What is the greatest common factor of the polynomial below?
12x²9x
OA. 4x
OB. 3x
OC. 4x²
OD. 3x²

Using limits the value of k is c √2

The limit of a function is the valuer the function tends to as the dependent variable tends to a particular value.

Given that the limit lim n → ∞ [x√(x + 1)[1 - √(2x + 3)]/(7 - 6x + kx²) = - 1, we desirte to find the value of k.

So, we proceed as follows

lim n → ∞ [x√(x + 1)[1 - √(2x + 3)]/(7 - 6x + kx²) = - 1

Factorizing out √2x, we have that

lim n → ∞ [x√(x + 1)[1 - √(2x√(1 + 3/√(2x)]/(7 - 6x + kx²) = - 1

lim n → ∞ [x√(x + 1)√(2x[1/√(2x - √(1 + 3/√(2x)]/(7 - 6x + kx²) = - 1

Also, factorizing out √x, we have that

lim n → ∞ [x√x√(1 + 1/√x)√2x[1/√(2x - √(1 + 3/√(2x)]/(7 - 6x + kx²) = - 1

lim n → ∞ [x√x√2x√(1 + 1/√x)[1/√(2x - √(1 + 3/√(2x)]/(7 - 6x + kx²) = - 1

lim n → ∞ [x√2x√(1 + 1/√x)[1/√(2x - √(1 + 3/√(2x)]/(7 - 6x + kx²) = - 1

lim n → ∞ [√2x²√(1 + 1/√x)[1/√(2x - √(1 + 3/√(2x)]/(7 - 6x + kx²) = - 1

Factorizing x² from the denominator, we have that

lim n → ∞ [√2x²√(1 + 1/√x)[1/√(2x - √(1 + 3/√(2x)]/x²(7/x² - 6/x + k) = - 1

lim n → ∞ [√2√(1 + 1/√x)[1/√(2x - √(1 + 3/√(2x)]/(7/x² - 6/x + k) = - 1

Now substituting x = ∞ into the equation, we have that

[√2√(1 + 1/√∞)[1/√(2∞ - √(1 + 3/√(2∞)]/(7/∞² - 6/∞ + k) = - 1

[√2√(1 + 0)[0 - √(1 + 0]/(0 - 0 + k) = - 1

[√2√(1)[- √1]/k = - 1

[√2(1)[- 1]/k = - 1

-√2/k = - 1

k = -√2/-1

k = √2

So, the value of k is c √2

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The frequency for the interval 160-169 seconds is 3.

The value that appears the most frequently in a data set is its mode. In the data set, it is the number that appears the most frequently. For instance, in the subsequent data set:

2, 3, 4, 4, 5, 5, 5, 6, 7, 8

Since no other value appears more frequently, the mode is 5, which only appears three times. The data set is considered to have several modes if various values occur with the same greatest frequency. There is no mode if no value appears more than once in the data collection.

From the given table we see that the songs that have the time duration between 160 and 169 is:

162, 168, 165

Hence, the frequency for the interval 160-169 seconds is 3.

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The complete question is:

The simplest form of the expression "(14ab³)/(7a⁻²b⁻¹)" is represented by the expression (d) 2a³b⁴.

To simplify the expression (14ab³)/(7a⁻²b⁻¹), we first simplify the terms with the same base,

First, we simplify the coefficients "14" and "7" by dividing them to get:

⇒ (14ab³)/(7a⁻²b⁻¹) = 2ab³/a⁻²b⁻¹;

Next, we simplify the variables "a" and "b" by subtracting the exponents of "a" and "b" in the denominator respectively,

We get,

⇒ 2ab³/a⁻²b⁻¹ = 2a¹⁻⁽⁻²⁾b³⁻⁽⁻¹⁾ = 2a¹⁺²b³⁺¹ = 2a³b⁴,

Therefore, the simplest form of the expression (14ab³)/(7a⁻²b⁻¹) is 2a³b⁴, the correct option is (d).

