Add the complex numbers: ​ ​(-3+4i)+(7-i)

The other root of the polynomial is 1 - √3.

The roots of a polynomial are the values of the independent variable at which the polynomial is zero.

If a polynomial has integral coefficients with 3 + i and 1 + √3  as roots, then what other roots must it have? To find the roots it has, we note that the root of a polynomial with a square root in the root also has the conjugate of the square root as a root.

So, since 1 + √3, the conjugate is also a root.

The conjugate is 1 - √3.

So, the other root is 1 - √3.

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Multiplication, division, subtraction, and addition are our four operations. Here are some crucial terms you should watch out for while reading an issue and an explanation of each

what are mathematical operation?

Addition, subtraction, multiplication, and division are the traditional concepts for basic arithmetic operations. A function that converts zero or more input values into clearly defined output values is referred to in mathematics as an operation. The operation's complexity is determined by its operand count. A mathematical activity is arithmetic. Mathematical operations including addition, subtraction, multiplication, division, and calculating square roots are a few examples.

Multiplication, division, subtraction, and addition are our four operations. Here are some crucial terms you should watch out for while reading an issue and an explanation of each. Two quantities are being merged in a situation known as addition. Sum, total, in all, integrated, and entirely are important terms.

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Henry must have to score 86 marks in the fifth exam to make an average of 80 marks.

What is the average?

This is the arithmetic mean and is calculated by adding a group of numbers and then dividing by the count of those numbers. For example, the average of 2, 3, 3, 5, 7, and 10 is 30 divided by 6, which is 5.

Henry scored 85, 76, 84, and 69, and let's suppose he scored 'x' marks in the fifth exam.

Average = sum of all marks/total number of exams

  80 =(85 + 76 + 84 + 69 + x)/5

 80 = 314 + x/5

 80 * 5 = 314 + x

 400 = 314 + x

  x = 400 - 314

  x = 86

Hence, Henry must have to score 86 marks in the fifth exam to make an average of 80 marks.

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Answer:

120

Step-by-step explanation:

5!, called 5 factorial is the product of all positive intergers from 5 down though 1. by definition, 0! is 0.

Factorials are basically the number times itself-1 the 2 the 3 until it times it by itself-(itself-1). n!=n*(n-1)*n(n-2).....*n-(n-1).

For example 2!=2*1=2 and 6!=6*5*4*3*2*1=720

keep in mind that I am not an expert so the blanks I filled in might be wrong and the explanation might have errors

5!, called "5 factorial," is the product of all positive integers from 5 down through 1. By definition, 0! is equal to 1.

Factorial is a mathematical operation denoted by an exclamation mark (!). It represents the product of all positive integers from a given number down to 1. In the case of 5!, it is calculated as 5 × 4 × 3 × 2 × 1, resulting in the value of 120.

The exclamation mark notation allows us to represent the factorial of a number concisely. For example, 5! represents the factorial of 5. It is important to note that 0! is defined to be equal to 1. This is a special case in factorial calculations. While it may seem counterintuitive, it is defined this way to maintain consistency and enable certain mathematical calculations and formulas.

Therefore, 5! is the product of all positive integers from 5 down through 1, equaling 120, and 0! is defined to be 1.

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Answer:

Volume of a cone = 1/3•pi r•r•h

V = 1/3•pi•2•2•8

V = 33.49333333333333

V = 33.5 inches squared

I hope this helps! Have a good day! :)

The volume of the considered cone whose heigth is 8 inches and radius of the base is 2 inches is 33.5 cubic inches approximately.

Suppose that the radius of considered right circular cone be 'r' units.

And let its height be 'h' units.

Then, its volume is given as:

\(V = \dfrac{1}{3} \pi r^2 h \: \rm unit^3\)

Right circular cone is the cone in which the line joining peak of the cone to the center of the base of the circle is perpendicular to the surface of its base.

The missing image for this problem is attached below.

For this case, the radius is of 2 inches, and height is of 8 inches, thus, the volume of the considered cone is:

\(V = \dfrac{1}{3} \pi r^2 h \: \rm unit^3 \approx \dfrac{1}{3} \times 3.14 \times (2)^2 \times 8 \approx 33.51 \approx 33.5 \: \rm in^3\)

(rounded to the nearest tenth, which is first place to right of the decimal point.

