find a degree 3 polynomial with real coefficients having zeros 5 5 and 2 i 2i and a lead coefficient of 1

The coordinates of B are (3, -8). Where the line-segment AB has the midpoint at M with coordinates (2, -1).

The midpoint on a line segment with two endpoints (x1, y1) and (x2, y2) is

Midpoint (x, y) = (\(\frac{x1+x2}{2}\), \(\frac{y1+y2}{2}\))

The given line segment is AB with coordinates A(1, 6) and B(x2, y2).

M is the midpoint of line segment AB. Its coordinates are M(2, -1)

Then, the coordinates of B are calculated by

M(x, y) = (\(\frac{x1+x2}{2}\), \(\frac{y1+y2}{2}\))

(2, -1) = (\(\frac{1+x2}{2}\), \(\frac{6+y2}{2}\))

In comparing both sides,

2 = (1 + x2)/2 and -1 = (6 + y2)/2

On simplifying,

2 = (1 + x2)/2

⇒ 4 = (1 + x2)

⇒ 1 + x2 = 4

⇒ x2 = 4 - 1

∴ x2 = 3

-1 = (6 + y2)/2

⇒ 6 + y2 = -2

⇒ y2 = -2 - 6

∴ y2 = -8

Thus, the coordinates of the required point are B(3, -8).

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Using the properties of parallelograms and the given information, we proved that BAEC is equal to FABC. We utilized angle-angle similarity and the proportional relationships of corresponding sides in similar triangles to establish the equality.

To prove that BAEC = FABC, we will use the properties of parallelograms and the given information.

Given:

ABCD is a parallelogram.

BE is parallel to CD.

BF is parallel to AD.

To prove:

BAEC = FABC

Proof:

Since ABCD is a parallelogram, we know that opposite sides are parallel and equal in length. Let's denote the length of AB as a, BC as b, AD as c, and CD as d.

Since BE is parallel to CD and AD is parallel to BF, we have angle ABE = angle CDF and angle ADB = angle BFD.

By alternate interior angles, angle CDF = angle FAB.

Now, we have two pairs of congruent angles: angle ABE = angle CDF and angle ADB = angle BFD.

Using angle-angle similarity, we can conclude that triangle ABE is similar to triangle CDF and triangle ADB is similar to triangle BFD.

As the corresponding sides of similar triangles are proportional, we have the following ratios:

AB/CD = AE/CF (from triangle ABE and triangle CDF similarity)

AD/BC = BD/CF (from triangle ADB and triangle BFD similarity)

Cross-multiplying the ratios, we get:

AB * CF = CD * AE (equation 1)

AD * CF = BC * BD (equation 2)

Adding equation 1 and equation 2, we have:

AB * CF + AD * CF = CD * AE + BC * BD

Factoring out CF, we get:

CF * (AB + AD) = CD * AE + BC * BD

Since AB + AD = CD (opposite sides of a parallelogram are equal), we have:

CF * CD = CD * AE + BC * BD

Simplifying, we get:

CF = AE + BC

Therefore, we have shown that BAEC = FABC.

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The number of portion with each having 12 fruits is at most 6 portions.

To divide the fruits into 12 portions

Total number of fruits = 80

Number of fruits per portion = 12

Number of fruits per portion = (Total number of fruits / Number of fruits per portion )

Number of fruits per portion = 80/12 = 6.67

Therefore, to divide the fruits into 12 fruits , There would be at most 6 portions.

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x=-5/√2 and x=-√2 are roots of the quadratic equation √2x²+7x+5√2=0

A quadratic equation is a second-order polynomial equation in a single variable x , ax2+bx+c=0. with a ≠ 0 .

The given quadratic equation is √2x²+7x+5√2=0

We will factorize  the middle term by middle term method

√2x²+2x+5x+5√2=0

√2x(x+√2)+5(x+√2)=0

(√2x+5)(x+√2)=0

√2x+5=0

√2x=-5

Divide both sides by √2

x=-5/√2

and x+√2=0

x=-√2

Hence, x=-5/√2 and x=-√2 are roots of the quadratic equation √2x²+7x+5√2=0

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The zeros of the quadratic function are given as follows:

x = -5 and x = -4.

