Find a degree 3 polynomial with real coefficients having zeros 2 and 4 i and a lead coefficient of 1. Write P in expanded form. Be sure to write the full equation, including P ( x ) =

Answer:

[tex] 5x + 3y = 15 [/tex]

Step-by-step explanation:

The x-intercept is 3, so the ordered pair of that point is (3, 0).

The y-intercept is 5, so the ordered pair of that point is (0, 5).

We need the equation of the line that passes through points (3, 0) and (0, 5). Also, from the y-intercept, we know that b = 5 in the slope-intercept form of the equation of a line,

y = mx + b

b = 5

We now have:

y = mx + 5

We can find the slope using the two given points.

[tex] m = \dfrac{y_2 - y_1}{x_2 - x_1} = \dfrac{5 - 0}{0 - 3} = -\dfrac{5}{3} [/tex]

[tex] y = -\dfrac{5}{3}x + 5 [/tex]

Now we change the equation into standard form,

ax + by = c

[tex] y = -\dfrac{5}{3}x + 5 [/tex]

Multiply both sides by 3.

[tex] 3y = -5x + 15 [/tex]

Rearrange terms.

[tex] 5x + 3y = 15 [/tex]

Answer:

Step-by-step explanation:

An arithmetic sequence also known as arithmetic progression is a sequence of numbers in which the difference between consecutive terms are always the same  eg 1 5 9 13 17 , the difference is always 4

so THE ANSWER TO YOUR QUESTION IS B

The value of the x-intercept is -6

According to the question we have been the equation which is :

                      2y - 5x = 30  (1)

The general expression of slope intercept form is given as :

                 y = mx + c

  where, m = slope

              c = y-intercept

To find the value of x-intercept we will write equation (1) as an equation for x that is

              -5x =-2y + 30

Dividing both the sides by -5 we get

               x = 2/5y + (-6)

Which is in the form of slope intercept form which is

                x = my + c   and the x- intercept will be c = -6

Hence the x-intercept is -6

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In 6A, 10.5 coulomb of charge is moved through the filament in 1.75 seconds.

The electrical current that flows across conducting wires is carried by electrons, which are tiny particles. Negatively charged particles are electrons.

Charge is expressed in coulombs, or C.

The charge of an electron is 1.6 x[tex]10^{-19}[/tex]C.

The connection between current I and charge amount Q

Charged particle flow is what makes up an electric current.

One ampere of current flows when one coulomb of charge passes through a certain place in a circuit once every second.

The magnitude of an electric current affects how quickly charges flow.

I =[tex]\frac{quantity of charge(Q)}{Time taken (t)}[/tex]

Given: current I= 6A at time t=1.75s,

I = Q / t

Q = I x t

Q = 6 x 1.75

Q =  10.5 coulomb

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Answer:

282 [in²].

Step-by-step explanation:

all the details are in the attachment.

The equation, in point-slope form, matches the graphed line shown is y + 2= 0.8(x - 2)

The points on the line are given as

(-3, -6) and (2, -2)

Calculate the slope (m) of the line using

m = (y2 - y1)/(x2 - x1)

So, we have

m = (-2 + 6)/(2 + 3)

Evaluate

m = 0.8

The linear equation is then represented as

y - y1 = m(x - x1)

So, we have

y + 2= 0.8(x - 2)

Hence, the equation, in point-slope form, matches the graphed line shown is y + 2= 0.8(x - 2)

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The turning point of the function f(x) = |x| + 4 lie on the y - axis and has coordinates (0, 4).

A stationary point is called a turning point if the derivative changes sign (from positive to negative, or negative to positive  ) at that point. There are two types of turning points - local maxima and local minima.

Given in the question is a modulus function -

f(x) = |x| + 4

In order to determine the turning point, we will first have to plot the graph of this function -

f(x) = |x| + 4

Now, we can write f(x) as -

f(x) = { (x + 4)  for x ≥ 0    and       (- x + 4) for x < 0} }

Alternatively, you can plot the graph of |x| and positive shift it by 4 units. Refer to the graph attached with the answer. From the graph you can see that after the coordinate (0, 4) the slope becomes positive. Slope of a line gives the rate of change of y with respect to x. So (0, 4) represents the turning point.

Therefore, the turning point of the function f(x) = |x| + 4 lie on the y - axis and has coordinates (0, 4).

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The probability of getting no 1 and no 6 is 0.01%

There are six possible outcomes in a role. Since no 1 and 6 are to be rolled. There would only be 4 possible outcomes.