Thus, the volume of the considered cone whose heigth is 8 inches and radius of the base is 2 inches is 33.5 cubic inches approximately.

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A z-score of -2 indicates that the sample mean does not occur very often by chance in the sampling distribution of means and probably did not come from the given population.

To answer this question, we need to calculate the z-score of the sample mean. The formula for the z-score is (sample mean - population mean) / standard error.

Plugging in the values given, we get:

z = (80 - 100) / 10 = -2

A z-score of -2 indicates that the sample mean is 2 standard errors below the population mean.

Based on this information, we can conclude that the sample mean does not occur very often by chance in the sampling distribution of means, and probably did not come from the given population.

This is because the z-score is beyond the typical range of values we would expect to see if the sample mean came from the population.

In this case, you have a random sample with a mean of 80, while the population mean is 100, and the standard error is 10.

To calculate the z-score, use the formula: (sample mean - population mean) / standard error, which is (80-100)/10 = -20/10 = -2.

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Answer:

Option D is correct.

A voluntary response error was made in this design. This type of sampling only targets those who are passionate about a specific act and call in to vote; it is not a good representation of the population.

Step-by-step explanation:

When humans are given the choice whether to participate in a survey like in this question, most often than not, the survey becomes biased.

This is because only the people or set of people who feel strongly the most about the subject matter of the poll will participate in the survey. This favours the group that disagrees as this group, if given the choice to express their opinion, will most likely be the set of people that will readily express their discontent.

Discontent is more visibly and strongly expressed in humans.

In order to remove this bias, people should have been chosen at random and their responses recorded.

Hope this Helps!!!

Kids in grade school have a maximum percentage of 32 reasons that Option (d) is the correct answer.

Korey did the market analysis section of his business plan after conducting a population survey of 3,520 homes within a 5-mile radius.

He discovered that younger children who read comic books as children are more likely to read them as adults, resulting in a current and future client base.

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In a proportional relationship between two quantities, the constant of proportionality, often denoted by the letter "k," represents the value that relates the two quantities. The equation y = kx is the standard form for expressing a proportional relationship, where "y" and "x" are the variables representing the two quantities.

Here's a breakdown of the components in the equation:

y: Represents the dependent variable, which is the quantity that depends on the other variable. It is usually the output or the variable being measured.

x: Represents the independent variable, which is the quantity that determines or influences the other variable. It is typically the input or the variable being controlled.

k: Represents the constant of proportionality. It indicates the ratio between the values of y and x. For any given value of x, multiplying it by k will give you the corresponding value of y.

The constant of proportionality, k, is specific to the particular proportional relationship being considered. It remains constant as long as the relationship between x and y remains proportional. If the relationship is linear, k also represents the slope of the line.

For example, if we have a proportional relationship between the distance traveled, y, and the time taken, x, with a constant of proportionality, k = 60 (representing 60 miles per hour), the equation would be y = 60x. This equation implies that for each unit increase in x (in hours), y (in miles) will increase by 60 units.

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Answer:

c sorry if im wrong

Step-by-step explanation:

soryy if im wrong please forgive me if i am

Answer:

D.the diagonal bisect each other.Since bisectors divide the diagonals equally in two parts.

Answer:

x=12.9444444

Step-by-step explanation:

Answer:

x=12.94

Step-by-step explanation:

Using the limit comparison test, we determined that the series (A) diverges, (B) converges, (C) diverges, and (D) converges.

We can use the limit comparison test with the series 1/n to determine whether the series converges or diverges:

lim n→∞ (n7 + n2) / n = lim n→∞ (n7/n + n2/n) = ∞

Since this limit diverges to infinity, we cannot use the limit comparison test with the series 1/n. We can try another convergence test.

We can use the limit comparison test with the series 1/n3 to determine whether the series converges or diverges:

lim n→∞ (3n3 − 2n) / (6n5 + 2n + 1) = lim n→∞ (n2 − 2/n2) / (2n5 + 1/n + 1/n5) = 1/2

Since this limit is a positive finite number, the series converges if and only if the series ∑ 1/n^3 converges. Since the p-series with p = 3 converges, the series ∑ (3n^3 - 2n) / (6n^5 + 2n + 1) also converges.

We can use the limit comparison test with the series 1/n to determine whether the series converges or diverges:

lim n→∞ 2n / (4n − n2) = lim n→∞ 2/n(4 − n) = 0

Since this limit is a finite number, the series converges if and only if the series ∑ 1/n converges. Since the harmonic series diverges, the series ∑ 2n / (4n - n^2) also diverges.

