10.Which of the following is HCF of 2x^2-18 and x^2-2x-3?

x+1

x+3

x-3

none of the above​

We have to show that cn(x) can easily be computed from cn-1(x).Then, cn(x) is given by:cn(x) = (1/n) * x * cn-1(x), for n>0, and c0(x) = 1. Let’s write a Python function to compute the Taylor series of the exponential function of order N. We will make it such that it only keeps two local variables.

We can compute the exponential function using the Taylor series as follows:

def exp_taylor(x, N):

sum = 1.0

term = 1.0

for n in range(1, N):

term *= x / n

sum += term

return sum

This function takes two arguments x and N, where x is the value for which the exponential function is to be computed, and N is the order of the Taylor series expansion. The function returns the sum of the Taylor series up to the Nth order.

Now, let’s make a plot of the convergence with N by comparing the result to numpy's evaluation of the exponential for some x. We can use the matplotlib library to make a plot.

The following code does this:

import numpy as npimport

matplotlib.pyplot as plt

#define the values of x

N = 100

x = np.linspace(-5, 5, N+1)

#compute the exponential using the Taylor series

y_taylor = [exp_taylor(xi, N) for xi in x]

#compute the exponential using numpy

y_np = np.exp(x)

#make the plot

plt.plot(x, y_taylor, label='Taylor')

plt.plot(x, y_np, label='Numpy')plt.xlabel('x')

plt.ylabel('y')plt.legend()plt.show()

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The probability that a total of k balls are withdrawn, given r red balls have been withdrawn from an urn containing n red and m blue balls, can be calculated using the hypergeometric probability formula.

To calculate the probability, we use the hypergeometric probability formula: P(X = k) = (C(r, k) * C(n-r, m-k)) / C(n, m), where P(X = k) represents the probability of drawing k balls, C denotes the combination function, and n, m, r, and k represent the number of red balls, blue balls, red balls already withdrawn, and total balls drawn, respectively.

The formula takes into account that the probability of drawing a specific combination of k balls from the remaining available red and blue balls changes as each ball is withdrawn. The combination function accounts for the number of ways to choose the desired number of red balls and the remaining blue balls.

By plugging in the appropriate values for n, m, r, and k into the formula, we can calculate the probability of obtaining a specific number of balls after r red balls have already been withdrawn.

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Answer:

no

Step-by-step explanation:

3 times -3 is -9. -9 - 5 is -14.

2 times -3 is -6. -6 + 4 is -2.

-14 is not equal to -2

Answer:

no

Step-by-step explanation:

3(-3)-5

-9-5=-14

is not =to

4+2(-3)

4+-6=-2

Answer:

\(6 \frac{1}{14}\)

Step-by-step explanation:

Write down the problem;

\(2 \frac{4}{7} + 3 \frac{2}{4}\)

Simplify

\(2 \frac{4}{7} + 3 \frac{1}{2}\)

Convert so that the fractions have a common denominator; multiply the numerator and denominator of both fractions such that the denominators are equal;

\(2 \frac{8}{14} + 3 \frac{7}{14}\)

Add the fractions;

\(5 \frac{15}{14}\)

Convert to mixed number;

\(6 \frac{1}{14}\)

When a 2 ft ribbon is cut into 10 proportional piece then each piece measures 0.2 ft. The model shows that there are 10 pieces that are each 0.2 ft long.

What is proportion?

In general, the term "proportion" refers to a part, share, or amount that is compared to a whole. According to the definition of proportion, two ratios are in proportion when they are equal.

From the given model, it is seen that Devin cut the ribbon in equal proportions. The number of proportions can be found by summing the different sections on the ribbon.

This number comes to 10 sections which means that Devin cut the ribbon into 10 pieces.

The length of each of these pieces is -

= Length of entire ribbon / Number of pieces

Substitute the values into the equation -

= 2 / 10

= 0.2 ft

Therefore, the length of each piece is 0.2 ft.

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Answer:

60%

Step-by-step explanation:

Answer:

60%

Step-by-step explanation:

Answer:

$3.0375

Step-by-step explanation:

Original price of dinner = $2.25

If cost percentage of 35%, then the additional cost paid will be;

35% * 2.25

= 0.35 * 2.25

= $0.7875

Target price = Original price + additional cost

Target price = $2.25 + $0.7875

Target price = $3.0375

Using linear approximation, we estimate that √65.3 ≈ 47.822, rounded to four decimal places.

To use linear approximation, we need to find the equation of the tangent line to the function f(x) at x=64. Then, we can use this tangent line to approximate the value of f(x) near x=64.