So, the chance of rolling no 1 and 6 is  

Since we have 5 rolls. Then we have:  1/6×1/6×1/6×1/6×1/6 =  =0.00013

Therefore, the probability of rolling no 1 and 6 is approximately 0.01%.

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it's  that a proposition is true.

he probability of an occasion is a number between 0 and 1, where, roughly speaking, 0 indicates the impossibility of the event and 1 indicates certainty.[note 1]]  the upper the probability of an event, the more likely it's that the event will occur.  an easy example is the tossing of a fair (unbiased) coin. Since the coin is fair,  the 2  outcomes ("heads" and "tails") are both equally probable; the probability of "heads" equals the probability of "tails"; and since no other outcomes are possible, the probability of either "heads" or "tails" is 1/2 (which could even be written as 0.5 or 50%).

These concepts are given an axiomatic mathematical formalization in probability theory, which is employed widely in areas of study such as statistics, mathematics, science, finance, gambling,  AI, machine learning,  computing,  theory of games, and philosophy,  for instance, draw inferences about the expected frequency of events.  applied mathematics is also used to describe the underlying mechanics and regularities of complex systems.

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Answer:

Rent-A-Truck-> 59.95+0.49m=c

Sam's U-Drive-> 81+0.38m=c

An equation to show the additional number of cases of water Mr. Brown needs is y = 24x - 3, where y = 333 bottles and x = 14.

An equation is a mathematical statement that claims that two mathematical expressions are equal.

An equation contains the equation symbol (=).

The number of bottles in his office = 17 bottles

The total number of bottles required = 350 bottles

The total number of additional bottles of water required, y = 333

1 case of water bottles = 24 bottles

The equation to show the additional cases required is y = 24x - 3, where y = 333 bottles and x = 14.

Check:

y = 24x - 3

333 = 24(14) - 3

333 = 336 - 3

333 = 333

Thus, an equation to show the additional number of cases of water Mr. Brown needs is y = 24x - 3, where y = 333 bottles and x = 14.

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The length and width of the screen is 9.71 inch and 12.71 inch.

A Rectangle is a four sided-polygon, having all the internal angles equal to 90 degrees. The two sides at each corner or vertex, meet at right angles.

Area of triangle = Length * Width

Let L be the length and W be the width of the rectangle.

Now it is given that,

Dimensions of a rectangular monitor screen are, its length is 3 in. more than its width.

⇒ L + 3 = W  

Therefore area is given as,

A = L * W

Put the value of W we get,

A = L * (L + 3)

Now, If the length were doubled and if the width were decreased by 1 in, the area would be increased by 104 in^2

Length = 2L

Width = W - 1

Thus area becomes,

A' = 2L(W - 1)

Now, the area would be increased by 104 in^2

A' = A + 104

Putting the value of A in A' we get,

A' = L * (L + 3) + 104

Now putting the value of A' we get,

2L(W - 1) = L * (L + 3) + 104

Expanding we get,

2LW - 2L = L^2 + 3L + 104

Since L + 3 = W  

Thus, putting W in above we get,

2L(L + 3) - 2L = L^2 + 3L + 104

Expanding the brackets we get,

2L^2 + 6L - 2L = L^2 + 3L + 104

Solving we get,

2L^2 + 4L = L^2 + 3L + 104

Taking all the terms together we get,

2L^2 + 4L - L^2 - 3L - 104 = 0

Solving alike terms we get,

L^2 + L - 104 = 0

Solving the above equation we get,

L = 9.71 inch, -10.71 inch

Since, Length cannot be negative

Thus,

L = 9.71 inch

Put the value of L in W we get,

9.71 + 3 = W  

⇒ W = 12.71 inch

Thus the required value of length and width is,

Length = 9.71 inch

Width = 12.71 inch

Thus, the length and width of the screen is 9.71 inch and 12.71 inch.

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The claimed made by Lawrence Summers that the women have a lower standards deviation IQ than men is not correct since only 0.15% population has IQ score more than 145

IQ, or intelligence quotient, is a measure of your ability to reason and solve problems. It reflects how well you did on a specific test compared to other people of your age group. While tests may vary, the average IQ on many tests is 100, and 68% of scores lie between 85 and 115.

Given that, suppose an IQ of 145 or higher is required to be a researcher at a top notch research institution

Use the idea of standard deviation, the Empirical Rule, and the fact that the mean and standard deviation IQ of  humans is 100 and 15, respectively, to explain summer's argument.

