Subtract these polynomials.

(2x²+2x+3)(x²+2x+1)=

A x² + 4x+2

B. +4

C. x² + 4x+4,

D. x² + 2

The distance of the base of the tower and the airplane is 348.5 ft,  and the right option is 4. 348.5 ft.

Distance is the length between two points.

To calculate the distance of the base of the tower and the airplane, we use the formula below.

Formula:

Where:

From the diagram,

Given:

SUbstitute these values into equation 1 and solve for A

Hence, the right option is 4. 348.5 ft.

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Answer:

There are 68,640 different ways the runners can finish first, second, and third in the race.

Concept of Permutations

The number of different ways the runners can finish first, second, and third in a race can be calculated using the concept of permutations.

Brief Overview

Since there are 42 runners competing for the top three positions, we have 42 choices for the first-place finisher. Once the first-place finisher is determined, there are 41 remaining runners to choose from for the second-place finisher. Similarly, once the first two positions are determined, there are 40 runners left to choose from for the third-place finisher.

Calculations

To calculate the total number of different ways, we multiply the number of choices for each position:

42 choices for the first-place finisher × 41 choices for the second-place finisher × 40 choices for the third-place finisher = 68,640 different ways.

Concluding Sentence

Therefore, there are 68,640 different ways the runners can finish first, second, and third in the race.

The simplified form of the expression 3(7/5x + 4) – 2(3/2 - 5/4x) is:

B. 67/10x + 9

To simplify the expression given, we will apply the PEMDAS rule. This means that we will first solve for the parentheses, the exponents, multiplication, division, addition, and subtraction in that order.

Applying this to the expression above, we will have;

3(7/5x + 4) – 2(3/2 - 5/4x)

= 21/5x + 12 - 6/2 + 10/4x

= 21/5x + 12 - 3 + 10/4x

= 21/5x + 9 + 10/4x

= 84/20x + 50/20x + 9

= 134/20x + 9

= 67/10x + 9

So, the simplified form of the expression is 67/10x + 9

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Answer:

Step-by-step explanation:

this is called a ratio and proportion or similar triangles

  21    =     35  

 31.5           x

do cross multiply:

21 x = 31.5 (35)

x = 1102.5 / 21

x = 52.5 cm

The net temperate on Thursday morning will be equal to -13 °F.

The four basic mathematical operations are the addition, subtraction, multiplication, and division of two or even more integers. Among them is the examination of integers, particularly the order of actions, which is crucial for all other mathematical topics, including algebra, data organization, and geometry.

As per the given information in the question,

The temperature on Wednesday, T1 = -5 °F

The temperature drop overnight, T2 = -8 °F

Then the temperature on Thursday morning will be,

T = T1 + T2

T = -5 °F + -8 °F

T = -13 °F.

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The limit of |a_(n+1)/a_n| is 7.

To apply the ratio test to the series ∑ \((n!)/(7n^3)\), we need to evaluate the limit: lim(n→∞) |a_(n+1)/a_n| = lim(n→∞) \([(n+1)!/(7(n+1)^3)] * [(7n^3)/(n!)]\)

= lim(n→∞)\([(n+1)/(7(n+1))^3] * [7n^3/n]\)

= lim(n→∞) \([(n+1)/7(n+1)^3] * [7n^3/n]\)

= lim(n→∞)\((n+1)/(7(n+1))^3 * 7n^3/n\)

= lim(n→∞) \((n+1)/(7n+7)^3 * 7n^3/n\)

Next, we simplify the expression:

= lim(n→∞)\([(n+1)/(7n+7)]^3 * 7n^2/n\)

= lim(n→∞)\((n+1)^3/(7n+7)^3 * 7n^2/n\)

As n approaches infinity, the terms with n in the numerator and denominator dominate, and we can neglect the constant terms:

= lim(n→∞) (n/n)² * 7 = 7

According to the ratio test, if the limit is less than 1, the series converges. If the limit is greater than 1, the series diverges. If the limit is exactly 1, the test is inconclusive.

