insert a monomial into each trinomial such that the results is a perfect square. 16y^2+ ...+81

Answer:

x=4

Step-by-step explanation:

-18 x 4 x -15 = -87

Answer:

-18x-15=-87

-(18x+15)=-(87)

18x+15=87

18x=87-15

18x=72

x=4

Let F (n) denote the integral,

∫ x (1 - ln(x))ⁿ dx

We attempt to find a power-reduction formula for F (n) in terms of F (n - 1). Integrate by parts, with

u = (1 - ln(x))ⁿ   →   du = - n/x (1 - ln(x))ⁿ ⁻¹ dx

dv = x dx   →   v = 1/2 x ²

Then

F (n) = u v - ∫ v du

F (n) = 1/2 x ² (1 - ln(x))ⁿ + n/2 ∫ x (1 - ln(x))ⁿ ⁻¹ dx

F (n) = 1/2 x ² (1 - ln(x))ⁿ + n/2 F (n - 1)

From this relation, we get

F (n - 1) = 1/2 x ² (1 - ln(x))ⁿ ⁻¹ + (n - 1)/2 F (n - 2)

F (n - 2) = 1/2 x ² (1 - ln(x))ⁿ ⁻² + (n - 2)/2 F (n - 3)

F (n - 3) = 1/2 x ² (1 - ln(x))ⁿ ⁻³ + (n - 3)/2 F (n - 4)

and so on, down to

F (1) = 1/2 x ² (1 - ln(x)) + 1/2 F (0)

where

F (0) = ∫ x dx = 1/2 x ² + C

By recursively substituting, we find

→   F (n) = 1/2 x ² (1 - ln(x))ⁿ + n/2 [1/2 x ² (1 - ln(x))ⁿ ⁻¹ + (n - 1)/2 F (n - 2)]

… = 1/2 x ² (1 - ln(x))ⁿ + n/2² x ² (1 - ln(x))ⁿ ⁻¹ + (n (n - 1))/2² F (n - 2)

→   F (n) = 1/2 x ² (1 - ln(x))ⁿ + n/2² x ² (1 - ln(x))ⁿ ⁻¹ + (n (n - 1))/2² [1/2 x ² (1 - ln(x))ⁿ ⁻² + (n - 2)/2 F (n - 3)]

… = F (n) = 1/2 x ² (1 - ln(x))ⁿ + n/2² x ² (1 - ln(x))ⁿ ⁻¹ + (n (n - 1))/2³ x ² (1 - ln(x))ⁿ ⁻² + (n (n - 1) (n - 2))/2³ F (n - 3)

→   F (n) = 1/2 x ² (1 - ln(x))ⁿ + n/2² x ² (1 - ln(x))ⁿ ⁻¹ + (n (n - 1))/2³ x ² (1 - ln(x))ⁿ ⁻² + (n (n - 1) (n - 2))/2³ [1/2 x ² (1 - ln(x))ⁿ ⁻³ + (n - 3)/2 F (n - 4)]

… = 1/2 x ² (1 - ln(x))ⁿ + n/2² x ² (1 - ln(x))ⁿ ⁻¹ + (n (n - 1))/2³ x ² (1 - ln(x))ⁿ ⁻² + (n (n - 1) (n - 2))/2⁴ x ² (1 - ln(x))ⁿ ⁻³ + (n (n - 1) (n - 2) (n - 3))/2⁴ F (n - 4)

and so on, down to

F (n) = 1/2 x ² (1 - ln(x))ⁿ + n/2² x ² (1 - ln(x))ⁿ ⁻¹ + … + (n (n - 1) … 2 × 1)/2ⁿ F (0)

F (n) = 1/2 x ² (1 - ln(x))ⁿ + n/2² x ² (1 - ln(x))ⁿ ⁻¹ + … + (n (n - 1) … 2 × 1)/2ⁿ ⁺¹ x ² + C

We can write this more compactly as the sum,

\(F(n)=\displaystyle\int f_n(x)\,\mathrm dx=x^2\sum_{k=0}^n \frac{n!}{2^{k+1} (n-k)!} (1-\ln(x))^{n-k} + C\)

or

\(F(n)=\displaystyle\int f_n(x)\,\mathrm dx=x^2\sum_{k=0}^n \frac{k!}{2^{k+1}}\binom nk(1-\ln(x))^{n-k} + C\)

where \(\binom nk=\frac{n!}{k!(n-k)!}\) is the binomial coefficient.