Approximately 99.7% of the data will lie within 3 standard deviations of the mean. That is, approximately 99.7% of the data lie between α-3β and

IQ scores between = α-3β and α+3β

IQ scores = 100-3x15 and 100+3x15

                = 55 and 145

We can see that approximately 99.7% of the population has IQ scores between 55 and 145

only 0.15% population has IQ score more than 145

Hence the claimed made by Lawrence Summers that the women have a lower standards deviation IQ than men is not correct since only 0.15% population has IQ score more than 145.

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Answer:

Lawrence Summers' assertion that women have a lower IQ standard deviation than men is untrue because only 0.15% of the population has an IQ higher than 145.

Step-by-step explanation:

Lawrence Summers' assertion that women have a lower IQ standard deviation than men is untrue because only 0.15% of the population has an IQ higher than 145.

Your capacity for reasoning and problem-solving is measured by your IQ, or intelligence quotient. It displays how well you performed on a certain test in comparison to other individuals in your age group. The average IQ on several tests is 100, and 68% of scores fall between 85 and 115, notwithstanding test variations.

Given that, let's assume that a prestigious research institute requires researchers to have an IQ of at least 145.

Explain summer's contention using the concept of standard deviation, the Empirical Rule, and the facts that human IQ has a mean of 100 and a standard deviation of 15, respectively.

The data will be within 3 standard deviations of the mean in about 99.7% of the cases. In other words, 99.7% of the values fall between -3 and

IQ scores ranging from -3 to +3

IQ scores are 100 x 3 x 15 and 100 x 3 x 15.

= 55 and 145

We can observe that between 55 and 145 is the range in which 99.7% of the population falls.

Only 0.15 percent of people have an IQ higher than 145.

Since just 0.15% of the population has an IQ score higher than 145, Lawrence Summers' claim that women have a lower standard deviation IQ than men is untrue.

Answer:

O If a ray bisects an angle, then it divides it into two congruent angles.

Step-by-step explanation:

(a) The value of f(83) is 5.

(b) It may or may not happen.

(c) The value of f(95) is 9.

Here, the height of the bar gives the marks at that particular point.

From the observations we can see,

(a) The interval 80-85 marks is point at the mark of 5. It means that there are 5 students who has scored in the interval of 80-85.

So, as are function is the exam score to the height of the bar whose interval contains that score.

Hereby, our value of f(83) will be equal to 5.

f(83) = 5.

(b) As, the marks are distributed over an interval. It can't be said that if any students scored exactly 83 marks or not. But the conclusion that we can draw is, that these 5 particular students have scored between 80-85 for sure.  

(c) The value of f(95) is equal to 9. as we can see that the interval is distributed in such a way that a group of five students is formed. and the last part of the interval is not included in the next interval. The interval here forms a pattern like this,

91-95, after that 96-100.

So here the value of f(95) will be 9.

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Based on the number, 98.48, the number you need to multiply by to get rid of the decimal is 100.

The number that you multiply a number with if you want to remove the decimal has to be a power of 10. The power of 10 used will depend on the number of figures after the decimal.

If there is a single number after the decimal point, then multiply by 10.

If there are two numbers after the decimal point, multiply by 100.

If there are three numbers after the decimal point, multiply by 1,000.

In the case of 98.48, there are two number after the decimal point so you'll multiply by 100 to get:

= 98.48 x 100

= 9,848

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Carl is outworked by Theresa in a given year.

What is work?

According to physics a push or pull in any substance which produces any displacement is called work. Activity in which one exerts strength or perform something or an activity that a person engages in regularly to earn a livelihood people looking for work.

Given:

Working day of Theresa/month=16

Working day of Carl/ month=20

Distance covered by Theresa in month= 56 miles round trip

Distance covered by Carl in month=56 miles round trip

Calculation

Distance covered by Theresa in month=56*2

Distance traveled by Theresa in a year=112*12

Distance traveled by Theresa in a year=1344 miles

Distance covered by Carl in month=112 miles

Distance traveled by carl in a year=112*11

Distance traveled by carl in a year=1232 miles

As the distance covered by Theresa is more than carl.

So Theresa travel more distance.

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Answer:

angle 1 = 6°
angle 2 = 84°

Step-by-step explanation:

since these 2 angles form 90°, they're called complementary

so when they're added they give 90°

x-6°+7x=90°, then we collect the like terms

x+7x=90°+6°, 8x=96°, divide both sides by 8 so we can get x

x=96/8, x=12, so now we substitute 12 in x so we can get the angles

FOR ANGLE 1:

12-6=6°

FOR ANGLE 2:

7(12)=84°

hope it helped, if it did mark me brainliest

Answer:

Is there more information

Step-by-step explanation:

I'll ll answer if there is

Answer:

Do the distributive property; your new equation will be 9x + 18 = 90

Step-by-step explanation:

The first step to the problem 9(x + 2) = 90 is the distribute property. Since we don't know what x is we can't add it to 2. Instead we do the distributive property, which is when you multiply the outside number to the terms inside the parenthesis.