Since the limit in this case is 7, which is greater than 1, the ratio test tells us that the series ∑ \((n!)/(7n^3)\) diverges.

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Answer:

For the pink triangle, \(\alpha +\beta = 90\) degrees

For the yellow triangle, \(\beta =35\) degrees

Step-by-step explanation:

You need side lengths to find the rest of the angle measures for the pink triangle and I'm not sure how to find side lengths with coordinates, I'm used to an integer with a unit of measure, maybe someone else could help with that.

Answer:

10x-2y

Step-by-step explanation:

distribute for both of them then multiply both answers by 2 and add them

2(x+y)= (2x+2y) x2= 4x+4y

3(x-y)= (3x-3y) x2= 6x-6y

4x+4y+6x-6x

10x-2y

The probability of finding  P(X > 150 ) with with mean 100 and standard deviation 50 is  0.1587.

1. To find the probability P(z > 1.61) for a standard normal variable z,

we can use the z-table or a calculator with a normal distribution function.

Step 1: Locate the value 1.61 on the z-table.

We will find the corresponding probability P(z < 1.61) = 0.9463.
Step 2: Since we want P(z > 1.61),

subtract the value found in Step 1 from 1:

P(z > 1.61) = 1 - P(z < 1.61) = 1 - 0.9463.
Step 3: Round to two decimal places: P(z > 1.61) ≈ 0.0537.

So, P(z > 1.61) ≈ 0.0537.

2. To find P(X > 150) for a normal distribution with mean μ = 100 and standard deviation σ = 50,

we have to first convert the value X = 150 to a z-score.

Step 1: Calculate the z-score using the formula z = (X - μ) / σ.

For X = 150, z = (150 - 100) / 50 = 1.
Step 2: Find the probability P(z > 1) using the z-table or a calculator.

You will find P(z < 1) = 0.8413.
Step 3: Since we want P(z > 1), subtract the value found in

Step 2 from 1: P(z > 1) = 1 - P(z < 1) = 1 - 0.8413.
Step 4: Round to two decimal places: P(z > 1) ≈ 0.1587.

So, P(X > 150) ≈ 0.1587.

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ABC is the intermediate, and A is the catalyst in this reaction mechanism.

In the given mechanism, an intermediate is a species that is formed in one step but is then consumed in a subsequent step.

In this mechanism, the species ABC is an intermediate because it is formed in step 1 but is then consumed in step 2.

This means that it does not appear in the overall equation for the reaction, as it is not a reactant or product.
On the other hand, a catalyst is a species that speeds up the rate of a reaction without being consumed itself.

In this mechanism, there is no catalyst because none of the species involved speeds up the reaction without being consumed itself.

All the species are either reactants or products or intermediates.
Overall,

The mechanism shows a reaction between A, B, and C, which involves two steps. In the first step, A reacts with BC to form the intermediate ABC.

In the second step, BC reacts with ABC to form A, B2, and C2.

The overall equation for the reaction shows that two moles of BC react to form one mole each of B2 and C2.

This mechanism represents a complex reaction that occurs in multiple steps, and it is important to understand the role of intermediates in these steps to better understand the reaction as a whole.

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In this mechanism, ABC is an intermediate because it is formed in the first step and consumed in the second step. BC is a catalyst because it is not consumed or formed in the overall reaction but it facilitates the reaction by participating in both steps. ABC is the intermediate and A is the catalyst in this reaction mechanism.

Let's analyze the given reaction mechanism to identify the intermediate and the catalyst.

Step 1: A + BC → ABC
Step 2: BC + ABC → A + B2 + C2
Overall: 2BC → B2 + C2

1. Identify the intermediate:
An intermediate is a species that is produced in one step and consumed in another. In this mechanism, ABC is formed in step 1 and consumed in step 2. Therefore, ABC is the intermediate.