HOPE IT HELPS YOU

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Answer:

Step-by-step explanation:

You want the area of a 16-unit circle using different values for pi.

The formula for the area of a circle is ...

  A = πr² . . . . . . where r is half the diameter

For the different values of pi, this will be (in square units) ...

  π(8²) = 64π . . . . exact

  3.14(8²) = 200.96 . . . . using 3.14 for π, slightly low

  22/7(8²) = 201 1/7 . . . . using 22/7 for π, slightly high

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A bird flies from a nest that is 822 3/10 feet above sea level to the bottom of a canyon that is 56 1/10 feet below it.

The canyon is 737 feet higher than the bird's nest, by a difference of 3 feet.

based on the facts provided, we know that;

The depth below sea level is 52 3/ 5 feet, hence the value would be negative.

The height above sea level is 789 3/ 10, which requires a positive number.

Let's convert the improper fractions from the mixed fractions;

= - 263/ 5 = - 52. 6 feet

789 3/ 10 = 7893/ 10 = 789. 3 ft

the canyon's and the bird's nest's contrasting elevations;

= -52. 6 + 789. 9

Equals 737. 3 feet

Consequently, there is a 737. 3 foot difference in height between the canyon and the bird's nest.

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The rational function represented in the given graph is; f(x) = 1/(x - 4)

From the given graph , the vertical asymptote is at x = 4

Let's find out the vertical asymptote of each function

To find out vertical asymptote we set the denominator = 0

A) x + 4 = 0

x = -4

This is not correct

B) 4x = 0

x = 0

Not correct

C) Denominator does not have a variable and so is also incorrect

D) x - 4 = 0

x = 4

Thus, this is correct

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(a) the expected value of the amount you win 2/9 , (b) the variance of the amount you win 5/18 , c) The expected value of the amount you win is -$0.0667 and d)The variance of the amount you win is 1.2898.

Let's calculate the expected value and variance of the amount you win step by step:

a) Calculate the probability of drawing two marbles of the same color.

First, calculate the probability of drawing two red marbles:

P(RR) = (5/10) * (4/9) = 20/90 = 2/9

Similarly, calculate the probability of drawing two blue marbles:

P(BB) = (5/10) * (4/9) = 20/90 = 2/9

b) Calculate the probability of drawing two marbles of different colors.

P(RB) = (5/10) * (5/9) = 25/90 = 5/18

P(BR) = (5/10) * (5/9) = 25/90 = 5/18

c) Calculate the expected value.

The expected value (EV) is calculated by multiplying each outcome by its probability and summing them up.

EV = (P(RR) * $1.10) + (P(RB) * -$1.00) + (P(BR) * -$1.00) + (P(BB) * $1.10)

= (2/9 * $1.10) + (5/18 * -$1.00) + (5/18 * -$1.00) + (2/9 * $1.10)

= $0.2444 - $0.2778 - $0.2778 + $0.2444

= -$0.0667

Therefore, the expected value of the amount you win is -$0.0667.

d) Calculate the variance.

The variance is a measure of the dispersion of the outcomes around the expected value. It is calculated as the sum of the squared differences between each outcome and the expected value, weighted by their probabilities.

