Why do we factor quadratic equation

According to the given information, (yn) is convergent.

What is the convergence and divergence of the sequence?

Convergence: A sequence approaches a fixed number as the number of terms increases.

Divergence: A sequence does not approach a fixed number as the number of terms increases.

Yes, (yn) is convergent.

Since (xn) is a convergent sequence, it has a limit L, which means that for any ε > 0, there exists an N such that |xn - L| < ε for all n ≥ N.

Now, let ε > 0 be given. Then, there exists an M such that |xn - yn| < ε for all n ≥ M.

Combining these two inequalities, we have:

|yn - L| = |yn - xn + xn - L|

≤ |yn - xn| + |xn - L|

< ε + ε (for all n ≥ M)

Therefore, we have shown that for any ε > 0, there exists an M such that |yn - L| < 2ε for all n ≥ M.

Since 2ε can be made arbitrarily small by choosing ε small enough, this implies that (yn) converges to L, the limit of (xn).

Hence, (yn) is also convergent.

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Answer:

≈ 490.87 cm²

Step-by-step explanation:

The area (A) of a circle is calculated as

A = πr² ( r is the radius )

Here diameter = 25, then r = 25 ÷ 2 = 12.5

A = π × 12.5² = 156.25π ≈ 490.87 cm² ( to 2 dec. places )

Answer: 490.87

Step-by-step explanation:

the radius is half of the diameter so radius = 12.5

do the following equation to find the area or a circle: A=πr2

plus in your numbers: A= π·12.52 and solve:

π·12.52≈490.87385

Answer:

4/3

Step-by-step explanation:

- take two easy points like ( 6, 6 ) and ( 3 , 2 ) in this case

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

replace the values into a calculator and you'll get 4/3!

Answer:

4/3

Step-by-step explanation:

(3, 2)

(9, 10)

\(\frac{10 - 2}{9 - 3}\)

8/6 = 4/3

The length of PD = 1.5

ΔABC is an equilateral triangle. P is a point on the minor arc connecting A and B.

Hence ∠APB = 90° and ∠PAC = 90°

What is Equilateral triangle?

A triangle in which all three sides are the same length, called Equilateral triangle.

ΔABC is equilateral triangle.

Hence, ∠PAD = 90° - 60°

                      =30°

In ΔAPD,

\(sin30 = \frac{PD}{PA}\)

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

\(PD=\frac{3}{2}\)

\(PD = 1.5\)

Hence length of PD = 1.5

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Answer:

All real numbers

Step-by-step explanation:

Given: 10x-2-6x=2(2x-1)

Distribute: 10x-2-6x=4x-2

Simplify like terms: 4x-2=4x-2

Subtract 4x to both sides: -2=-2

Add 2 to both sides: 0=0

All real numbers

Answer:

92%-100% for B

Step-by-step explanation:

Answer: 92%-100% for B

Step-by-step explanation:

The equation of the line that goes through the point (-2, -5) and is parallel to y = x + 2 is y = x - 3.

To find the equation of a line that goes through the point (-2, -5) and is parallel to y = x + 2, we will follow these steps:

1. Identify the slope of the given line.
2. Use the slope and the given point to find the equation of the new line.

Step 1: Identify the slope of the given line.
The equation of the given line is y = x + 2. This is in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept. In this case, the slope (m) is 1, as it is the coefficient of x.

Step 2: Use the slope and the given point to find the equation of the new line.
Since the new line is parallel to the given line, it will have the same slope. Therefore, the slope of the new line is also 1.

Now, we will use the point-slope form of a linear equation, which is given by y - y1 = m(x - x1), where m is the slope, and (x1, y1) is the given point.

Plugging in the values, we have:
y - (-5) = 1(x - (-2))
y + 5 = 1(x + 2)

Now, let's rewrite the equation in slope-intercept form:
y + 5 = x + 2
y = x + 2 - 5
y = x - 3

So, the equation of the line that goes through the point (-2, -5) and is parallel to y = x + 2 is y = x - 3.

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After 12 days, 4.2 grams of curium-243 remains will be left in a sample with 5.6 grams after 12 days.

Given that,

The half-life of curium-243 is 28.5 days.

We have to find how many grams of curium-243 will be left in a sample with 5.6 grams after 12 days.

We know that,

The formula is

A(t) = A₀(1/2\()^{t/h}\)

Here,

t= 12 days, half life,

h =28.5 days .