2. Identify the catalyst:
A catalyst is a species that is consumed in one step and regenerated in another step without being consumed in the overall reaction. In this mechanism, A is consumed in step 1 and regenerated in step 2. Since A does not appear in the overall reaction, it is the catalyst.

In conclusion, ABC is the intermediate and A is the catalyst in this reaction mechanism.

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To find the equation of the plane that passes through P(2, −3, 4) and is parallel to the y-axis, we can take two points, P(2, −3, 4) and Q(0, y, 0), The equation of the plane Substituting x = 2, y = −3 and z = 4, Hence, the equation of the plane is 2x − 4z − 2 = 0.

The distance between two skew lines, F = (4, −2, −1) + t(1, 4, −3) and F = (7, −18, 2) + u(−3, 2, −5), can be found using the formula:where, n = (a2 − a1) × (b1 × b2) is a normal vector to the skew lines and P1 and P2 are points on the two lines that are closest to each other. Thus, n = (1, 4, −3) × (−3, 2, −5) = (2, 6, 14)Therefore, the distance between the two skew lines is \(|(7, −18, 2) − (4, −2, −1)| × (2, 6, 14) / |(2, 6, 14)|.\) Ans: The distance between the two skew lines is \($\frac{5\sqrt{2}}{2}$.\)

To find the equation of the plane that passes through P(2, −3, 4) and is parallel to the y-axis, we can take two points, P(2, −3, 4) and Q(0, y, 0), where y is any value, on the y-axis. The vector PQ lies on the plane and is normal to the y-axis.

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The basic solutions on the interval [0,2\pi)[0,2π) for the equation 2\(\sin 2x+\sin x=12sin2x+sinx=1\) are x=\(\frac{\pi}{6}\)   and x=\(\frac{5\pi}{6}\). The correct option is c.

​

To find the solutions to the equation \(2\sin 2x+\sin x=12sin2x+sinx=1\), we can start by rearranging the equation to obtain \(2\sin 2x+\sin x-1=02sin2x+sinx−1=0.\) Next, we can apply the double angle identity for sine, which states that\(\sin 2x = 2\sin x\cos xsin2x=2sinxcosx\). By substituting this into the equation, we get 4\sin x\cos x+\sin x-1=04sinxcosx+sinx−1=0.

Now, we can factor out the common term \sin xsinx from the equation: \(\sin x(4\cos x+1)-1=0sinx(4cosx+1)−1=0.\) This equation holds true if either \(\sin x = 0sinx=0 or 4\cos x+1=14cosx+1=1.\)From \sin x = 0sinx=0, we find one solution \(x=\frac{\pi}{2}\)

​ From\(4\cos x+1=14cosx+1=1\), we have \(4\cos x = 04cosx=0\), which gives us \(\cos x = 0cosx=0\). The solutions for \(\cos x = 0cosx=0\) on the interval [0,2\pi)[0,2π) are\(x=\frac{\pi}{2} and x=\frac{3\pi}{2}.\)

​ Combining all the solutions, we have\(x=\frac{\pi}{2}, x=\frac{3\pi}{2} , x=\frac{\pi}{6}, and x=\frac{5\pi}{6}\)

​ However, we need to consider that the interval given is [0,2\pi)[0,2π), so the solutions outside this interval are not valid. Therefore, the valid solutions on the interval [0,2\pi)[0,2π) are \(x=\frac{\pi}{6} and x=\frac{5\pi}{6}\)

​

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To determine the number of WINS by which one occurrence of the maximum value can be reduced without changing the value at the 55th percentile.

We need to find the maximum value in the dataset and evaluate its impact on the percentile.

Let's assume the maximum value for WINS is X. To maintain the value at the 55th percentile (23.5), we need to find the threshold value below which the dataset will not be affected by reducing the maximum value.