We can use the limit comparison test with the series 1/n^2 to determine whether the series converges or diverges:

lim n→∞ sin(1/n) / (1/n^2) = lim n→∞ sin(1/n) * n^2 = 1

Since this limit is a positive finite number, the series converges if and only if the series ∑ 1/n^2 converges. Since the p-series with p = 2 converges, the series ∑ sin(1/n) / n also converges.

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It will take approximately 27 years to accumulate $100,000 in the savings account.

To calculate the time required, we can use the future value of an ordinary annuity formula. In this case, the annuity is the annual savings of $1,300, the interest rate is 5%, and the desired future value is $100,000. By plugging these values into the formula, we can solve for the number of periods (years) it will take to reach the target amount.

The formula is:

FV = P * ((1 + r)^n - 1) / r

Where FV is the future value, P is the annual payment, r is the interest rate, and n is the number of periods. Rearranging the formula to solve for n, we have:

n = log((FV * r / P) + 1) / log(1 + r)

Substituting the given values, we get:

n = log((100000 * 0.05 / 1300) + 1) / log(1 + 0.05)

Evaluating this expression, we find that n is approximately equal to 27. Therefore, it will take approximately 27 years to accumulate $100,000 in the savings account by saving $1,300 annually at an interest rate of 5%.

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Answer:

-3/4

Step-by-step explanation:

Formula: y2-y1/ x2-x1, so

9-6= 3

2-6= -4

Answer:

3/-4

Step-by-step explanation:

use the slope formula y-y/(x-x)

9-6/(2-6) and just do the math

3/-4.

its a and c maybe. cuz im smart

Answer:

a continuous function is a function that does not have any abrupt changes in value, known as discontinuities. If not continuous, a function is said to be discontinuous.

Step-by-step explanation:

got me a 100 in the journal activity

A function is continuous if the graph of function is an unbroken curve; that is, the graph has no holes, gaps, or breaks.

A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

We have to given that;

To describe means for something to be continuous.

Now, We know that;

A function is continuous at a point, if it must be defined at that point, its limit must exist at the point, and the value of the function at that point must equal the value of the limit at that point.

Thus, A function is continuous if the graph of function is an unbroken curve; that is, the graph has no holes, gaps, or breaks.

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The third member of the Pythagorean triple is 28 and this can be determined by using the Pythagorean theorem.

Given :

21 and 35 are two members of a Pythagorean triple.

The following steps can be used in order to determine the third member of the Pythagorean triple:

Step 1 - The Pythagorean theorem can be used in order to determine the third member of the Pythagorean triple.

\(H^2 = P^2+B^2\)

where the hypotenuse is H, the perpendicular is P, and the base is B of the right-angle triangle.

Step 2 - Now, substitute the value of H and P in the above expression in order to determine the value of 'B'.

\(35^2 = 21^2+B^2\)

Step 3 - Simplify the above expression.

\(B^2= 784\)

\(B = 28\)

So, the third member of the Pythagorean triple is 28.

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The distance between each pair of points (-1,4) and (1,-1) exists √29 units after utilizing the distance formula.

It is defined as the formula for finding the distance between two points. It has given the shortest path distance between two points.

The distance formula can be given as:

\($\mathrm{d}=\sqrt{\left(\mathrm{x}_2-\mathrm{x}_1\right)^2+\left(\mathrm{y}_2-\mathrm{y}_1\right)^2}\)

It is given that:

The distance between each pair of points (-1,4) and (1,-1)

Two points are (-1,4) and (1,-1)

To estimate the distance between the above two points utilize the distance formula:

\($\mathrm{d}=\sqrt{(1-(-1))^2+(-1-4)^2}$$\)

\($\mathrm{d}=\sqrt{(1+1)^2+(-1-4)^2}$$\)

The arithmetic operation can be described as the operation in which we do the addition of numbers, subtraction, multiplication, and division

d = √[(2)² + (-5)²]

simplifying the above equation, we get

d = √(4 + 25)

d = √29 units

Therefore, the distance between each pair of points (-1,4) and (1,-1) exists √29 units after utilizing the distance formula.