The equation will then be: 9x + 18 = 90

! --- Note: I'm not too sure what you are trying to ask because your question is unclear but hope this helps in some way

----------------------------------------------------------------------------------------------------

! --- If you are also looking for what x is, x = 8

Answer:

distance = 13

Step-by-step explanation:

The formula used to calculate the distance between two points given their coordinates is:

[tex]\boxed{\mathrm{distance = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}}}[/tex],

where [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] are the given coordinates.

In this question, we are given the coordinates (8, -4) and (3, 8).

Using these coordinates and the formula above, we can calculate the distance between the points:

[tex]\mathrm{distance = \sqrt{(3 - 8)^2 + (8- (-4))^2}}[/tex]

             [tex]= \sqrt{(-5)^2+(12)^2}[/tex]

             [tex]= \sqrt{25 + 144}[/tex]

             [tex]= \sqrt{169}[/tex]

             [tex]= \bf 13[/tex]

Therefore, the distance between the two points is 13 units.

Answer:

In the expression

[tex] {x}^{2} - 11x + 10[/tex]

a in the formula will be substituted for 1

b in the formula will be substituted for -11

c in the formula will be substituted for 10

The type of reasoning for each statement is as follows:

Deductive reasoning is the type of reasoning that follows a more general statement to reach a specific conclusion. The conclusions of inductive reasoning is most likely true. This is the type of reasoning used in mathematics.

Inductive reasoning uses a more specific statement and arrive to a general conclusion. It is goes from bottom to up. The conclusion here is strongly persuasive to be true but still has false probability

For instance, in the second statement "Every Tuesday that Yolanda's family has visited a specific local restaurant, the kids' meals have been free" This does not logically mean the kids' meal is free but it is assumed to be free as it has been happening. more like taking a specific events that has happened for a while and assume it will always be so.

Abductive reasoning is the type of reasoning that follows an incomplete observation to reach a more likely conclusion. The conclusions of abductive reasoning is more of a probability. This is the type of reasoning used in used in our day to day events.

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Answer:

Step-by-step explanation

x1 = X sub-one, y1 = Y sub-one, x2 = x sub-two, y2 = y sub-two

Midpoint Formula

M (x1 + x2/2, y1 + y2)/2)

-4 = x1, 5 = y1 and 5 = x2, -3 = y2

L(-4,5) and N (5,-3)

-4 + 5/2 = 1/2 or 0.5

5 + (-3)/2 = 2/2 = 1

Midpoint : (1/2, 1)

Answer:

1/4

32%

0.4

Step-by-step:

1/4 = 0.25

32 = 0.33

0.4 = 0.40

The value of B is -7 and no decimal number.

So, in the sequence:

We can easily say that the value of B will be -7 and no decimal number.

So,

Therefore, the value of B is -7, and no decimal number.

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Step-by-step explanation:

the cost for n shirts is c=15+9(n-1)

c=15+9n-9 simplify

c=9n+6

n represents the number of shirts

so for the cost of 2 shirts, n=2

c=9(2)+6

c=24

therefore it costs $24 for 2 shirts

for the cost of 5 shirts, n=5

c=9(5)+6

c=51

therefore the cost of 5 shirts is $51

1 shirt = $15

2 shirts =$24

3 shirts =$33

24-15 =9

33-24=9

so 9 is the common difference which means each additional shirt is $9 more than the price of all the previous shirts

Answer:

33000

Step-by-step explanation:

To estimate the product of two numbers, round the individual numbers to numbers that you can multiply mentally.

Round 298 to the nearest hundred → 300.

(We don't need to round 110 as it is a multiple of 10, and therefore easy to multiply mentally).

Therefore,

⇒ 110 × 298 ≈ 110 × 300

To multiply 110 by 300, separate the 110 into 100 + 10:

⇒ 110 × 300 = (100 + 10) × 300

Apply the distributive property of multiplication:

⇒ (100 + 10) × 300 = 100 × 300 + 10 × 300

To multiply a number by 100, add two zeros.

To multiply a number by 10, add one zero.

Therefore:

⇒ 100 × 300 + 10 × 300 = 30000 + 3000 = 33000

Check

110 × 298 = 32780

32780 rounded to the nearest thousand is 33000.