We can start by arranging the data in ascending order and finding the value at the 55th percentile. Since we have 44 seasons, the 55th percentile would be approximately at the (55/100) * 44 = 24.2nd value.

Now, we compare the value at the 24th position and the value at the 25th position in the dataset. If both of these values are below 23.5, reducing the maximum value by any amount will not change the value at the 55th percentile.

For example, if the value at the 24th position is 23 and the value at the 25th position is 24, reducing the maximum value by any amount will still keep the 55th percentile at 23.5.

However, if either the value at the 24th position or the value at the 25th position (or both) is 23.5 or higher, reducing the maximum value will impact the 55th percentile.

Therefore, to accurately determine the number of WINS by which one occurrence of the maximum value can be reduced without changing the value at the 55th percentile, we need to know the specific values at the 24th and 25th positions in the dataset.

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Problem: how would I translate this sentence into an equation?



Twice the difference of a number and 5 is 9



use the variable w for the unknown number​.

Solution:

Denote the unknown number by w.

Now, the difference between a number (w) and 5 is:

w-5

twice the above is:

2(w-5)

and from the statement we know that the above must be equal to 9, that is:

2(w-5) = 9

then, the solution would be:

2(w-5) = 9

The integral, ∫ [ (9ˣ - eˣ )/3ˣ ] dx evaluate value is 3ˣ/ ln(3) - eˣ/3ˣ(1 - ln 3). So, the correct answer is option (c).

Integration is defined as the process of finding the area of the region under the curve. This is done by drawing as many small rectangles covering up the area and summing up all their areas. If d/dx(F(x) = f(x), then ∫ f(x) dx = F(x) + C, where C is integration constant and indefinite integrals. We have an integral, say , I = ∫ [ (9ˣ - eˣ )/3ˣ ] dx

and we have to determine its value.

I = ∫ [ (9ˣ - eˣ )/3ˣ ] dx

=> I = ∫ [ (9ˣ/3ˣ - eˣ/3ˣ ] dx

=> I = ∫ [ (3²ˣ/3ˣ - eˣ/3ˣ ] dx

=> I = ∫ [ (3²ˣ/3ˣ - eˣ/3ˣ ] dx

=> I = ∫ [ (3ˣ - eˣ/3ˣ ] dx

=> I = ∫ 3ˣ dx - ∫ eˣ3⁻ˣ dx

=> I = 3ˣ/ ln(3) - eˣ/3ˣ(1 - ln 3) + C

( since, ∫aˣ dx = aˣ/ln a)

where C --> integration constant

So, the required value is 3ˣ/ln(3)-eˣ/3ˣ(1 - ln 3).

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Complete question:

Find integral ∫ [ (9ˣ - eˣ )/3ˣ ] dx .

a) 3ˣ - eˣ/(1 - ln 3) + C

b) 9ˣ/2ln3 - eˣ/(3ˣ ln 3) + C

c) 3ˣ/ln3 - eˣ/3ˣ(1 - ln 3) + C

d) 3ˣ/ln3 - eˣ/3ˣ + C

El dominio de la sucesión aritmética generada por s(n) = 7 + 3 · n es n ≥ 1.

En este problema tenemos que David derivó una formula para generar los elementos de la sucesión aritmética s(n) = 7 + 3 · n, cuyo dominio es el conjunto de elementos de números naturales n tal que los elementos de la sucesión aritmética son generados.

Se puede apreciar que el dominio está constituido por un conjunto discreto y semi-infinito, esto es, un conjunto de números naturales que tiene un valor mínimo, más no un valor máximo. Es preciso determinar el valor más pequeño de n tal que s(n) = 10:

7 + 3 · n = 10

3 · n = 10 - 7

3 · n = 3

n = 1

En consecuencia, la expresión dada tiene un dominio consistente en todo número natural n tal que n ≥ 1.