Variance = (P(RR) * ($1.10 - EV)²) + (P(RB) * (-$1.00 - EV)²) + (P(BR) * (-$1.00 - EV)²) + (P(BB) * ($1.10 - EV)²)

Variance = (2/9 * ($1.10 - (-$0.0667))²) + (5/18 * (-$1.00 - (-$0.0667))²) + (5/18 * (-$1.00 - (-$0.0667))²) + (2/9 * ($1.10 - (-$0.0667))²)

= (2/9 * $1.1667²) + (5/18 * -$0.9333²) + (5/18 * -$0.9333²) + (2/9 * $1.1667²)

= 1.2898

Therefore, the variance of the amount you win is 1.2898.

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Answer: The distance between points A and B is 32 units.

Step-by-step explanation:

The general equation for a line in slope-intercept form is:

y = a*x +b

Where a is the slope, and b is the y-intercept.

We know that two lines are parallel if the lines have the same slope and different y-intercept.

Now, in this case we have the line:

5*x + 4*y = 16

We can rewrite this in slope-intecept form if we isolate the "y" in the left side:

4*y = -5*x + 16

y = (-5/4)*x + 16/4

y = (-5/4)*x+ 4

The slope is (-5/4) and the y-intercept is 4.

We know that line L₂ is parallel to this line, then this line will also have a slope equal to (-5/4) and a y-intercept equal to c.

y = (-5/4)*x + c

And we know that this line passes through the point (8, 15)

This means that when x = 8, the value of y must be 15.

We could just replace these two values in the above equation to find the value of c.

15 = (-5/4)*8 + c

15 + (5/4)*8 = c = 25

Then the line L₂ is:

y = (-5/4)*x + 25.

Now, we know that this line passes the x-axis at the point A.

The line will pass through the x-axis when y = 0, then we need to find the value of x such that y = 0.

0 = (-5/4)*x + 25

(5/4)*x = 25

x = 25/(5/4) = 20

Then point A is the point (20, 0)

And point B is when the line passes through the y-axis, this is when x = 0.

y = (-5/4)*0 + 25

y = 25

Then point B is the point (0, 25)

Now we want to find the distance between points A and B, which is equal to the distance between points (20, 0) and (0, 25).

When we have two points (a, b) and (c, d), the distance between them is:

distance = √( (a - c)^2 + (b - d)^2)

In this case, the distance between (20, 0) and (0, 25) is:

distance = √( (20 - 0)^2 + (0 -25)^2) =  32

The distance between points A and B is 32 units.

The three angle bisector of a triangle intersect at a single point that point of concurrency of the angle of bisectors is called the incenter.

Given:

the 3 angle bisectors of a triangle intersect.

when three angle bisector of a triangle intersect then that point of concurrency is called incenter.

Incenter:

The incenter of a triangle is the intersection point of all the three interior angle bisectors of the triangle. In other words, it can be defined as the point where the internal angle bisectors of the triangle cross. This point will be equidistant from the sides of a triangle, as the central axis’s junction point is the center point of the triangle’s inscribed circle.

Incenter formula:

= (ax1+bx2+x3 / a+b+c  , ay1+by2+y3 / a+b+c).

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The general solution of non-homogeneous system can be written as:

x = xh + xp = [2t + 1, t, -2s - 2] + [-1, -28, 1]

We can now write the augmented matrix of the system as:

[2    -4    5     8]

[-7   14   4   -28]

[3   -6    1      12]

We can use row reduction to determine whether the system is consistent and to find its solutions.

Performing the row reduction, we get:

[1  -2  0  2]

[0   0  1 -2]

[0   0  0 0]

From the last row of the row-reduced matrix, we can see that the system has a dependent variable, which means that there are infinitely many solutions. We can write the general solution as:

x = x1 = 2t + 1

y = y1 = t

z = z1 = -2s - 2

Here, t and s are arbitrary parameters.