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The given question is incomplete, the complete question is

Look at this expression. (14ab³)/(7a⁻²b⁻¹),

Which of the following is the simplest form of the expression above?

(a) 2a⁻²b⁻³

(b) 2a⁻¹b²

(c) 2[tex]a^{-\frac{1}{2} }[/tex]b⁻³

(d) 2a³b⁴.

It shtbe noted that 68% of the data should fall in the interval from 616 to 756.

z score for values:

z = (X-µ)/σ = (616-686)/70 = -1

z = (X-µ)/σ = (756-686)/70 = 1

Approximately 68% of the data should fall in the interval from 616 to 756.

b) B. 71% of the data falls in the interval from 616 to 756. The estimate is very close to the value predicted by the Empirical Rule.

c) (µ - 2*σ, µ + 2*σ)

(686 - 2*70, 686 + 2*70)

(546, 826)

You expect to find about 95% of the teams between the two values 546 and 826.

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Answer:

a) The scale factor is [tex]\frac{4}{5}[/tex]

b) [tex]t=5\frac{3}{5}[/tex]

Step-by-step explanation:

The scale factor from shape A to shape B is the value that is multiplied by the side measures of shape A to arrive at the side measures of shape B.

In other words, 5 times a certain value is 4, 15 times a certain value is 12. and 7 times a certain value is t.

Let's start by calling our "certain value" k.

[tex]5k=4=\\k=\frac{4}{5}[/tex]

Let's check 15 to make sure k is 4/5, like so:

[tex]15(\frac{4}{5})=\\\frac{60}{5} =\\12[/tex]

Since 15 times 4/5 is twelve, our initial answer was correct.

So, the scale factor, or k, is 4/5.

Following this logic, we know that 7 multiplied by the scale factor is equal to t.

Let's set up an equation and solve for t:

[tex]7(\frac{4}{5} )=t=\\\frac{28}{5} =t=\\5\frac{3}{5} =t[/tex]

So, [tex]t=5\frac{3}{5}[/tex]

Answer: #1

Step-by-step explanation:

In situation number one, the equation for the garden's area would be [tex]x^2[/tex] which is nonlinear. The other questions map to linear equations in the form [tex]y = mx + b[/tex]

Answer:

Linear relationship always produces a straight line and are without exponential.

2.the height, y, of a 6-foot tree that grows 0.2 feet per month for x months

3.the total cost, y, of a ski rental from a company that charges $15 plus an additional $8 per day rented for x days

4. the total miles, y, traveled by a car going 62 miles per hour in x hours

Step-by-step explanation:

Hope this helps! =D

Answer:

The answer is D. 4(sqrt(5))

Step-by-step explanation:

To find this we use the Pythagorean Theorem a^2+b^=c^2

So making 4 = to a, and 8 = to, and x = to, we do

4^2+8^2= 80

Then we take the square root of 80 to find the missing side, which is equal to 4(sqrt(5)

Good luck!

The average height of the soccer team is 77.45 inches, and the average height of the basketball team is 79 inches.

To find the average height of each team, we'll sum up the heights and divide by the number of players on each team.

Soccer team average height:

Sum of heights: 60+61+...+87+88 = 2,246 inches

Number of players: 29

Average height: 2246 / 29 = 77.45 inches

Basketball team average height:

Sum of heights: 72+73+...+86+87 = 1,264 inches

Number of players: 16

Average height: 1264 / 16 = 79 inches

So, the average height of the soccer team is 77.45 inches, and the average height of the basketball team is 79 inches.

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Soccer team heights (in inches):

60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88

Basketball team heights (in inches):

72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87

Jason wants to find more information about the heights of players on his school's soccer team and his school's basketball team. Jason surveys 29 members of the soccer team and 16 members of the basketball team. The heights of the soccer team and basketball team players are given above. What is the average height of the soccer team and the basketball team?

A line plot that represents the data is shown in the image attached below.