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Answer:

$30.41

Step-by-step explanation:

24.20 + 24.20(0.05) + 5 =

24.20 + 1.21 + 5 = 30.41

the 1.21 represents the amount she paid in sales tax

Step-by-step explanation:

x+x-7=11

2x+7=11

2x=18

2x/2=18/2 = x=9

9-7=2

So, FG=2

The value of the segment FG is equal to 2.

We have,

To solve for FG, we can use the given information that EG = 11, EF = x, and FG = x - 7.

Now, we know that EG = EF + FG.

Substituting the values, we have:

11 = x + (x - 7)

Simplifying the equation:

11 = 2x - 7

Adding 7 to both sides:

11 + 7 = 2x

18 = 2x

Dividing both sides by 2:

18/2 = x

9 = x

The value of x is 9.

Now,

To find FG, substitute the value of x back into the expression FG = x - 7:

FG = 9 - 7

FG = 2

Thus,

The value of the segment FG is equal to 2.

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This looks like a parallelogram.

So JK would be the same as ML.

JK = 20.

Transformations, congruence, and similarity are all concepts related to geometry and the study of shapes.

Transformations refer to changes in the position, orientation, or size of a shape. There are several types of transformations, including translation (moving a shape without rotating or reflecting it), rotation (turning a shape around a fixed point), reflection (flipping a shape across a line), and dilation (stretching or shrinking a shape by a certain factor).

Congruence is a term used to describe two shapes that are identical in size and shape. In other words, they have the same angles and side lengths. If two shapes are congruent, they can be moved, rotated, or reflected so that they exactly overlap.

Similarity is a term used to describe two shapes that have the same shape but different sizes. Similar shapes have the same angles but different side lengths. If two shapes are similar, they can be resized (dilated) so that they have the same shape but different sizes.

These concepts are important in many areas of geometry, including the study of polygons, triangles, circles, and three-dimensional shapes.

They are also useful in practical applications such as architecture, engineering, and computer graphics.

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The use of prime factorization to find the exponents of the given numbers gives  625 = 5⁴, 343 = 7³, 216 = 6³,  169 = 13², 256 = 4⁴; 256 =  2⁸ and 729 = 9³; 729 = 3⁶

When a number is written as a product of its prime factors, we have the prime factorization of the number e.g 8 = 2×2×2

An exponent is defined as a way of expressing large numbers in terms of powers e.g 81 = 3×3×3×3 = 3⁴

Thus, you can use prime factorization to find the exponent of the given numbers as follows:

625 as a power of 5

625 = 5×5×5×5 = 5⁴

343 as a power of 7

343 = 7×7×7 = 7³

216 as a power of 6

216 =  6×6×6 = 6³

169 as a power of 13

169 = 13×13 = 13²

256 as a power of 4; as a power of 2

256 = 4×4×4×4 = 4⁴

256 = 2×2×2×2× 2×2×2×2 = 2⁸

729 as a power of 9; as a power of 3

729 = 9×9×9 = 9³

729 = 3×3×3×3×3×3 = 3⁶

Therefore, 625 as a power of 5, 343 as a power of 7, 216 as a power of 6, 169 as a power of 13, 256 as a power of 4; as a power of 2 and  729 as a power of 9; as a power of 3 are 5⁴, 7³, 6³, 13², 4⁴; 2⁸ and 9³; 3⁶ respectively

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Explanation:

The rule says "whatever x is, add 1 to it to get y"

So for instance, if x = 3, then y = x+1 = 3+1 = 4

Now if x = 7, then y = x+1 = 7+1 = 8

Answer:

\(\huge\boxed{Answer\hookleftarrow}\)

Given that,

\(1 + 1 = 2 \\ 2 + 1 = 3 \\ 3 + 1 = 4 \\ 4 + 1 = 5...\)

So from this we can infer that, \(\large\bold{ x + 1 = y}\)

Now,

\(x = 7 \\ y= \: ?\)

Use the rule ⎆ \(\large\bold{ x + 1 = y}\)

\(x + 1 = y \\ 7 + 1 = y \\ 8 = y\)

✐ The value of y is 8.