First, let's find the equation of the tangent line to f(x) at x=64. The slope of the tangent line is given by the derivative of f(x) at x=64:

f'(x) = √3/2x^(1/2)

f'(64) = √3/2(64)^(1/2) = √3/2 * 8 = 4√3

Equation of tangent line f(x) at x=64:

y - f(64) = f'(64)(x - 64)

y - 64√3 = 4√3(x - 64)

y = 4√3x - 128√3

Now, we can use this tangent line to approximate f(x) near x=64. We want to estimate √65.3, which is close to x=64. Let's substitute x=65.3 into the equation of the tangent line:

y = 4√3(65.3) - 128√3 ≈ 47.822

Therefore, using linear approximation, we estimate that √65.3 ≈ 47.822, rounded to four decimal places.

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The ratio v2/v1 is the same for any non-zero direction vector of the line l, which shows that the concept of slope is well defined. If v is a direction vector of the line with slope alpha, then (1, alpha) is also a direction vector of the line. The equation of the line through P with slope alpha is y - y1 = alpha(x - x1).

To show that the concept of slope is well defined, we need to prove that the ratio v2/v1 is the same for any non-zero direction vector of the line l. Let u = (u1, u2) be another non-zero direction vector of the line l.

Then, u1v2 = u2v1, since both vectors point in the same direction. Dividing by v1u1 (which is non-zero, since both vectors are non-zero), we get v2/v1 = u2/u1. Therefore, the concept of slope is well defined.

Let v = (v1, v2) be a direction vector of the line l with slope alpha. Then, we have v2/v1 = alpha. Multiplying both sides by v1, we get v2 = alpha v1. Therefore, v = (v1, alpha v1) = v1(1, alpha). Since v1 is non-zero, (1, alpha) is also a direction vector of l.

Let (x, y) be any point on the line through P = (x1, y1) with slope alpha. Then, the direction vector of the line is given by v = (1, alpha). Since P is a point on the line, the vector from P to (x, y) is parallel to v, so we can write (x - x1, y - y1) = t(1, alpha) for some scalar t. Solving for y, we get y - y1 = alpha(x - x1), which is the equation of the line through P with slope alpha.

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Answer:

-127.02 Hope this helps

60% male and 40% female

2y + 2x = 8

2y - 4x = 2

solve both for 2y

2y + 2x = 8

2y = 8 - 2x

second

2y - 4x = 2

2y = 4x + 2

they are both equal to 2y, so you can set them equal to each other

4x + 2 = 8 - 2x

4x = 6 - 2x

6x = 6

x = 1

2y -4(1) = 2

2y - 4 = 2

2y = 6

y = 3

check

2(3) + 2(1) = 8

6 + 2 = 8

true

9514 1404 393

Answer:

Step-by-step explanation:

The shaded area contains area A and two of area B. The expression for that area can be written ...

  Area of trapezoid = A + 2×B

__

The overall rectangle has an area of D. The areas labeled C can be subtracted from that to leave the shaded area. The expression for that is ...

  Area of trapezoid = D - 2×C

The formula predicting the number of US billionaires in any given year (t) is:f(t) = 17.2t - 34,129. We can assume a linear growth model on the based of given information.

The given data states that in the year 1985, there were 13 US billionaires. Whereas in 1990, there were 99 US billionaires. We have to find out the formula that predicts the number of US billionaires in any given year (t).

The yearly increase remains constant, so we can consider the formula for the linear function.f(t) = mt + b

where

t is the year and f(t) is the number of US billionaires in that year (t).

m is the slope of the line and b is the y-intercept.

The slope of the line is given by the formula:m = (y₂ - y₁) / (x₂ - x₁)

Let's plug in the given values to find the slope of the line.m = (99 - 13) / (1990 - 1985)m = 86 / 5m = 17.2 .The y-intercept of the line can be found by substituting the values of t and f(t) from any of the given points into the equation of the line.

Let's use the point (1985, 13).f(t) = mt + b => f(1985) =17.2(1985) + b => f(1985) = 34,142 + b =>b = 13 - 34,142 & b = -34,129.

The formula predicting the number of US billionaires in any given year (t) is:f(t) = 17.2t - 34,129

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Answer:

This problem has no answer.

Step-by-step explanation:

24+6k<-6(-4-k)

24+6k<24+6k

24-24<6k-6k

0<0k

This problem has no answer.

Answer:

- 4x² - 8x + 13

Step-by-step explanation:

To obtain g(h(x)) substitute x = h(x) into g(x), that is

g(x² - 4 + 2x)

= - 4(x² - 4 + 2x) - 3 ← distribute parenthesis by - 4

= - 4x² + 16 - 8x - 3 ← collect like terms

= - 4x² - 8x + 13 ← in standard form

Answer:

x=34

Step-by-step explanation:

36+40= 76

180-110=70

76+70=146

180-146=34

vertical angles are equivalent so x=34

Answer:

(x + 6)(x + 7)

Step-by-step explanation:

To factor the trinomial x^2 + 13x + 42, we need to find two numbers that multiply to 42 and add up to 13.

One way to do this is to list all the pairs of factors of 42 and see which pair adds up to 13:

1, 42 -> 1 + 42 = 43

2, 21 -> 2 + 21 = 23

3, 14 -> 3 + 14 = 17

6, 7 -> 6 + 7 = 13

So the pair of factors that we want is 6 and 7. We can use these numbers to rewrite the middle term of the trinomial:

x^2 + 13x + 42 = x^2 + 6x + 7x + 42

Next, we can group the first two terms and the last two terms:

x^2 + 6x + 7x + 42 = (x^2 + 6x) + (7x + 42)

Now, we can factor out the greatest common factor from each group:

x(x + 6) + 7(x + 6)

Notice that we have a common factor of (x + 6) in both terms. We can factor this out:

(x + 6)(x + 7)

Answer:

second one

Step-by-step explanation:

Altitude and perpendicular bisector of a side are always perpendicular to a side of a triangle.

How do triangles work?

A triangle is a three-sided polygon with three vertices. The angles of the triangle are formed by the three sides' end-to-end connections at a point.

               The triangle's three angles add up to a total of 180 degrees.

In a triangle, what is the altitude?

The perpendicular line drawn from a triangle's vertex to its opposite side is the definition of a triangle's altitude.

                       The altitude forms a right-angle triangle with the base and is also referred to as the triangle's height.

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Answer:

Step-by-step explanation:

y-8

Answer:

y - 8

Step-by-step explanation:

Answer:

Step-by-step explanation:

An equilateral right-angled triangle is impossible to draw. Equilateral means all the sides measure the exact same length. In a right triangle, by definition, the hypotenuse is longer than either of the other sides. so the last choice is the one you want.

Answer:

an equilateral right triangle cannot exist, all angles are 60° and therefore NOT right

Step-by-step explanation:

an equilateral right triangle cannot exist, all angles are 60° and therefore NOT right

Answer:

B. 5 1/3

Step-by-step explanation:

5 4/12=5 1/3

Answer:

m% of n is (m/100)(n)

Step-by-step explanation:

When removing a %, you just move the period two places to the left (ex. 50% = 0.50), or just divide the number by a 100 (ex. 50% = 50/100). So then, m% of n is just the product of m/100 and n.

The measure of angle IMJ is 62.5 degrees

To solve for angle IMJ, we make use of the following arc intercept theorem.

Angle IMJ = 0.5 * (Arc IJ + Arc LK)

So, we have:

Angle IMJ = 0.5 * (40 + 85)

Evaluate the product

Angle IMJ =62.5

Hence, the measure of angle IMJ is 62.5 degrees

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Keiko purchased a prepaid phone card for $25 . long distance calls cost 9 cents a minute using this card. If the remaining credit on her card is $23.92 , then the call lasted for 12 minutes.

When Keiko made her call, she used some of the credit on her prepaid phone card. To find out how many minutes her call lasted, we need to determine the cost of the call and divide that by the cost per minute.

First, we find the difference between the original value of the card ($25) and the remaining value ($23.92), which gives us the cost of the call: $25 - $23.92 = $1.08.

Next, we need to determine the cost per minute for the long distance calls made with the card. We know that the calls cost 9 cents per minute, so we convert this to dollars: 9 cents * $0.01/cent = $0.09/minute.

Finally, we divide the cost of the call by the cost per minute to get the number of minutes: $1.08 / $0.09/minute = 12 minutes. So, Keiko's call lasted for 12 minutes.

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Answer:

length times width for area so its 5x6=30

The length of arc EG is approximately 7.35 units.

To find the length of arc EG, we need to use the formula:

length of arc = (central angle/360°) × 2πr

where r is the radius of the circle and the central angle is in degrees.

We are given that m∠EFG = 58°, and EF = 6 units. Since EF is a chord of the circle, we can use the chord-chord angle theorem to find that m∠EGF = ½(180° - 58°) = 61°.

Now, we can use the Law of Cosines to find the length of GE:

GE² = EF² + FG² - 2(EF)(FG)cos(∠EGF)

GE² = 6² + FG² - 2(6)(FG)cos(61°)

Since FG = 2r (because it is the diameter of the circle),

GE² = 36 + (2r)² - 12r cos(61°)

We can simplify this to:

GE² = 4r² - 12r cos(61°) + 36

GE² = 4(r² - 3r cos(61°) + 9)

Now, we can use the formula for the length of the arc:

length of arc EG = (m∠EGF/360°) × 2πr

length of arc EG = (61/360) × 2πr

length of arc EG = (61/180) × πr

Substituting the expression for GE² in terms of r, we get:

length of arc EG = (61/180) × π √[4(r² - 3r cos(61°) + 9)]

We can now use a calculator to find the approximate value of the length of arc EG.

Rounded to the nearest hundredth, the length of arc EG is approximately 7.35 units.

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