A fraction of an hour which Rita spend most days writing is 3/4.

The difference between the greatest amount of time spend writing and the least is 3/4.

In Mathematics and Statistics, a line plot is a type of graph that is used for the graphical representation of data set above a number line, while using crosses, dots, or any other mathematical symbol.

In this scenario and exercise, we would use an online graphing calculator to graphically represent the given data set on a line plot as shown in the image attached below.

Additionally, we can logically deduce that the mode of the data set is equal to 3/4 (the fraction of an hour Rita spend most days writing) because it has the highest frequency of 5.

Difference = greatest amount of time - least amount of time

Difference = 1 - 1/4

Difference = 3/4.

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Answer:

y =- [tex]\frac{3}{4}[/tex] x + 1

Step-by-step explanation:

This is a linear equation: y = mx + b

Answer:

The area of the shaded region is 27 units^2.

Step-by-step explanation:

Area of outer square = 6^2 = 36 units^2

Area of inner square = 3^2 = 9 units^2

Area of shaded region

= 36 units^2 - 9 units^2 = 27 units^2

The area of a shaded region in a unit grid can be found either by subtracting the area of unshaded regions from the total grid area or by adding up the areas of identifiable shapes within the shaded region.

To find the area of the shaded region without counting every square, you can use a few different strategies, such as identifying and subtracting the area of unshaded regions from the total grid area, or recognizing and adding together larger, easily countable shapes within the shaded region.

For example, if your grid is 10x10 units, the total area would be 100 square units. If, within that grid, there are 20 unshaded squares, you can subtract this from the total area to find the area of the shaded region. So, 100 total square units - 20 unshaded square units = 80 shaded square units. This approach works best when the number of unshaded squares is relatively small or easily countable.

Alternatively, if the shaded region forms easily identifiable shapes (like a 5x5 square or a 3x10 rectangle), you can add the areas of these shapes together to get the total shaded area. This approach works best when the shaded region forms a few large, simple shapes.

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Answer:

x<1

Step-by-step explanation:

looking at the graph, the x values are 0,-1,-2,-3,-4,-5.

therefore, all the values of x are below 1.

x<1 is the suitable inequality that matches the graph.

Therefore , the solution of the given problem of volume comes out to be the other leg of the right triangular pyramid's base is 12 yards long.

The volume of a three-dimensional item, which is measured in cubic units, describes how much room it occupies. Litre and in3 are the symbols for cubic measurements. However, in order to determine an object's dimensions, you must be aware of its volume. It's common practise to translate an object's weight onto metric units like kilogrammes.

Here,

Let's use "x" yards to represent the unknown leg of the right triangular pyramid's base.

A pyramid's volume can be calculated using the following equation: => => Volume = (1/3) * Base Area * Height

In this instance, the height of the pyramid is 14 yards, and its base is a right triangle with legs that are 8 yards and 'x' yards in length.

Consequently, we can formulate the equation for the pyramid's volume as follows:

=> 168 = (1/3) * (8 * x) * 14

The simplified formula gives us 168 = (4/3) * 14 * x.

We may find "x" by dividing both sides of the equation by

=> [(4/3)*14]: 168 / [(4/3)*14] = x.

=> x = 12

Therefore, the other leg of the right triangular pyramid's base is 12 yards long.

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The measures of the angles are

MSR = 42

MSCQ = 138 degree

mSQR = 318 degrees

mQV = 42 dgerres

MSCQ + MSCR = 180

MSR = MSCR = 42

MSCQ + 42 = 180

MSCQ = 138 degree

MSQR = 360 - 42

= 318 degrees

MQV = MSR vertically opposite

= 42 degree

MQSR = 1/2 x 42

= 21 degrees

MQV = 1/2 x 180 = 90 degrees

The measures of the angles have been solved for

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The number of hours Matt babysits his sister is 1 and half hours.

Given that, Matt's parents pay him $5.50 for each half hour he babysits his sister, plus a two dollar tip.