To find a particular solution, we can use any method we like. One method is to use the method of undetermined coefficients. We can guess that xp is a linear combination of the columns of A, with unknown coefficients:

xp = k1[2 -7 3] + k2[-4 14 -6] + k3[5 4 1]

where k1, k2, and k3 are unknown coefficients.

We can substitute this into the system and solve for the coefficients. This gives:

k1 = -1

k2 = -2

k3 = 1

Therefore, a particular solution is:

xp = [-1 -28 1]

So the general solution can be written as:

x = xh + xp = [2t + 1, t, -2s - 2] + [-1, -28, 1]

where t and s are arbitrary parameters.

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the probability of "heads" on the first flip of this coin will be 1/2.

What is probability and example?

Probability = the number of ways of achieving success. the total number of possible outcomes. For example, the probability of flipping a coin and it being heads is ½, because there is 1 way of getting a head and the total number of possible outcomes is 2 (a head or tail). We write P(heads) = ½ .

The chances of an event occurring are defined by probability. Probability has several uses in games, in business to create probability-based forecasts,

"Heads" is the result of the latest flip and the preceding four flips. The total sample space for the heads.

P(A^B)=(1/2)^5

The preceding four flips in a row all resulted in "heads."

P(B)=(1/2)^4

The probability that the 5th flip lands head is;

⇒P(A^B)/p(B)= (1/2)⁵/(1/2)⁴

⇒P(A^B)/p(B)= 1/2

Hence, the probability of "heads" on the next (5th) flip of this coin will be 1/2.

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Answer:

∡A  =115°

as for your question ... m is asking for the  "m" (measure) of angle A

Step-by-step explanation:

Answer:

∠ A = 118°

Step-by-step explanation:

The sum of the 3 angles in a triangle = 180°

Sum the 3 angles and equate to 180

3x + 13 + x - 8 + x = 180, that is

5x + 5 = 180 ( subtract 5 from both sides )

5x = 175 ( divide both sides by 5 )

x = 35

Then

∠ A = 3x + 13 = 3(35) + 13 = 105 + 13 = 118°

Answer:

58

Step-by-step explanation:

i think

Answer:

Step-by-step explanation:

center: (-2,3)

Radius: 5

Answer:

x ≈ 15.4 cm

Step-by-step explanation:

using the sine ratio in the right triangle

sinΘ = \(\frac{opposite}{hypotenuse}\) = \(\frac{y}{x}\) , then substituting values

sin19° = \(\frac{5}{x}\) ( multiply both sides by x )

x × sin19° = 5 ( divide both sides by sin19° )

x = \(\frac{5}{sin19}\) ≈ 15.4 cm ( to 1 decimal place )

The term for the value that occurs most often in a series of numbers is called the mode.

The mode is one of the three main measures of central tendency, along with the mean and the median. It is a useful descriptive statistic that can provide insights into the characteristics of a dataset.

To find the mode of a set of data, you first need to arrange the data in order, either in increasing or decreasing order. Then, you simply identify the most frequent data point, which is the mode. In some cases, there may be more than one mode if multiple data points occur with the same maximum frequency.

The mode is particularly useful when dealing with categorical or nominal data, where there are distinct categories or values that cannot be ordered in a meaningful way. For example, the mode can help identify the most popular color among a group of people or the most common type of car on a given street. It can also be used for continuous data, although it may be less useful in this case than the mean or median.

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Answer:

378

Step-by-step explanation:

We know that she bought a television for $350 and the tax rate is 8%. This means the equation will be 350+(0.08*350). We can solve that equation using benchmark fractions since that's the quicker method of doing it.

To find 8% of 350, we can do 1% of 350 = 3.5 and we just multiply 3.5*8 which is 28. So we do 350+28.