ʰᵒᵖᵉ ⁱᵗ ʰᵉˡᵖˢ

# ꧁❣ RainbowSalt2²2² ࿐

Answer:

A.

continuous data

Step-by-step explanation:

Function A(n) = 2n is continuous data.

" Discrete data is the data which represents finite number and not related to any other variable. It is isolated."

" Continuous data represents the infinite data and it is obtained by measuring. It is related."

According to the question,

A supermarket sell string beans for $2 a pound.

Function A(n) = 2n

It represents the relation between selling of string beans to the price.

Therefore, it is continuous data.

Hence, function A(n) = 2n is continuous data.

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Answer:

y=3

Step-by-step explanation:

hope i help youuuuu :)

Answer:

1/17

Step-by-step explanation:

You're on the right track so far!

(2³ + 3²) ⁻¹

= (8 + 9) ⁻¹

= (17) ⁻¹

= 1/17 (Remember, (a)⁻ⁿ = 1 / aⁿ)

Hi there!! (✿◕‿◕)

⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐

A = 2   B = 3

(a^b + b^a)^-1

(2^3 + 3^2)^-1

1/7 or 0.058824

Hope this helped!!  ٩(◕‿◕｡)۶

a) f is positive on the intervals (-∞, 1/3) and (3, ∞).

b) f is negative on the intervals (-1, 2) and (4, ∞).

c) f is decreasing on the interval (1/3, 3) for a given polynomial function.

d) f is increasing on the intervals (-∞, -1) and (2, 4).

Polynomial functions are functions that are defined by polynomial expressions. A polynomial expression is a finite sum of terms that are each monomial expression, which means they consist of a constant coefficient multiplied by a variable raised to a non-negative integer power.

The general form of a polynomial function is:

f(x) = \(a_n\) \(x^{n\) + \(a_{n-1}\)\(x^{{n-1}}\) + ... + \(a_1 x\) + a_0

where n is a non-negative integer, \(a_n\), \(a_{n-1}\), ..., \(a_1,\) \(a_0\) are constants (called the coefficients), and x is the variable.

Using the graph of the polynomial function f(x) = -\(x^{3}\) + 5\(x^{2}\) - 2x - 8, we can complete the sentences as follows:

a) f is positive on the intervals (-∞, 1/3) and (3, ∞). This is because the graph of the function is above the x-axis on these intervals.

b) f is negative on the intervals (-1, 2) and (4, ∞). This is because the graph of the function is below the x-axis on these intervals.

c) f is decreasing on the interval (1/3, 3). This is because the graph of the function is sloping downward from left to right on this interval.

d) f is increasing on the intervals (-∞, -1) and (2, 4). This is because the graph of the function is sloping upward from left to right at these intervals.

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Answer:

10 $ a year

Step-by-step explanation:

Answer:

16 dollars

Step-by-step explanation:

earned in first 6 years: 100 dollars

100/6 is roughly 16 dollars

hope this helps! :)

The required  types of dilation are the given scale factors are,
Scale factor  =    -4     [contaction]
Scale factor = 2.5       [Expansion]
Scale factor = 2/3       [contraction]
Scale factor = -3/4      [contraction]

The scale factor is defined as the ratio of the modified change in length to the original length.

here,
The type of dilation can be stated as if the scale factor is positive and greater than 1 there must be an expansion while if the scale factor is less than 1 then there will be a contraction.

So
From the table,
Scale factor  =    -4     [contaction]
Scale factor = 2.5       [Expansion]
Scale factor = 2/3       [contraction]
Scale factor = -3/4      [contraction]

Thus, the required solution is given above,

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Answer:

4+2x = 12

Step-by-step explanation:

sum means add an is means equal

4+2x = 12

Step-by-step explanation:

the sum of 4 and twice a number is 12: