both sides:

\(\frac{1}{2n}=3\\\)

Multiplying both sides by n:

\(\frac{1}{2}=3n\)

Dividing Both sides by 3:

\(\frac{1}{2\cdot3}=n\)

So, the solution is given by:

\(\boxed{\mathbf{n=\frac{1}{6}}}\\\)

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Answer:

jakfl;jkafjd; free points ha on u

Step-by-step explanation: