True or false If a system produced a true statement by the elimination method. It has no solution?

Answer:

Step-by-step explanation:

Let the width be w. The length is then 3w (length is 3 times its width).

The formula for the perimeter is 2l + 2w (2 times the length + 2 times the width)

So, in our case we have 2(3w) + 2w = 72

                                  6w + 2w = 72

                                  8w = 72   divide both sides by 8

                                  w = 9

So the length = 3w = 3 x 9 = 27

Double check: we have l = 27 and w= 9. (2 x 27) + (2 x 9) = 54 + 18 = 72  Yay!!!

Answer:

1539/4 (improper fraction) or 384 3/4 (simplified fraction)

Step-by-step explanation:

To find the improper fraction, write 384.75 as a fraction:

384.75/1

Then, since you have 2 decimal places after the ., multiply the entire fraction by 100:

38475/100

Next, find the GCF, which is 25, and simplify this fraction to find the final improper fraction:

1539/4

To find the simplified fraction, we already have the whole number, 384, so we have to convert 0.75 to a fraction which is 3/4, because 0.75 is 3/4 of 100:

384 3/4

Hope this helps :)

Answer:

4<2

Step-by-step explanation:

Answer:

4-2

Step-by-step explanation:

A Negative correlation coefficient means that as one variable increases, the other decreases (i.e., an inverse relationship).

In factored form, the same expression is thus:

8(x² + 2x + 3)

The expression can be factored to provide the common factor of 8:

8x² + 16x + 24 = 8(x² + 2x + 3)

We must now factor the quadratic expression within the parenthesis. The quadratic formula can be used:

x = [-b ± sqrt(b² - 4ac)] / 2a

We have a = 1, b = 2, and c = 3 for the formula x2 + 2x + 3. When we plug these numbers into the quadratic formula, we get:

x = [-2 ± sqrt(2² - 4(1)(3))] / 2(1)

x = [-2 ± sqrt(-8)] / 2 x = (-1 ± i√2)

The quadratic expression does not factor over the real numbers because the discriminant (\(b^{2}\) - 4ac) is negative. As a result, the factored equivalent expression is:

8(\(x^{2}\)+2x+3) = 8(x - (-1 + i2))(x - (-1 - i2))

8x²+16x+24 = 8(x+1)(x+3)

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Answer:

  A)  yes. √2.89 = 1.7

  B)  no. √0.004 = (√10)/50, an irrational number

Step-by-step explanation:

You want to know if 2.89 and 0.004 are perfect squares, and why or why not.

A number is considered to be a perfect square if it has a rational square root. Usually, we use the term perfect square to refer to the squares of integers. However, the square of any rational number can be considered to be a perfect square.

A number is not a perfect square if its root is irrational.

The root of 2.89 is 1.7. 2.89 has a rational square root, so can be considered to be a perfect square.

The root of 0.004 is (√10)/50. The square root of 10 is irrational, so 0.004 is not considered to be a perfect square.

__

Additional comment

The number of decimal digits in the fractional portion of the square root of a decimal will be half the number of the digits in its decimal portion. That is, the number 0.0040 will have 2 decimal digits in its root if it is a perfect square. For example, √0.0036 = 0.06. If your calculator tells you the root has more digits than this, the number is not a perfect square.

You will notice 2.89 has 2/2 = 1 decimal digit in its root, 1.7.

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There are values of 'a' such that all real numbers are solutions of the compound inequality x < 8 and x > a. Any 'a' value greater than 8 would satisfy this condition.

To find values of 'a' such that all real numbers are solutions of the compound inequality x < 8 and x > a, we need to determine the range of 'a' that satisfies both conditions simultaneously.

The compound inequality x < 8 implies that 'x' must be less than 8. This sets an upper limit on the possible values of 'x'. On the other hand, the inequality x > a implies that 'x' must be greater than 'a'. This sets a lower limit on the possible values of 'x'.

For all real numbers to be solutions of the compound inequality, we need to find an 'a' value that satisfies both conditions, regardless of the value of 'x'.

Since the inequality x < 8 sets the upper limit, any value of 'a' that is greater than 8 would satisfy the compound inequality for all real numbers. This is because no matter how large 'a' is, there will always be values of 'x' that are less than 8.

In summary, there are values of 'a' such that all real numbers are solutions of the compound inequality x < 8 and x > a. Any 'a' value greater than 8 would satisfy this condition.

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The Surface Area of Pyramid is 85 cm².

We have,

Simply calculating the areas of each face in a figure is surface area. It is considerably simpler for us to calculate because the amount is supplied to us as a net of.

So, Area of square base= (side²)

= 5²

= 25 cm²

and, Area of one triangular face

= (1/2 x b x h)

=1/2 x 5 x 6

= 15 cm²

Now, Multiply by 4 as we have 4 triangular faces

= 15 cm² x 4

= 60 cm²

Then, Surface Area of Pyramid is

= 25 cm² + 60 cm²

= 85 cm²

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The equation of the hyperboloid of one sheet passing through the points (±5,0,0),(0,±5,0)(±5,0,0),(0,±5,0) and (±10,0,4),(0,±10,4) is \(\frac{(x^2)}{25} + \frac{(y^2)}{25} - \frac{(z^2)}{(29/4)} = 1\).

To find the equation of the hyperboloid of one sheet passing through the given points, we can start by setting up a general equation for a hyperboloid of one sheet:
\(\frac{((x-a)^2)}{A^2} + \frac{((y-b)^2)}{B^2} - \frac{((z-c)^2)}{C^2} = 1\)
where (a,b,c) is the center of the hyperboloid and A, B, and C are the lengths of the semi-axes.

We can then use the given points to set up a system of equations and solve for the unknowns a, b, c, A, B, and C.

The system of equations is:

\((\pm5-a)^2/A^2 + (-b)^2/B^2 + (-c)^2/C^2 = 1\\(-a)^2/A^2 + (\pm5-b)^2/B^2 + (-c)^2/C^2 = 1\\(\pm10-a)^2/A^2 + (-b)^2/B^2 + (4-c)^2/C^2 = 1\\(-a)^2/A^2 + (\pm10-b)^2/B^2 + (4-c)^2/C^2 = 1\)

We can simplify the system by using the fact that the hyperboloid is symmetric about the x, y, and z-axes.

This means that a, b, and c are all equal to zero. We can also assume that A = B and use the first two equations to solve for A:

\((\pm5)^2/A^2 + (-c)^2/A^2 = 1\\(-c)^2/A^2 + (\pm5)^2/A^2 = 1\)

Solving for A, we get A = 5 and C = √(29)/2.

Therefore, the equation of the hyperboloid of one sheet passing through the given points is:
\(\frac{(x^2)}{25} + \frac{(y^2)}{25} - \frac{(z^2)}{(29/4)} = 1\).

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Answer: its 9

Step-by-step explanation:

Answer: 2/3, or 0.6666666667

Step-by-step explanation:

Answer:

The simplest form of 6/9 is 2/3.

Step-by-step explanation:

1) Divide both the numerator and denominator by three(does not apply to all situations).

2) Outcome should be 2/3 or .666

The planning value for the population standard deviation is estimated to be $3,350, and sample sizes of approximately 46, 566, and 2,262 would be needed to achieve desired margins of error of $500, $200, and $100, respectively.

(a) Desired margin of error = $500

The formula for the sample size required to estimate the population mean with a desired margin of error is:

n = (Z * σ / E)²

Where:

n = sample size

Z = Z-score corresponding to the desired confidence level (95% confidence level corresponds to a Z-score of 1.96)

σ = population standard deviation

E = desired margin of error

Since we don't have the actual population standard deviation, we can estimate it using the planning value.

Range of expected salaries = $55,400 - $42,000 = $13,400

Planning value for standard deviation = Range / 4 = $13,400 / 4 = $3,350

Substituting the values into the formula:

n = (1.96 * $3,350 / $500)² ≈ 45.96

Since we can't have a fraction of a sample, we need to round up to the nearest whole number.

Therefore, the sample size needed for a desired margin of error of $500 is 46.

(b) Desired margin of error = $200

Using the same formula:

n = (1.96 * $3,350 / $200)² ≈ 565.44

Rounding up to the nearest whole number, the sample size needed for a desired margin of error of $200 is 566.

(c) Desired margin of error = $100

Using the same formula:

n = (1.96 * $3,350 / $100)² ≈ 2,261.76

Rounding up to the nearest whole number, the sample size needed for a desired margin of error of $100 is 2,262.

(d) Would you recommend trying to obtain the $100 margin of error? Explain.

Obtaining a margin of error as low as $100 would require a sample size of 2,262. While this larger sample size may provide a more precise estimate, it also increases the cost and time required for data collection and analysis. Therefore, the decision to obtain such a small margin of error should be based on the practicality and resources available. It is important to consider the trade-off between the desired level of precision and the associated costs and efforts.

Therefore, the planning value for the population standard deviation is estimated to be $3,350, and sample sizes of approximately 46, 566, and 2,262 would be needed to achieve desired margins of error of $500, $200, and $100, respectively.

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Trevor and Kim will be situated 21 kilometers apart from each other at 1:30 PM. They will be separated by a distance of 21 km when the clock strikes 1:30 in the afternoon.

To determine at what time Trevor and Kim will be 21 km apart, we can set up a distance-time equation based on their relative speeds and distances.

Let's assume that t represents the time elapsed in hours since noon. At time t, Trevor would have traveled a distance of 8t km, while Kim would have traveled a distance of 6t km in the opposite direction.

Since they are running in opposite directions, the total distance between them is the sum of the distances they have traveled:

Total distance = 8t + 6t

We want to find the time when this total distance equals 21 km:

8t + 6t = 21

Combining like terms, we have:

14t = 21

To solve for t, we divide both sides of the equation by 14:

t = 21 / 14

Simplifying, we find:

t = 3 / 2

So, they will be 21 km apart after 3/2 hours, which is equivalent to 1 hour and 30 minutes.

Therefore, Trevor and Kim will be 21 km apart at 1:30 PM.

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d. Expected life in years of the depreciable asset. The acceptable way to express the useful life of a depreciable asset is in terms of the expected life in years.

The useful life refers to the period of time over which the asset is expected to contribute to the revenue-generating activities of a business.

While options a, b, and c may be relevant factors for certain specific assets (such as units produced, hours of productivity, or miles driven), they do not encompass the overall concept of useful life. Useful life is a broader measure that takes into account the anticipated duration of productive use, regardless of specific output or activity metrics.

Expressing the useful life in years provides a common standard for comparison and allows for consistency in depreciation calculations and financial reporting. It is a practical and widely accepted approach to estimating the lifespan of a depreciable asset.

It is worth noting that the estimated useful life in years may vary depending on the nature of the asset and industry practices. It is typically determined based on factors such as technological advancements, physical wear and tear, economic obsolescence, and the intended purpose of the asset.

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Answer:

f(0) = 3x : 0

f(1) = 3x : 3

f(2) = 3x : 6

f(3) = 3x : 9

Step-by-step explanation:

Answer:

x=75

Step-by-step explanation:

\(We\ are\ given\ that, \\Angle GFE=105\\We\ observe\ that, \\Angle\ GFE\ and Angle\ EFB\ form\ a\ linear\ pair\ and\ hence,\ are\ supplementary.\\Hence,\\Angle\ GFE\ + Angle\ EFB=180\\Hence,\\105+Angle\ EFB=180\\Angle\ EFB=180-105\\Angle\ EFB=75\\We\ know\ observe\ that\ Angle\ EFB\ and\ Angle\ ABC\ are\ corresponding\ angles\ and\ are\ equal\\Hence,\\Angle\ EFB\ = \ Angle\ ABC\\75=Angle\ ABC\\75=x\\x=75\)

If an invertible symmetric n×n matrix A has a nonzero vector v in R^n such that Av is orthogonal to v, then it means that the dot product of Av and v is equal to zero. In other words, Av . v = 0. Using th peroperties of the dot product, we can rewrite this equation as:
v . A^T v = 0

Since A is symmetric, A^T = A, and we can rewrite the equation as:
v . A v = 0
This equation can be further simplified using the properties of the dot product:
v . A v = (A v) . v = 0
From this equation, we can see that the eigenvalues of A must be either positive or negative. If the eigenvalues of A are all positive, then v . A v > 0, which contradicts the equation v . A v = 0. Similarly, if the eigenvalues of A are all negative, then v . A v < 0, which also contradicts the equation v . A v = 0.
Therefore, the only way for there to exist a nonzero vector v in R^n such that Av is orthogonal to v is if the eigenvalues of A are both positive and negative. In other words, A must have both positive and negative

eigenvalues.

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Answer: 2

Step-by-step explanation: It is 2. You can use the vertex formula x= (-b/2a) 4/2(1), which is 2 and x=2 is the x intercept.

To calculate the cost of driving a diesel tractor trailer truck for 175.0 miles, we need to determine the number of gallons of fuel required and then multiply it by the cost per gallon.

Calculate the number of gallons of fuel needed. Given that the truck gets 8.500 miles per gallon, we divide the total distance (175.0 miles) by the fuel efficiency: 175.0 miles / 8.500 miles per gallon

= 20.59 gallons (approximately)

Calculate the cost of the fuel.Since diesel fuel costs $3.599 per gallon, we multiply the number of gallons needed by the cost per gallon: 20.59 gallons x $3.599/gallon = $73.89 (approximately) Therefore, it will cost you approximately $73.89 to drive the diesel tractor trailer truck for 175.0 miles, assuming it gets 8.500 miles per gallon and diesel fuel costs $3.599 per gallon.

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They are related as u^T transposes of each other. v and v^T u are scalar values that represent the dot product of u and v. uv^T and vu^T are matrices of size n x n that represent the outer product of u and v.

If u and v are vectors in R^n, then:

u^T v and v^T u are related as transposes of each other. Specifically, if

u = [u_1, u_2, ..., u_n]^T

and v = [v_1, v_2, ..., v_n]^T

then:

u^T v = v^T u

= u_1 * v_1 + u_2 * v_2 + ... + u_n * v_n

So, u^T v and v^T u are scalar values that represent the dot product of u and v.

uv^T and vu^T are related as transposes of each other. Specifically, if u = [u_1, u_2, ..., u_n]^T and v = [v_1, v_2, ..., v_n]^T

then:

uv^T = [u_1 * v_1, u_1 * v_2, ..., u_1 * v_n;

u_2 * v_1, u_2 * v_2, ..., u_2 * v_n;

...;

u_n * v_1, u_n * v_2, ..., u_n * v_n]

vu^T = [v_1 * u_1, v_2 * u_1, ..., v_n * u_1;

v_1 * u_2, v_2 * u_2, ..., v_n * u_2;

...;

v_1 * u_n, v_2 * u_n, ..., v_n * u_n]

So, uv^T and vu^T are matrices of size n x n that represent the outer product of u and v.

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To argue why the liberal arts are so important in education and leisure, one must discuss its Greek origin and how it is received today.

The term "liberal arts" comes from the Latin word "liberalis," which means free. It was used in the Middle Ages to refer to topics that should be studied by free people. Liberal arts refers to courses of study that provide a general education rather than specialized training. It encompasses a wide range of topics, including literature, philosophy, history, language, art, and science.The liberal arts curriculum is based on the idea that a broad education is necessary for individuals to become productive members of society. In ancient Greece, education was focused on developing the mind, body, and spirit.  

The study of the liberal arts is necessary to create well-rounded individuals who can contribute to society in meaningful ways. While the importance of the liberal arts has been debated, it is clear that they are more important now than ever before. The study of the liberal arts is necessary to develop the skills that are required in a rapidly advancing technological world.

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Answer:

$

$fktstwiat8atia8at8tew5d9hs9h9sysy9s

Profit or gain   =    When (SP) > (CP) then there is a gain.

                                Gain = (SP) - (CP) = 15

Cost price (CP)  =  The amount for which an article is bought is called its cost price.

Selling price (SP) =  The amount for which an article is sold is called its selling price.

a) Profit or gain   =    When (SP) > (CP) then there is a gain.

                                Gain = (SP) - (CP)

 =    40 > 25

profit = 40 - 25 = 15

b) ten torches bought for Rs 500, which means one = 50

  sold for Rs 288 each then, 10 * 288 = 2880

   profit =   When (SP) > (CP) then there is a gain.

