5{[(4+6-8)-4]-(1+2⁴-3+6)}​

Option B is correct, the inequality which represents the  length of segment AB is greater than  length of segment AD is 9x-16>1.5x+42

The given rectangle is ABCD.

The length of segment AB is 9x-16 units

The length of segment AD is 1.5x+42 units

We have to find the inequality which represents the  length of segment AB is greater than  length of segment AD

> is the symbol used to represent greater than

AB>AD

9x-16>1.5x+42

Hence, option B is correct, the inequality which represents the  length of segment AB is greater than  length of segment AD is 9x-16>1.5x+42

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Answer: 2 is the answer

Step-by-step explanation:

The horse is a domesticated one-toed hoofed mammal. It belongs to the taxonomic family Equidae and is one of two extant subspecies of Equus ferus. The horse has evolved over the past 45 to 55 million years from a small multi-toed creature, Eohippus, into the large, single-toed animal of today.

All horse breeds are classified into three main groups: heavy horses, light horses, and ponies. Heavy horses are the largest horses, with large bones and thick legs. Some weigh more than 2,000 pounds. Light horses are smaller horses, with small bones and thin legs.

Horses can't breathe through their mouth. ...

Horses can sleep standing up. ...

Horses have lightning fast reflexes. ...

Horses have 10 different muscles in their ears. ...

Horses have a nearly 360 degree field of vision.

The complete table using the given function y = 3x²- 12x + 6 is below

x     y

1     -3

3     -3

0      6

4      6

The table is competed by using the function and solving for y at different times

The function given to complete the table is

y = 3x²- 12x + 6

substituting the different values of x gives y values

at x = 1

y = 3(1)²- 12 * 1 + 6 = -3

at x = 3

y = 3(3)²- 12 * 3 + 6 = -3

at x = 0

y = 3(0)²- 12 * 0 + 6 = 6

at x = 4

y = 3(4)²- 12 * 4 + 6 = 6

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An infinite geometric series is one in which each term is equal to the preceding term multiplied by a fixed non-zero number, known as the common ratio.

The first term is called a1, and the common ratio is represented by r.In this particular question, we are required to find the value of a1 and r for an infinite geometric series. The partial sum S2 will also need to be found.For a geometric sequence that is infinite, the formula for the partial sum, Sn, is:Sn = a1 / (1-r), where a1 is the first term and r is the common ratio.To solve for a1, it is necessary to know two other variables: the common ratio r and the value of the first term a1. S2 is the sum of the first two terms, so: S2 = a1 + arTo find S2, we must first determine a1 and r. a1 is the first term in the sequence, and r is the common ratio. We can obtain both a1 and r by dividing the second term by the first term.The formula is:r = (ar/a1) = a2/a1 Substitute the value of r and a1 into the formula for S2 to obtain the result: S2 = a1 + ar = a1 + a1r = a1(1+r) Therefore, the value of a1 is a constant number that will appear in the series, and the common ratio, r, will be multiplied by this number to obtain the next value in the series.

So, a1 is the first term, and r is the common ratio of the infinite geometric series. S2, the sum of the first two terms, is found by using the formula S2 = a1 + ar where a1 is the first term and r is the common ratio.

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The green shaded region does not represent the solution to the system of linear inequalities y ≥ 2 and 3.5x + 2y ≤ 20 because it includes points that do not satisfy both inequalities simultaneously.

To determine the solution to the system of linear inequalities, we need to find the region that satisfies both inequalities simultaneously.

In this case, the first inequality, y ≥ 2, represents the region above the line y = 2, including the line itself.

The second inequality, 3.5x + 2y ≤ 20, represents the region below the line 3.5x + 2y = 20, including the line itself. To graph this line, we can rewrite it as 2y = -3.5x + 20, or y = -1.75x + 10.

Now, if we shade the region that satisfies both inequalities simultaneously, we find that it does not match the green shaded region. The green shaded region may include points that satisfy one inequality but not the other.

To accurately represent the solution to the system of linear inequalities, we need to identify the overlapping region that satisfies both inequalities.

This can be determined by finding the intersection points of the two lines and considering the region bounded by those intersection points.

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The relation R on the set (1, 2, 3, 4) can be represented by an arrow diagram and a matrix. The arrow diagram visually depicts the connections between the elements.

To represent the relation R on the set (1, 2, 3, 4) using an arrow diagram, we draw a directed arrow from each element in the set to the element it is related to. For example, we draw an arrow from 1 to 3 and 4, an arrow from 2 to 1, an arrow from 3 to 2 and 4, and an arrow from 4 to 2. The resulting arrow diagram shows the connections between the elements in the relation.