You could also do 350*.08 but that's less efficent

Answer:

a = 1 and b = -7

Step-by-step explanation:

Given the expression

(3 + i)(1+2i)

On factorizing we have;

(3 + i)(1+2i)

= 3(1)+3(2i)+1(i)+i(2i)

= 3 + 6i + i + 2i²

= 3 + 7i + 2i²

Since i² = -1

The expression becomes;

= 3 + 7i + 2(-1)

= 3 + 7i -2

= 1 - 7i

On comparing with a + bi

a = 1 and b = -7

Answer:

152 in. squared

Step-by-step explanation:

Surface area = L×W + L×W+ 1/2 ×h ×b+ 1/2 × b×h + L×W

= 7×6 + 6×5+ 1/2×4×8 +1/2×4×8 +6×8

= 42+ 30 +16 +16 +48

=152 in. squared

43 kg is equal to 94.8 lbs. A kilogram (kg) is said to weigh 2.2 times more than a pound (represented as lbs). As a result, 2.26 pounds equal one kilo of mass.

The International System of Units' unit of mass is the kilogram, which is represented by the unit sign kg. It is a measurement scale that is widely used in science, engineering, and business all around the world. Its meaning is "1,000 grams." As a result, the ratio of kilograms to grams is 1: 1000. Moreover, it implies that a kilogram and a kilogram are equivalent. The basic unit is typically referred to as grams. As a result, we typically convert from grams to kilograms. In the metric system, the prefix "kilo" denotes division by 1000 in decimal units (103). In the International System of Units, it is denoted by the lowercase letter k.

43 kg = 94.8 lbs

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The values of c and d are c = 4.2, d=−12, c = −5, d=−8/4 and c = −1/5, d=11

The complete question is added as an attachment

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

d = integers

c = rational numbers

Integers are numbers without decimal and rational numbers can be expressed as fractions

Using the above as a guide, we have the following possible values

c = 4.2, d=−12, c = −5, d=−8/4 and c = −1/5, d=11

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Answer:

y = 25m + 350

Step-by-step explanation:

She already has 350 and every month she will add an additional 25

Answer:

Anna saving her money from m months is 375

445 .                       Answer:

Step-by-step explanation:

Answer:

23

Step-by-step explanation:

6×3+5(3-2)

6×3+5×1

18+5

23

Answer:

T=7

Step-by-step explanation:

(T-8) x (-t+15)

Then 15-8

T= 7

Absolute value represents a value's distance from zero (0) on the number line. It is expressed using a pair of vertical bars. In the order of operations, absolute value signs are considered like parenthesis and other grouping symbols. We complete the operations inside the absolute value signs first to get a single number. Then we take the absolute value of the number at the same time we evaluate exponents in the expression.

A number line can be defined as a type of graph with a graduated straight line which contains both positive and negative numerical values (numbers) that are placed at equal intervals along its length.

An absolute value function can be defined as a type of function that consist of an algebraic expression, which placed within absolute value symbols.

Mathematically, the standard form of the equation for an absolute value function is given by:

y = a|x - h| +k.

Where:

h and k are the vertex of the graph.

Absolute value represents a value's distance from zero (0) on the number line. Also, it is typically expressed using a pair of vertical bars. In the order of operations, absolute value signs are considered like parenthesis and other grouping symbols such as brackets.

Furthermore, you should complete the operations inside the absolute value signs first to get a single number. Then, you take the absolute value of the number at the same time when you evaluate exponents in the expression.

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Answer: The slope is - 1/2.

Step-by-step explanation:

Without changing the value, Marcus can add 3 positive counters and 3 negative counters. Option d is correct.

To determine the difference -8 - 3 (+3), Marcus wants to use a model with counters. He starts with 8 negative counters, and in order to add 3 positive counters without changing the value, he can add 3 positive counters and 3 negative counters.

By adding 3 positive counters, he is increasing the value by 3. However, since he wants to maintain the same value, he also needs to add 3 negative counters. This ensures that the net change in value remains zero.

So, by adding 3 positive counters and 3 negative counters to the model, Marcus can represent the difference -8 - 3 (+3) without changing the overall value. Therefore, d is correct.

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