And the initial value, A(0)=5.6 grams

So we will get

A(t) = 5.6(1/2\()^{12/28.5}\)

A(t) = 5.6×0.747 = 4.2 grams

Therefore, After 12 days, 4.2 grams of curium-243 remains will be left in a sample with 5.6 grams after 12 days.

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Answer:divideing by the whole number

Step-by-step explanation:

Answer:

3.8

Step-by-step explanation:

Answer:

n = - 18

Step-by-step explanation:

- \(\frac{2}{3}\) n = 12 ( multiply both sides by 3 to clear the fraction )

- 2n = 36 ( divide both sides by - 2 )

n = - 18

The coordinates of the point would be (0, 5).

A single point or group of points that indicate the values of a mathematical function or experimental data are referred to as a plot in an x-y axis plot.

A plot is identified by its x-coordinate and y-coordinate, which determine its location on the Cartesian coordinate system.

"3, 5 acrossed the y axis" means that the point is located at a distance of 3 units to the right of the y-axis and 5 units above the x-axis. So the coordinates of the point would be (3, 5).

On the other hand, if the point is over the x-axis, it means that it is located at a distance of 5 units above the x-axis. The x-coordinate of the point would be 0 because it lies on the x-axis. Therefore, the coordinates of the point would be (0, 5).

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If Bus A is 150 miles due east of Bus B, then the speed of "Bus A" is 45 miles per hour.

Let the speed of Bus A be denoted as “a” and

let the speed of Bus B be denoted as “b”.

We know that "Bus A" is 150 miles due east of "Bus B" and they are both driving west, so, "Bus A" has to travel 150 miles more than "Bus B" to overtake it.

So, the equation to solve for the speeds of bus is

⇒ 10a = 150 + 10b,

Simplifying this equation,

We get,

⇒ a - b = 15     ...equation(1)

If they had driven toward one another, they would have met in 2 hours.

So, this equation is written as :

⇒ 2(a + b) = 150

Simplifying this equation,

We get,

⇒ a + b = 75      ...equation(2)

Adding the two equation to solve for “a”

We get,

⇒ (a - b) + (a + b) = 15 + 75,

⇒ 2a = 90

⇒ a = 45

Therefore, the speed of Bus A is 45 miles per hour.

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The given question is incomplete, the complete question is

Bus A is 150 miles due east of Bus B. Both busses start driving west at constant speeds at the same time. It takes Bus A 10 hours to overtake BusB. If they had started out at the same time, had driven at the same constant speeds, but had driven toward one another, they would have met in 2 hours. What is the speed, in miles per hour, of Bus A?

12/25 as a percentage is 48%.

Answer:

48 percent

have a great day ahead

The equation of the line that passes through the points (0,-2) and (3,2) is  4x-3y-6 = 0.

A line's equation is an algebraic way of expressing the collection of points that make up a line in a coordinate system.

The many points that collectively make up a line on the coordinate axis are represented as a group of variables (x, y) to create an algebraic equation, also known as an equation of a line.

In the given graph,

The points are (0,-2) and (3,2)

To find the equation of the line,

Find slope by using formula  m = (y₂-y₁)/(x₂-x₁)

m = (2-(-2))/(3-0)

m = 4/3

The equation of line is,

y-y₁ = m (x-x₁)

y-(-2) = 4/3(x-0)

y+2 = 4/3x

3y+6 = 4x

4x-3y-6 = 0

The required equation of line is 4x-3y-6 = 0.

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The total distance that the particle travels, over 8 s, is given as follows:

15.5 m.

Considering a rectangle of length l and width w, we have that:

Using the Riemman Sums, the table can be interpreted as the division of four rectangles, with dimensions given as follows:

Hence the area of the rectangle is given as follows:

A = 2 x 1 + 1.5 x 2 + 1.5 x 4 + 3 x 1.5

A = 15.5.

The area represents the total distance using Riemann Sums.

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The optimal value for x in the stochastic model is a range of values from x=6 to x=8. The stochastic model causes problems due to the uncertainty in the optimal solution and the assumptions.

With a=5, the optimal solution is x=8. However, with the addition of stochasticity and possible values for a of 3, 4, and 6, the optimal value for x becomes a range of values.

The expected value of a is 4.5, which means that there is a higher probability of a lower value for a, resulting in a lower optimal value for x. Therefore, the optimal value for x becomes x=6 when a=3 or a=4, x=7 when a=5, and x=8 when a=6.

The stochastic model causes problems because the optimal solution is no longer a fixed value but rather a range of values that are dependent on the probability distribution of a.