The matrix representation of a relation uses a table to show the presence or absence of connections between elements. For the relation R on the set (1, 2, 3, 4), we create a 4x4 matrix where the rows and columns correspond to the elements of the set. We fill in the matrix with 1s to indicate that there is a connection between the respective elements and 0s otherwise. In this case, the matrix would be:

| 0 0 1 1 |

| 1 0 0 0 |

| 0 1 0 1 |

| 0 1 0 0 |

In the matrix, a 1 in the i-th row and j-th column indicates that the element i is related to the element j. For example, the entry in the first row and third column is 1, indicating that 1 is related to 3.

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Answer:

yes!

Step-by-step explanation:

they have the same 3 angles in both

Answer:

true

Step-by-step explanation:

its 12.0

Step-by-step explanation:

Answer:

A. Horizontal Stretch and vertical shift down 4

Step-by-step explanation:

When multiplying by a number greater than one, its a stretch. When it is less than one it is a compression.

2 is greater than 1 so its a horizontal stretch.

When there is a number outside of the () then that number determines how high or how low you go depending on the sign.

Our number is -4 so we go down 4.

Answer: you

Step-by-step explanation:

Answer:

going in the order top to bottom

i)

2

2

2

2 and 2

ii)

2 and 2

2

2

2 and 2

iii)

2

2

2 and 2

2 and 2

Step-by-step explanation:

you have to find out what number you times to get the number they have given you (eg: you have to get 4 and they have given you the number 2, 2 times what makes 4? the answer is 2)

Answer:

median = 55.5

Step-by-step explanation:

Here we have 10 numbers which is an even number

then the median for the data set is the average of the two middle numbers

firstly ,we have to put the number of the set in order from least to greatest like this :

3 < 12 < 38 < 38 < 46 < 65 < 71 < 78 < 87 < 99

————————                     ————————-

As you can see the middle two numbers are : 46 and 65

Now, we calculate their average :

\(\large \text Median = \frac{46+65}{2}= 55.5\)            

Answer:

-7x(16)

Step-by-step explanation:

The only thing you can combine is the 7+9

The output y(t) and settling time for the step response of a system with a closed-loop transfer function can be determined based on the characteristics of the transfer function.

The settling time refers to the time it takes for the response to reach and stay within a certain range of the final value. To calculate these values, we need to analyze the transfer function's poles and zeros.

In the case of a step response, the output y(t) represents the system's response to a unit step input. The settling time is the time it takes for the response to stabilize within a specified tolerance. It is influenced by the location of the poles in the transfer function. If all the poles of the transfer function are located in the left-half plane of the complex plane (i.e., they have negative real parts), the system is stable, and the settling time is determined by the dominant pole. The dominant pole is the pole with the largest magnitude and closest to the imaginary axis. The settling time is typically considered to be around four to five times the inverse of the dominant pole's real part.

In summary, to determine the output y(t) and settling time for the step response of a system with a closed-loop transfer function, we need to analyze the transfer function's poles and zeros. The settling time is influenced by the location of the poles, with the dominant pole playing a crucial role in determining the response's stabilization time.

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Answer:

add up ??

Step-by-step explanation:

Answer:

C choice.

Step-by-step explanation:

Since line a is given a slope as -4.

Another line which is line b is given that it's perpendicular to line a or we can say that line a is perpendicular to line b.

Perpendicular is defined as:

\( \displaystyle \large{m_1m_2 = - 1}\)

Both slopes multiply and yield -1.

We know that m1 is -4; we want to find m2 which is slope of line b.

\( \displaystyle \large{ - 4m_2 = - 1}\)

Divide both sides by -4.

\( \displaystyle \large{ \frac{ - 4m_2}{ - 4} = \frac{ - 1}{ - 4} } \\ \displaystyle \large{ m _2 = \frac{1}{4} }\)

Therefore, the slope for line b is 1/4.

Thus, the C choice is correct.

To determine the maximum number of 2/0 AWG THW aluminum compact conductors permitted in a 2½-inch PVC conduit, Schedule 80, we need to consult the applicable electrical code or standards.

The number of conductors allowed in a conduit is typically governed by factors such as fill capacity and heat dissipation.

The specific requirements may vary depending on the jurisdiction and the electrical code being followed. It is recommended to consult the local electrical code or a qualified electrician to ensure compliance with the regulations in your area.

They will be able to provide the precise guidelines and restrictions for conductor fill capacity based on the conduit size, type, and the specific application.

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Answer:

60

Step-by-step explanation:

If you multiply 5 by 60 you will get the total number of people, 300. If you then multiply 4 by 60, you get 240. That means 60 people dont have pets.

The answer is 60.

If you multiply 5 by 60 you will get the total number of people, 300. If you then multiply 4 by 60, you get 240. That means 60 people don't have pets.

Problem-solving is the act of defining a problem; determining the cause of the problem; identifying, prioritizing, and selecting alternatives for a solution; and implementing a solution.

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Given that "a" is an approximate value for a quantity with a true value of "t" and a relative error of "r," we need to prove that "a" can be expressed as "t(1+r)" using the definitions of these terms.

The relative error "r" is defined as the absolute difference between the true value "t" and the approximate value "a," divided by the true value "t." Mathematically, this can be expressed as r = |t - a| / t.

To prove that a = t(1 + r), we start by rearranging the definition of relative error:

r = |t - a| / t

Multiply both sides by t:

rt = |t - a|

Since the absolute value of t - a is equal to a - t (as the true value "t" is assumed to be larger than the approximate value "a"), we can rewrite the equation as:

rt = a - t

Rearranging the equation, we have:

a = t + rt

Factoring out t, we get:

a = t(1 + r)

Thus, we have proven that "a" can be expressed as "t(1 + r)" based on the definitions of "a," "t," and "r." This equation shows the relationship between the approximate value "a," the true value "t," and the relative error "r."

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Step-by-step explanation:

Hey there!

Given;

f ( x ) = x² + 2x - 1

g ( x ) = 3x - 2

To verify:

\(( \frac{f}{g} )(2) = \frac{f(2)}{g(2)} \)

LHS:

\( (\frac{f}{g} )(x) = \frac{ {x}^{2} + 2x - 1}{3x - 2} \)

~ Insert "2" instead of "x".

\( (\frac{f}{g} )(2) = \frac{ {2}^{2} + 2 \times 2 - 1 }{3 \times 2 - 2} \)

Simplify it;

\( \frac{f}{g} (2) = \frac{4 + 4 - 1}{6 - 2} \)

Therefore; (f/g)(2) = 7/4.

RHS:

\( \frac{f(x)}{g(x)} = \frac{ {x}^{2} + 2x - 1}{3x - 2} \)

~Insert "2" instead of"x".

\( \frac{f(2)}{g(2)} = \frac{ {2}^{2} + 2 \times 2 - 1 }{3 \times 2 - 2} \)

Simplify it.

\( \frac{f(2)}{g(2)} = \frac{4 + 4 - 1}{6 - 2} \)

Therefore, f(2)/g(2) = 7/4.

Since (f/g)(2) = f(2)/g(2) = 7/4.

Proved!

Hope it helps!

Step-by-step explanation:

Soo :

\( \tt( \frac{f}{g} )(2) = \frac{f(2)}{g(2)} \)

\( \tt( \frac{ {x}^{2} + 2x - 1 }{3x - 2} )(2) = \frac{ {2}^{2} + 2(2) - 1 }{3(2) - 2} \)

\( \tt( \frac{ {2}^{2} + 2(2) - 1}{3(2) - 2} )= \frac{7}{4} \)

\( \boxed{ \tt \frac{7}{4} = \frac{7}{4} }\)

Soo true.

To find the equation of a line passing through the point (9, -3) and perpendicular to the line with the equation x - 6y - 7 = 0, we can use the point-slope form of a line.

The given equation x - 6y - 7 = 0 can be rewritten in slope-intercept form as y = (1/6)x - 7/6. The slope of this line is 1/6.

Since the line we want to find is perpendicular to this line, its slope will be the negative reciprocal of 1/6, which is -6/1 or -6.

Using the point-slope form of a line, y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope, we can substitute the values (9, -3) and -6 into the equation:

y - (-3) = -6(x - 9)

Simplifying further, we have:

y + 3 = -6x + 54

To express the equation in standard form, we can rearrange it as:

6x + y = 51

Therefore, the equation of the line passing through (9, -3) and perpendicular to x - 6y - 7 = 0 is 6x + y = 51.

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Answer:

A downloadable and printable table of perfect square roots and cubes!  This is a great reference sheet!

Analyzing a perfect square, such as the square root of 4.

Understanding the Product Property of Radicals (Includes an example with real numbers!)

Simplify the square root of 18.

Simplify the negative square root of 125.