Let the number of half an hours Matt babysits his sister be x.

Matt made $18.50

So, equation is 5.50x+2 =18.50

5.50x=16.50

x=16.50/5.50

x= 3

Which means 1 and half hours he babysits his sister.

Therefore, the number of hours Matt babysits his sister is 1 and half hours.

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a) Jill receives £45

b) Jack receives £20 the following Christmas

c) Jack will be 5/4 years old, which is equivalent to 1 year and 3 months when he receives £25 from Uncle Fred.

Explain the term years

Years are a unit of time measurement used to quantify the duration of one complete orbit of the Earth around the sun. A year consists of 365 days, except in a leap year when an extra day is added. The concept of a year is used in various fields, including astronomy, geology, and history.

According to the given information

(a) Let's first find the total ratio of their ages:

1 + 3 = 4

So Jack's share will be:

1/4 x £60 = £15

And Jill's share will be:

3/4 x £60 = £45

Therefore, Jill receives £45.

(b) The next Christmas, Jack will be 2 and Jill will be 4. We can use the same ratio to find Jack's share:

2/6 x £60 = £20

So Jack receives £20.

(c) Let x be the age of Jack when he receives £25 from Uncle Fred. We know that:

1/4 x £60 = £25

Multiplying both sides by 4/60, we get:

x = 5/4

So Jack will be 5/4 years old, which is equivalent to 1 year and 3 months, when he receives £25 from Uncle Fred.

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There are a total of 2000 workers in​ all in the company

From the question, we have the following parameters that can be used in our computation:

Women percentage = 80%

People not women = 400

Using the above as a guide, we have the following:

People not women percentage = 1 - 80%

Evaluate

People not women percentage = 20%

So, we have

People not women = People not women percentage * Total

substitute the known values in the above equation, so, we have the following representation

20% * Total = 400

Divide

Total = 2000

Hence. there are 2000 people in the company

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Total stored energy = (1/625) ∞

Voltage, also known as electric potential difference, is the measure of the electric potential energy per unit of charge in an electric circuit. It is the force that drives the electric charge in a circuit, similar to how pressure drives water through a pipe. Voltage is measured in volts (V) and is usually represented by the symbol "V". Voltage can be either positive or negative, depending on the direction of current flow and the orientation of the voltage source.

A. The voltage across an inductor is proportional to the time derivative of the current through it, according to Faraday's law of electromagnetic induction. This can be expressed mathematically as:

v(t) = L di/dt

where v(t) is the voltage across the inductor, L is the inductance in henries, and di/dt is the time derivative of the current through the inductor.

In this case, we have [tex]v(t) = 8e^{(-4t)[/tex] V and L = 250 H. Integrating both sides of the above equation with respect to time gives:

∫v(t) dt = L ∫di/dt dt

∫[tex]8e^{(-4t)} dt = 250[/tex] ∫di/dt dt

[tex]-2e^{(-4t)[/tex]= 250i(t) + C

where C is the constant of integration. We can assume that the initial current is zero, so at t = 0, i(0) = 0. This means that C = -2. Substituting this into the equation above, we get:

[tex]-2e^{(-4t)[/tex]= 250i(t) - 2

Solving for i(t), we get:

i(t) = (2/250) [tex]- (2/250)e^{(4t)[/tex]

B. The power absorbed by an inductor is given by:

P = i² R

where P is the power, i is the current, and R is the resistance of the circuit. In an ideal inductor, the resistance is zero, so the power absorbed is also zero.

However, the energy stored in an inductor can be calculated using the following formula:

E = 1/2 L i²

where E is the energy stored, L is the inductance, and i is the current.