                                Gain = (SP) - (CP)

                     =      2880 >  500

       profit = 2880 - 500 = 2380

c)  Loss  =              When (SP) < (CP) then there is a loss.

                              Loss = (CP) - (SP).

  1050 =  4000 < CP

  CP = 4000 - 1050

   CP = 2950

d) Loss  =              When (SP) < (CP) then there is a loss.

                              Loss = (CP) - (SP).

72.22 = SP <  388.72

72.22  =   388.72 - SP

SP =          388.72 - 72.22

SP  = 316.5

e)  Loss  =              When (SP) < (CP) then there is a loss.

                              Loss = (CP) - (SP).

                960 < 1020

               1020 - 960

loss = 60

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Personal car would be the best option to manage both tasks efficiently. While the train is a reliable mode of transportation, it may have fixed schedules that might not align perfectly with Patrick's needs.

On the other hand, using his personal car provides more flexibility and allows him to tailor the departure time according to his daughter's coding class schedule.

If Patrick decides to take the train, he would need to check the train schedule to see if there are convenient departure and arrival times for both the soccer game and the coding class. This option would require planning and coordination to ensure he arrives at the game on time and can pick up his daughter afterward.

Using his personal car gives Patrick the freedom to leave at a time that accommodates both the soccer game and the coding class. He can drop off his daughter at her coding class, attend the soccer game, and then pick her up afterward without being restricted by train schedules.

Considering the circumstances, Patrick might find it more convenient to use his personal car to manage both tasks effectively and ensure he can attend his son's soccer game while also ensuring his daughter arrives at her coding class on time.

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Answer:

The lines are parallel

Step-by-step explanation:

When lines are parallel they travel side-by-side without ever crossing paths.

Answer: Parallel

Step-by-step explanation:

Two parellel lines have the same slope, thus will never cross, regardless of how far in each direction you go. This is true of the image attached, thus the lines are parallel.

There is no curve that describes the level curve of value c for the given surface, as the condition c < 0 makes it impossible to find a real solution.

In two- or three-dimensional space, a curve is a mathematical object that symbolises a continuous, smooth path. Curves can be derived from geometric operations, parametric equations, or mathematical equations. They are commonly used to simulate real-world processes in physics, engineering, mathematics, and many other disciplines.

To find the level curve of value c for the given surface \(z = f(x, y) = (x^2/4) + (y^2/25) = c\), where c < 0, follow these steps:

Step 1: Write down the equation of the surface.
\(z = f(x, y) = (x^2/4) + (y^2/25)\)

Step 2: Replace z with the constant c.
\(c = (x^2/4) + (y^2/25)\)

Step 3: Rearrange the equation to isolate \(y^2\).
\(y^2 = 25(c - (x^2/4))\)

However, note that we're given that c < 0. This means that the value inside the parentheses (c - (\(x^2/4\))) must also be negative. Since y^2 can't be negative, there's no real solution for this equation.

In conclusion, there is no curve that describes the level curve of value c for the given surface, as the condition c < 0 makes it impossible to find a real solution.

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Step-by-step explanation:

the inner WU arc angle is 23x - 5.

the outer WU arc angle is 37x + 5.

together they must be 360°, as this is the full circle.

so, we have

360 = 23x - 5 + 37x + 5 = 60x

x = 6

therefore, the angle at V is

V = 5x + 17 = 5×6 + 17 = 30 + 17 = 47°

inner WU arc angle = 23x - 5 = 133°

outer WU arc angle = 37x + 5 = 227°

this also fits with

V = (outer arc angle - inner arc angle)/2 =

= (227 - 133)/2 = 94/2 = 47°

Answer:

sin²A-5 sinA+6

=sin²A-(3+2)sinA+6

=sin²A-3sinA-2sinA+6

=sinA(SinA-3)-2(sinA-3)

=(sinA-2) (sinA-3)

hope this help you

Answer:

sin²A-5 sinA+6

=sin²A-(3+2)sinA+6

=sin²A-3sinA-2sinA+6

=sinA(SinA-3)-2(sinA-3)

=(sinA-2) (sinA-3)