The quadratic function for this problem is defined as follows:

f(x) = x² + 9x + 20.

Hence the coefficients are given as follows:

a = 1, b = 9, c = 20.

The discriminant is of:

D = b² - 4ac

D = 9² - 4 x 1 x 20

D = 1.

Hence the first root is of:

x = (-b + sqrt(D))/2a

x = (-9 + 1)/2

x = -4.

The second root is of:

x = (-b - sqrt(D))/2a

x = (-9 - 1)/2

x = -5.

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The equation in slope-intercept form is y = 4x + 1

Given,

Points (x, y) = (-1, 5)

Parallel to y = 4x - 5

Now,

Recall that a parallel line to the one given has to have the same slope. The slope of the line given is "4" (the coefficient that accompanies "x").

Therefore the equation of a parallel line has to be of the form:

y = 4x - b

5 = 4(-1) - b

5 = -4 - b

b = -4 - (-5)

b = -4 + 5

b = 1

So the equation now becomes:

y = 4x + 1

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The rejection region for a two-tailed test at a 10% level of significance can be found by dividing the significance level (0.10) equally between the two tails of the distribution. The critical values for rejection are determined based on the distribution associated with the test statistic and the degrees of freedom.

In a two-tailed test, we are interested in detecting if the population mean differs significantly from a hypothesized value in either direction. To find the rejection region, we need to determine the critical values that define the boundaries for rejection.

Since the significance level is 10%, we divide it equally between the two tails, resulting in a 5% significance level in each tail. Next, we consult the appropriate statistical table or use statistical software to find the critical values associated with a 5% significance level and the degrees of freedom of the test.

The critical values represent the boundaries beyond which we reject the null hypothesis. In a two-tailed test, we reject the null hypothesis if the test statistic falls outside the critical values in either tail. The rejection region consists of the values that lead to rejection of the null hypothesis.

By determining the critical values and defining the rejection region, we can make decisions regarding the null hypothesis based on the observed test statistic.

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Equation of a Line

The slope-intercept form of a line is:

y = mx + b

Where m is the slope.

We are given the equation of a line:

24x - 2y = 38

Subtracting 24x:

-2y = -24x + 38

Dividing by -2:

y = (-24/-2)x + 38/(-2)

Operating:

y = 12x - 19

We can see that b = 12, thus the slope of the graph is 12

Answer:

D. 12

Answer:

  (a)  0.0062

Step-by-step explanation:

You want the probability P(X > 14.5) given that X has a normal distribution with mean 2 and variance 25.

This probability can be found using a suitable calculator or spreadsheet. The calculator in the attachment specifies the normal distribution using mean and standard deviation, so we need to find the square root of the variance.

  P(X > 14.4) ≈ 0.0062

<95141404393>

From the probability distribution for the number of defective items in a random sample, the expected value of X is 2.82.

To calculate the expected value of X, we need to multiply each possible value of X by its corresponding probability and sum them up.

The expected value of X, denoted as E(X) or μ, is calculated using the formula:

E(X) = ∑ (x * p(x))

where x represents each possible value of X and p(x) represents the corresponding probability.

In this case, the probability distribution for X is given as follows:

x: 0 1 2 3 4

p(x): 0.1 0.15 0.13 0.07 0.55

To calculate the expected value, we perform the following calculations:

E(X) = (0 * 0.1) + (1 * 0.15) + (2 * 0.13) + (3 * 0.07) + (4 * 0.55)

E(X) = 0 + 0.15 + 0.26 + 0.21 + 2.2

E(X) = 2.82

The expected value represents the average value or mean of the probability distribution. In this case, it represents the average number of defective items we expect to find in a random sample based on the given probabilities.

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Answer:

The number 10/2 = 5 is an integer.