In this case, we have L = 250 H and i(t) = (2/250) [tex]- (2/250)e^{(4t)[/tex]Substituting these values into the above equation, we get:

E = 1/2 (250) [(2/250) [tex]- (2/250)e^{(4t)]^2[/tex]

Simplifying this expression, we get:

E = (1/625) [tex]- (2/625)e^{(4t)[/tex]+ (2/625)e^(8t)

To determine the total stored energy, we need to integrate this expression over the interval 0 to infinity, since the voltage and current are given for all values of t. This gives:

Total stored energy = ∫E dt from 0 to infinity

Total stored energy = (1/625) ∫1 dt from 0 to infinity[tex]- (2/625) ∫e^{(4t)[/tex]dt from 0 to infinity + (2/625) ∫e^(8t) dt from 0 to infinity

Total stored energy = (1/625) ∞ [tex]- (2/625) [1/4 e^{(4t)][/tex]from 0 to infinity + (2/625) [1/8 e^(8t)] from 0 to infinity

Since the integrals involving exponential functions go to infinity as t goes to infinity, these terms become zero. Therefore, we are left with:

Total stored energy = (1/625) ∞

which is an infinite value. This is because the energy stored in an inductor is not finite, but rather is dependent on the magnetic field generated by the inductor, which can extend infinitely far.

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Answer:

See below!

Step-by-step explanation:

Length = x + 4 cm

Width = 2x - 7 cm

Perimeter:

Put the given data.

36 = 2(x + 4) + 2(2x - 7)

36 = 2x + 8 + 4x - 14

36 = 2x + 4x + 8 - 14

36 = 6x - 6

36 + 6 = 6x

42 = 6x

42/6 = x

7 = x

OR

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

Put x = 7

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

Area = 11(14 - 7)

Area = 11(7)

[tex]\rule[225]{225}{2}[/tex]

Answer: (a) x=7

(b) area of this rectangle = 77[tex]cm^{2}[/tex]

Step-by-step explanation:

(a) the perimeter of a rectangle = 2 * [  l + b ]

36 = 2 * [ (x + 4) + (2x - 7) ]

36 / 2 = x + 4 + 2x - 7

18 = 3x -3

18 + 3 = 3x

21 = 3x

x = 7

(b) the area of a rectangle = l * b

l = x + 4 = 11cm

b = 2x -7 = 7cm

therefore, 11cm * 7cm = 77[tex]cm^{2}[/tex]

The calculated area of each piece is 1/12 acre

If Barry buys a plot of land that measures 1/4 acre, then the total area of the land is 1/4 acre.

If he divides the land into 3 equal pieces, then each piece will have 1/3 of the total area.

So the area of each piece will be:

Area of each piece = (1/3) x (1/4) acre

Multiplying the fractions, we get:

Area of each piece = 1/12 acre

Therefore, each piece of land will have an area of 1/12 acre.

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The values of x, y and z are given as follows:

The geometric mean theorem states that the length of the altitude drawn from the right angle of a triangle to its hypotenuse is equal to the geometric mean of the lengths of the segments formed on the hypotenuse.

The bases for the triangle in this problem are given as follows:

6 and 19.

Hence the segment x is obtained as follows:

x² = 6 x 19

x = sqrt(6 x 19)

x = 10.68.

Applying the Pythagorean Theorem, the value of y is given as follows:

y² = 6² + 10.68²

y = sqrt(6² + 10.68²)

y = 12.25.

The value of z is given as follows:

z² = 10.68² + 19²

z = sqrt(10.68² + 19²)

z = 21.8.

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Answer:

(a) The product xy is negative because one of the factors (x) is negative and the other factor (y) is positive. Therefore, the sign of xy is negative.

(b) The expression x^2y is also negative because x^2 is positive (the square of any real number is positive) and y is positive, so their product is positive. But since x is negative, the overall product is negative.

(c) The expression x/y + x can be written as (x/x)y + x, which simplifies to y + x. Since y is positive and x is negative, the sum y + x could be either positive or negative, depending on which absolute value is greater. If |y| > |x|, then y + x is positive. If |x| > |y|, then y + x is negative.

(d) The expression y-x is positive because y is greater than x and y is positive while x is negative. So the difference y-x is positive.

As a result, the sequence's tenth term is 142 as the 10th term of the arithmetic sequence with a first term of 7 and a common difference of 15.

An arithmetic progress (AP) in mathematics is a set of numbers where each term following the first is formed by adding a predetermined constant to the term before it. The mathematical progression's common difference is the name of this unchanging constant. For instance, the number progression 3, 7, 11, 15, 19,... has a common difference of 4 and is an arithmetic progression. The formula: yields the nth word of an arithmetic progression. a n = a 1 + (n - 1)d where n is the desired term's number, a n is the sequence's nth term, a 1 is its first term, d is its clear differentiation, and n is its number.

given

We can use the following formula to determine the 10th term of the arithmetic sequence with a first term of 7 and a common difference of 15:

a n = a 1 + (n - 1) * d

where a n represents the nth term in the series, a 1 represents the first term, d represents the common difference, and n is the desired term's number.

Inputting the values provided yields:

[tex]a 10 = 7 + (10 - 1) (10 - 1) * 15 \\a 10 = 7 + 9 * 15 \\a 10 = 7 + 135 \\a 10 = 142[/tex]

As a result, the sequence's tenth term is 142 as the 10th term of the arithmetic sequence with a first term of 7 and a common difference of 15.

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Answer:

380

Step-by-step explanation:

The formula for the area of a circle is A = pi r^2

radius is half the diameter so you would do 11 (half of diameter) to the second power, which is 121. Now you would do 121 times pi, which would be 380.132711084. When rounded to the nearest whole, it is 380.

SORRY IF THIS DIDN'T MAKE SENSE!

As a result, the square office's carpet replacement would cost $786.69 in total as where a square meter costs $87.41.

The geometric shape of a square has 4 equal ends and four equal, right-angled angles (90 degrees). It is an unusual instance of a rectangle with equal sides. The symbol "" is frequently used to denote a square, which is a two-dimensional figure. A square's area is equal to the sum of its sides doubled, or s2, where s denotes the width of a side. The circumference of a square, or 4s, where s is the height of a side, is the total of the lengths among all four sides. Many real-world uses for squares can be found in the fields of mathematics, architecture, construction, and design.

given

The square office's area is:

[tex]C = 9 \times $87.41 = $786.69[/tex]

A = s2 = 3 2 = 9 metres square

To completely replace the carpet, it would cost:

Cost per square meter equals C = A.

where a square meter costs $87.41. When we change the values, we obtain:

As a result, the square office's carpet replacement would cost $786.69 in total as where a square meter costs $87.41.

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Answer:

Step-by-step explanation:

125 pounds decreased by 4%  it would be 120 because 4% of 125 is 5, so you subtract 5 from 125 and then you get 120.

The surface area of the triangular prism is 672 square millimeters.

what is surface area ?

Surface area is a metric used to determine how much overall space an object occupies. the total volume of the area of surface of a three-dimensional shape. The term "surface area" refers to a three-dimensional shape's entire surface area.

The triangular base has a height of 7 mm and a base of 24 mm, so its area is:

[tex]1/2 * base * height = 1/2 * 24 \ mm * 7\ mm = 84 \ mm^2[/tex]

There are two identical triangular faces, so their combined area is:

[tex]2 * 84 \ mm^2 = 168\ mm^2[/tex]

The three rectangular faces are all the same size, with a length of 24 mm and a height of 7 mm, so the area of each is:

[tex]length * height = 24 \ mm * 7 \ mm = 168 \ mm^2[/tex]

There are three rectangular faces, so their combined area is:

[tex]3 * 168\ mm^2 = 504\ mm^2[/tex]

To find the total surface area, we add the area of the two triangular faces to the area of the three rectangular faces:

[tex]168 \ mm^2 + 504 \ mm^2 = 672 \ mm^2[/tex]

Therefore, the surface area of the triangular prism is 672 square millimeters.

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