Simplify the product of the square root of 8 and square root of 3.

Answer:

2x(x-5)(x-2)

Step-by-step explanation:

Answer:

11

Step-by-step explanation:

11 is greater than 6, meaning it satisfies the inequality.

Answer:

vertex is (-2,0)

Step-by-step explanation:

In McDougal Littell Pre-Algebra, the formula to find the length and width of a rectangle is not explicitly provided since it is a basic concept widely covered in elementary mathematics. However, the general formula for finding the length and width of a rectangle is derived from its properties.

A rectangle is a quadrilateral with four right angles. It has two pairs of opposite sides that are equal in length. Let's assume the length of the rectangle is L and the width is W. To find the length and width, we need additional information such as the area or perimeter of the rectangle.

If we know the area of the rectangle (A), the formula to find the length and width is:

A = L * W

We can rearrange this formula to solve for either the length or the width. For example, to find the length:

L = A / W

Similarly, to find the width:

W = A / L

If we know the perimeter of the rectangle (P), we can use the following formulas:

P = 2L + 2W

Again, we can rearrange these formulas to solve for the length or width. For instance, to find the length:

L = (P - 2W) / 2

And to find the width:

W = (P - 2L) / 2

By utilizing the appropriate formula and plugging in the given values, we can determine the length and width of a rectangle in McDougal Littell Pre-Algebra or any mathematics curriculum that covers basic geometric concepts.

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Substituting the value of \( r \), we get \( V \approx 1105.4 \) mm³. Finally, dividing the mass of the ball-bearing (11.9 g) by its volume (1105.4 mm³) and converting the units, we can determine the density in g/cm³. The density is approximately 0.0108 g/cm³.

To explain the process in more detail, we start by finding the radius of the ball-bearing using the circumference formula. The circumference is given as 43.4 mm, so dividing it by 2π gives us the radius of approximately 6.912 mm.

Next, we calculate the volume of the sphere using the formula \( V = \frac{4}{3}\pi r^3 \). Plugging in the radius value, we obtain the volume of the metal ball-bearing as approximately 1105.4 mm³.

To calculate the density, we divide the mass of the ball-bearing (11.9 g) by its volume (1105.4 mm³). However, to obtain the density in g/cm³, we need to convert the volume from mm³ to cm³ by dividing it by 1000. After performing the division and conversion, we find the density of the metal ball-bearing to be approximately 0.0108 g/cm³.

Density is a fundamental property of matter that describes how much mass is contained within a given volume. In this case, it allows us to understand the mass-to-volume ratio of the metal ball-bearing. By calculating the density, we can characterize the compactness or heaviness of the material.

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The density of the metal in the ball-bearing is approximately 10.981 g/cm^3.

To find the density of the metal in g/cm^3, we need to calculate the volume of the metal ball-bearing and divide it by its mass.

Given information:

Circumference of the ball-bearing = 43.4 mm

Weight of the ball-bearing = 11.9 g

To calculate the volume of the ball-bearing, we need to find its radius (r). We can use the formula for the circumference of a circle:

Circumference = 2πr

Substituting the given circumference

43.4 mm = 2πr

To find the radius, divide both sides by 2π:

r = 43.4 mm / (2π) ≈ 6.9134 mm

Next, let's convert the radius to centimeters:

r = 6.9134 mm / 10 ≈ 0.69134 cm

Now we can calculate the volume of the ball-bearing using the formula for the volume of a sphere:

V = (4/3)πr^3

Substituting the radius:

V = (4/3)π(0.69134 cm)^3

Calculating this expression:

V ≈ 1.083 cm^3

Finally, to find the density, we divide the mass by the volume:

Density = Mass / Volume

Density = 11.9 g / 1.083 cm^3

Calculating this expression:

Density ≈ 10.981 g/cm^3

Therefore, the density of the metal in the ball-bearing is approximately 10.981 g/cm^3.

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The number 4.838 expressed as a ratio of integers is:

4.838 = 2419/500

To express 4.838 as a ratio of integers, we can follow these steps:

Multiply the number by a power of 10 to eliminate the decimal point. In this case, we can multiply by 1000, since there are three decimal places in 4.838:

4.838 x 1000 = 4838

Simplify the resulting fraction by dividing both the numerator and denominator by their greatest common factor (GCF). In this case, the GCF of 4838 and 1000 is 2, so we can divide both by 2:

4838 ÷ 2 = 2419

1000 ÷ 2 = 500

Therefore, 4.838 expressed as a ratio of integers is:

4.838 = 2419/500

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