Step-by-step explanation:

An integer is a whole number which cannot be expressed in fractions. For example, 1, 2, 3...

Integer can be positive,  negative of zero.

\(\frac{10}{2}=5\)

It is a whole number so it is an integer.

- 0.3

It is not an integer as it has a fractional part.

\(\sqrt20\)

It also has a fractional part, so it is not an integer.

0.4

It also has a fractional part, so it is not an integer.

Answer:

A. a = 10, b = -9

Step-by-step explanation:

We are given:

(a+bi)-(3-5i) = 7-4i

We know that a and b are both real numbers, and we want to find what a and b are.

For imaginary numbers, a is the real part, and bi is the imaginary part. This means that we consider the real numbers like terms, and the imaginary numbers like terms.

So to start, we can open the equation to become:

a + bi - 3 + 5i = 7 - 4i

Based on what we mentioned above:
a - 3 = 7

  + 3   +3

_____________

a = 10

And:

bi + 5i = -4i

    -5i    -5i

____________j

bi = -9i

Divide both sides by i.

bi = -9i

÷i    ÷i

_________

b = -9

So, a = 10, b= -9. The answer is A.

Answer:

7,9,11,13,15 are going in order of odd numbers soo

7,9,11,13,15,17,19,21,23,25,27,29,31,33,35,37,39,41,43,45,47,49,51,53,55,57,59,61,63,65,67,69,71,73,75,77,79,81,83,85,87,89,91,93,95,97,99,101,103,105

9th term is 23

and the 50th term is 105

hope it helps you

make me brainliest plz

Step-by-step explanation:

theeeee 50th term is 105

:)

Answer:

10 meters

Step-by-step explanation:

it is the highest point of the graph

AC=BD

64 units=10x+24

64-24=10x

40=10x

X=40 divided by 10= 4

hope it helps:)))

The relation d. {({a}, b), (b, {a, {b}}), (c, b)} is a strict partial order on the set S. To determine which of the given relations on the set S = {{a}, b, {a, {b}}, c} is a strict partial order, we need to check if the relation satisfies the three conditions of a strict partial order: irreflexivity, asymmetry, and transitivity.

a. {(c, {a}), (b, {a}), ({a, {b}}, {a})}

This relation is not a strict partial order because it violates asymmetry. For example, (b, {a}) and ({a, {b}}, {a}) are both present, but neither (b, {a}) nor ({a, {b}}, {a}) are present, violating asymmetry.

b. {({a}, {a}), (b, b), (c, c)}

This relation is not a strict partial order because it violates asymmetry. All elements have a reflexive pair (e.g., ({a}, {a}), (b, b), (c, c)), violating asymmetry.

c. {({a}, b), (c, {a, {b}}), (b, c)}

This relation is not a strict partial order because it violates transitivity. ({a}, b) and (b, c) are present, but ({a}, c) is not present, violating transitivity.

d. {({a}, b), (b, {a, {b}}), (c, b)}

This relation satisfies all three conditions of a strict partial order: irreflexivity, asymmetry, and transitivity. Therefore, the correct answer is (d).

In summary, the relation d. {({a}, b), (b, {a, {b}}), (c, b)} is a strict partial order on the set S.

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Answer:

9/11

Step-by-step explanation:

Therefore, the value of x that divides the area bounded by the x-axis and the function 3/(2y^2) = x^3 into two sectors of equal area is [(4/9)ln(2y^2)/a^3]^(-1/3).

To find a value of x that divides the area bounded by the x-axis and the function 3/(2y^2) = x^3 into two sectors of equal area, we need to solve for x.

The area bounded by the x-axis and the function is given by:

A = ∫(3/(2y^2)) dx from x = 0 to x = x

Using u-substitution with u = 2y^2 and du/dx = 6x^2, we can rewrite the integral as:

A = ∫(3/u) du/6x^2 from u = 0 to u = 2y^2

A = (1/2) ln(u) / 6x^2 from u = 0 to u = 2y^2

A = (1/2) ln(2y^2) / 6x^2 - (1/2) ln(0) / 6x^2

Note that the ln(0) term is undefined and can be ignored since we are only interested in finding the value of x that divides the area into two equal parts.

To find the value of x that divides the area into two equal parts, we set the integral expression equal to half of the total area:

(1/2) ln(2y^2) / 6x^2 = 1/2 ∫(3/(2y^2)) dx from x = 0 to x = a

Simplifying and solving for x, we get:

x = [ln(2y^2) / 9 ∫(3/(2y^2)) dx from x = 0 to x = a)]^(-1/3)

Evaluating the integral and simplifying further, we get:

x = [(4/9)ln(2y^2)/a^3]^(-1/3)

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Simplify the equation for d.

Answer:

m = -1/3

Step-by-step explanation:

m= rise over run

2-4                1

____    =   -  __

9-3                3

Answer:

-1/3  is the slope

Step-by-step explanation:

I attached an image below to show you how i did this. I hope this helps :)

A chi-squared statistic provides strong evidence in favor of the alternative hypothesis if its value is A.  a large positive number.

Chi-squared statistics or chi-squared test is a statistical method used to find out if there is a significant difference between the expected and observed frequencies in one or more categories of a contingency table. This test is used to determine whether the null hypothesis can be rejected or not. Chi-squared statistics are a non-parametric test that helps to determine whether the data is close to what is expected or not. This test is used when the data is ordinal or nominal.

Chisquare test is often used for: Testing if the observed frequencies of a nominal variable are significantly different from the expected frequencies Assessing if two or more distributions are the same. The chi-squared statistic provides evidence for or against the null hypothesis. A large positive value of the chi-squared statistic indicates that the null hypothesis can be rejected.

Therefore, option A. a large positive number, is the correct answer.

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Answer:

-24

Hope that this helps!

Answer:

He spent on fruit after 5 months is $110.

In 15 months he spent $280.

Step-by-step explanation:

Fixed pay for membership is $25

And enrollment fee is $17 for each month.

The equation represents this situation is

y= 17 x + 25

He is going to stop receiving fruits once he spent $280.

Now, to find how much he spent on fruit after 5 months is plugin x as 5 into

y=17x+25 for x

y=17(5)+25

y=85+25

y=110 dollars

Now, to find how many months until $280 is to plug in y as 280 then solve the equation for x.

280 = 17 x+25

Subtract both sides 25

255 =17 x

Divide both sides by 17

x= 15 months

Answer:

i have no idea to big of a question byt why would your teacher give you that kind of math

Step-by-step explanation:

Answer:

# = 80 - x

Step-by-step explanation:

You can't solve it :/ I don't think

I hope this helped

The possible variable terms are a^5b^3, b^8, a^4b^4, a^8, ab^7

The expression is given as:

(2a + 3b)^8

The power of the above expression is 8

When expanded, the sum of powers on each variable must be 8.

Using the above explanation, we have the following possible variable terms:

a^5b^3, b^8, a^4b^4, a^8, ab^7

This is because the sum of powers equals 8

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Answer:

her grade is 90

Step-by-step explanation:

The length of JL can be found by subtracting the length of ML from the sum of LK and LN. Therefore, JL = 28 + 16 - 12 = 32.

To find the length of JL, first we can add the lengths of LK and LN. LK = 28 and LN = 16, so 28 + 16 = 44. Then, we can subtract the length of ML from the sum of LK and LN. ML = 12, so 44 - 12 = 32. Therefore, JL = 32.

This can be done by visualizing the diagram. The length of JL can be found by adding the lengths of LK and LN, which can be seen as the two sides of the right triangle that form the line MN. Then, the length of ML can be subtracted from the sum of LK and LN to get the length of JL. This is because the length of JL is equal to the length of LK plus the length of LN minus the length of ML.

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Answer:

25%

Step-by-step explanation:

7/28=.25

A quicker way to fingure it out is that 7*4=28, so 1/4 of the fruit is oranges. Which is 25%

Hope this helps!!!!