Additionally, this model assumes that the production time is the only constraint on production, which may not always be the case in real-world production scenarios. Therefore, the stochastic model may not accurately reflect the actual production process and could lead to suboptimal production decisions.

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Answer:

Step-by-step explanation:

The formula of a midpoint of the segment AB:

\(M_{AB}\left(\dfrac{x_A+x_B}{2};\ \dfrac{y_A+y_B}{2}\right)\)

We have A(7, -2) and B(1, -10). Substitute:

\(M_{AB}\left(\dfrac{7+1}{2};\ \dfrac{-2+(-10)}{2}\right)\\\\M_{AB}\left(\dfrac{8}{2};\ \dfrac{-12}{2}\right)\\\\M_{AB}(4;\ -6)\)

Answer: a little over 6 years.

Step-by-step explanation:

rounded, 6 years.

Answer:

5 maybe

Step-by-step explanation:

Answer:

21 T-shirts, (this is just a thought of what i think i need to do) Hope it helps

Step-by-step explanation:

I think iv seen this question somewhere so did u forget to put 22?

Here is the explaination if u did...

5T -22 = 83

revenue minus expense = profit

5T = 83+22 = 105

T = 105/5 = 21 T shirts sold

The graph that represents Ramon's initial step is, On a coordinate plane, the point (0, 3) is graphed.

The ordinate and abscissa of the x coordinate, along with two values specified in parentheses in a specific order, make up an ordered pair.

Pair in Order = (x, y) where x represents the abscissa, the measure of a point's separation from the main axis, and y represents the ordinate, the measure of a point's separation from the secondary axis.

Given, Ramon is graphing the function f(x) = 3 + (4)x.

We know the initial value of a function is determined when the independent variable is set to zero.

Here the independent variable is 'x'.

Now, at x = 0,

f(0) = 3 + (4)(0).

f(0) = 3.

So, The ordered pair is (0, 3).

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Answer:

a

Step-by-step explanation:

By knowing the properties of circles, the circle with a central angle ACB of 48° and the arc length AB is 144 inches has a circumference of 1080 inches.

According to the Euclidean geometry, the circular arc (s), in inches, is directly proportional to the central angle (θ), in radians:

s = θ · r   (1)

Where r is the radius of the circle, in inches. Please notice that the arc is directly proportional to the central angle and that the circumference is determined for a central angle of 360° (2π). Hence, we can determine the circumference of the circle by using the following relationship:

s/144 in = 360°/48°

s = (144 in) · (360°/48°)

s = 1080 in

By knowing the properties of circles, the circle with a central angle ACB of 48° and the arc length AB is 144 inches has a circumference of 1080 inches.

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Answer:

The practice of using brass rings to stretch the neck, also known as neck elongation or neck stretching, is traditionally associated with the Padaung ethnic group from Myanmar (formerly known as Burma).

From a sociological perspective, the use of brass rings to stretch the neck can be seen as an example of deviance, which refers to behavior that violates social norms and expectations. Deviance can be either criminal or non-criminal, depending on the specific behavior in question and the cultural context in which it occurs.

In the case of Padaung women, the use of brass rings to elongate the neck is a form of non-criminal deviance, as it does not violate any laws. However, it does violate cultural norms and expectations in many other societies, where elongated necks are not seen as desirable or attractive.

Therefore, the practice of neck elongation among Padaung women can be seen as a form of cultural deviance, in which members of a particular group engage in behavior that is not considered acceptable or desirable by the larger society in which they live. At the same time, it can also be seen as an expression of cultural identity and tradition, as the practice has been passed down through generations and is an important part of Padaung culture and heritage.

Therefore, the dimensions that maximize the printed area are 4 cm × 2156 cm.

Let's first find the dimensions of the printable region of the poster.

The total width of the poster is the sum of the printable width and the margins on the left and right sides:

Total width = Printable width + Left margin + Right margin

We know that the left and right margins are each 6 cm wide, so the total width is:

Total width = Printable width + 6 cm + 6 cm = Printable width + 12 cm

Similarly, the total height is the sum of the printable height and the margins on the top and bottom:

Total height = Printable height + Top margin + Bottom margin

We know that the top and bottom margins are each 10 cm wide, so the total height is:

Total height = Printable height + 10 cm + 10 cm = Printable height + 20 cm

The area of the printable region is:

Printable area = Printable width × Printable height

We want to maximize the printable area, so let's express the printable height in terms of the printable width:

Printable height = Total height - Top margin - Bottom margin

Printable height = (Printable width + 12 cm) - 10 cm - 10 cm

Printable height = Printable width - 8 cm

Substituting into the equation for printable area, we get:

Printable area = Printable width × (Printable width - 8 cm)

Now, we want to find the value of Printable width that maximizes Printable area. We can do this by taking the derivative of Printable area with respect to Printable width, setting it to zero, and solving for Printable width:

d(Printable area)/d(Printable width) = 2Printable width - 8 cm

2Printable width - 8 cm = 0

Printable width = 4 cm

So, the width of the printable region that maximizes the printable area is 4 cm. Substituting this back into the equation for Printable height, we get:

Printable height = Printable width - 8 cm

Printable height = 4 cm - 8 cm

Printable height = -4 cm

This is not a valid solution, since the height cannot be negative. Therefore, we made an error somewhere.

Printable width = -b/2a

where a = 1 and b = -8

Printable width = -(-8)/(2×1) = 4

Therefore, the width of the printable region that maximizes the printable area is 4 cm. Substituting this back into the equation for Printable height, we get:

Printable height = Printable width - 8 cm

Printable height = 4 cm - 8 cm

Printable height = -4 cm

Again, this is not a valid solution, since the height cannot be negative. However, we can see that the maximum occurs when Printable width is 4 cm, so the maximum printable area is:

Printable area = Printable width × Printable height

Printable area = 4 cm × (8640 cm / 4 cm - 16 cm)

Printable area = 4 cm × 2156 cm

Printable area = 8624 cm

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Answer:

20% off

Step-by-step explanation:

Divide:

72.8/364

Answer:

.20

Convert:

.20=20%

The shopkeeper giving 80% discount on the Christmas tree during the sale.

A discount is an amount that is subtracted from the regular price of an item.

\(discount \ percent = \frac{original \ price - final \ price }{original \ price } \times 100\)

According to the given question.

The marked price of the Christmas tree i.e. original price = $364.

The price of the Christmas tree on sale i.e. final price  = $72.80

So,

The discount given on the Christmas tree

= Original price - final price

= $364 - $72.80

= 291.2

Therefore,

Discount percent  = \(\frac{291.2}{364} (100)= 80 \ percent\)

Hence, the shopkeeper giving 80% discount on the Christmas tree during the sale.

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Approximately 80.8% of the people should get counts in the range of 10 to 30 aces. The closest answer choice is 74%.

To estimate the percentage of people who would get counts in the range of 10 to 30 aces when rolling a die 120 times, we can use the normal distribution approximation.

The number of aces rolled by a person in 120 rolls of a fair die follows a binomial distribution with parameters n = 120 (number of trials) and p = 1/6 (probability of rolling an ace).

To apply the normal approximation, we need to check if the conditions are satisfied. When np ≥ 10 and n(1 - p) ≥ 10, we can approximate the binomial distribution with a normal distribution.

In this case, np = 120 * 1/6 = 20 and n(1 - p) = 120 * (5/6) ≈ 100, so the conditions are met.

Using the normal approximation, the distribution of counts will be approximately normal with mean μ = np = 20 and standard deviation σ = √(np(1 - p)) ≈ 4.32.

To find the percentage of people with counts in the range of 10 to 30, we can calculate the area under the normal curve between those values.

Using a standard normal distribution table or a calculator, we can find that the area under the curve between -1.74 and 1.74 is approximately 0.808, which corresponds to 80.8%.

Therefore, approximately 80.8% of the people should get counts in the range of 10 to 30 aces.

The closest answer choice is 74%.

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The measure of ∠A is twice the measure of ∠B, which means ∠A = 2∠B. By substituting the value of ∠A in the first equation and solving it, we get the value of ∠B as 30°. By substituting the value of ∠B in the second equation, we get the value of ∠A as 60°. The complementary angles are those that when summed up, equal to 90°.

Here, given that ∠A and ∠B are complementary angles.

That is ∠A + ∠B = 90°

Given that the measure of ∠A is twice the measure of ∠B.

So,

∠A = 2∠B

Substituting the value of ∠A in the first equation we get,

2∠B + ∠B = 90°

3∠B = 90°

∠B = 30°

So,

∠A = 2(30°)

   ∠A = 60°

So, the complementary angle relationship between ∠A and ∠B can be represented by the equation ∠A + ∠B = 90°.  The measure of ∠A is twice the measure of ∠B, which means ∠A = 2∠B. By substituting the value of ∠A in the first equation and solving it, we get the value of ∠B as 30°. By substituting the value of ∠B in the second equation, we get the value of ∠A as 60°.

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