The complete question is:

Find the distance between each pair of points (-1,4) and (1,-1)

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The experimental probability that she will get a hit in her next at bat is: Experimental probability = 20 / 50 = 0.4

The experimental probability is calculated by dividing the number of successful outcomes (getting a hit) by the total number of outcomes (times at bat).

In this case, the softball player got a hit in 20 of her last 50 times at bat.

To find the experimental probability of getting a hit in her next at-bat, we can use the formula:

Experimental probability = Number of successful outcomes / Total number of outcomes

In this case, the number of successful outcomes is 20 (the number of times she got a hit) and the total number of outcomes is 50 (her total times at bat).

Therefore, the experimental probability that she will get a hit in her next at bat is:

Experimental probability = 20 / 50 = 0.4

So, the experimental probability is 0.4 or 40%.

This means that there is a 40% chance that the softball player will get a hit in her next at-bat, based on the data from her last 50 times at bat.

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The proof is completed and showed that < 2 ≅ < 3 as required.

Given data

<1 and <2 are linear pair

<1 + <3 = 180 degrees

required to proof <2 ≅ <3

linear pair implies mathematically that the sum of the two angles are 180 degrees, hence we have:

< 1 + < 2 = 180 degrees    equation 1

also given that,

< 1 + < 3 = 180 degrees    equation 1

equating equation 1 and equation 2 gives

< 1 + < 2 = < 1 + < 3

< 2 = < 3

Hence the required proof

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Answer:

I dont know I just really need points. Please Mark Brainliest

Step-by-step explanation:

Sorry

Answer:

1.C      2.  576 feet

Step-by-step explanation:

Answer:

(-1, 1)

Step-by-step explanation:

um i kinda feel like i got it wrong buuuuuuut yea

y=x²+2x+2

First, we should try to change the last number in a way so we can factor the entire thing

y=x² + 2 x + 1

tooo make it look like y=(x + 1 )²

the only difference between the original y=x² + 2x + 2

and the factor-able y=x² + 2x + 1 is simply changing the

2 to a 1 (Since we can't randomly change the 2 to a 1, we can add 1 and subtract a 1 to the equation at the same time to keep it balanced.)

ummmmm yeeaaa <3

We can represent "f(x)" as:

The derivate of a monomial we multiply the monomial by its expoent and subtract one on the expoent. We have:

The correct option is "a".

56/120

Step-by-step explanation:

The body masses of the two children in terms of their father's body mass, x, are:

First child's body mass = 5x/6 kg

Second child's body mass = 4x/5 kg

To express the body mass of the man's two children in terms of their father's body mass, we can use the given ratios.

Let the body mass of the man be x kg.

The first child's body mass is five-sixths of their father's body mass:

Body mass of the first child = (5/6) * x

= 5x/6 kg.

The second child's body mass is four-fifths of their father's body mass:

Body mass of the second child = (4/5) * x

= 4x/5 kg.

Therefore, the body masses of the two children in terms of their father's body mass, x, are:

First child's body mass = 5x/6 kg

Second child's body mass = 4x/5 kg

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A number is decreased by 8%, the result is 79. So the original number to the nearest tenth is 85.8.

These are the specified parameters:

a number is decreased by 8%, the result is 79.

Suppose, a number = x

a number - 8% a number = 79

x - 8/100 x = 79

100/100 x - 8/100 x = 79

92/100 x = 79

            x = 79 × 100/92

            x = 7900/92

            x = 85.8

So these numbers are 85.8.

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The Blu-ray movie will cost approximately $36.42 in 5 years with an inflation rate of 12% and continuous compounding.

To calculate the future cost of the Blu-ray movie in 5 years with an inflation rate of 12% and continuous compounding, we can use the formula for continuous compound interest:

A = P * e^(rt)

Where:

A = Future value

P = Present value

e = Euler's number (approximately 2.71828)

r = Annual interest rate (in decimal form)

t = Time period in years

In this case, the present value (P) is $19.99, the inflation rate (r) is 12% or 0.12, and the time period (t) is 5 years. Substituting these values into the formula, we get:

A = 19.99 * e^(0.12 * 5)

Calculating the exponent first:

0.12 * 5 = 0.6

Then:

e^0.6 ≈ 1.82212

Finally:

A = 19.99 * 1.82212 ≈ 36.42

Using the formula for continuous compound interest, we calculated that a Blu-ray movie that costs $19.99 today will cost approximately $36.42 in 5 years, assuming an inflation rate of 12% and continuous compounding.

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