Write a polynomial function P(x) with rational coefficients so that P(x) = 0 has the given roots. 2+√2i, 4+i

Answer:

The area of the trapezoid should be:

A = (a + b)/2 · h = (4 + 8)/2 · 4 = 24

So the area of the trapezoid is 24 square units.

The answer is B.) 24 square units

Answer:

f(x)= x^3-5x^2-23x-12

Step-by-step explanation:

Given:

function f(x) divided by x + 2, the quotient is x2 – 7x – 9 and the

remainder is 6

When a polynomial f(x) is divided by any another polynomial d(x) and there is q(x) and r then it can be written as:

f(x)= d(x)q(x) + r

Now putting values of d(x)= x+2, q(x)= x2 – 7x – 9 and r=6, we get

f(x)= (x+2)(x^2-7x-9)+6

f(x)= x^3 -7x^2-9x+2x^2-14x-18+6

    = x^3-5x^2-23x-12 !

Final answer:

To find the function given a quotient and remainder when divided by x + 2, combine the terms to get f(x) = x² - 7x - 3. The resulting function f(x) is in standard form.

Explanation:

The function f(x) is a polynomial that can be expressed as f(x) = x² - 7x - 9 + 6/(x + 2). Finding the function in standard form involves combining the quotient and remainder terms.

To write it in standard form, simplify the expression to f(x) = x² - 7x - 3.

Therefore, the function f(x) = x² - 7x - 3.

Answer:

m∠8 = 123°

Step-by-step explanation:

∠1 and ∠8 are alternate exterior angles, and since lines A and B are parallel, then they must be congruent.

So, m∠1 = m∠8

Substitute: 123 = m∠8

Answer:

1.400 as a common fraction is 7/5

as a percentage 140%

Step-by-step explanation:

1.4 written as a fraction is;

[tex]\frac{14}{10}[/tex]

simplifying we have;

[tex]\frac{14}{10}=\frac{7}{5}[/tex]

Converting to percentage we simply multiply by 100.

[tex]\frac{7}{5}*100=140[/tex]

B and D are clearly permutation. A and B are selections but arrangement should be done for A where as C only requires selection so C is the combination.

The example which describes combination is:

Combination--

It is a method of choosing or selecting some items from a group of items.

The formula for choosing r items out of a total of n items is given by the formula:

[tex]n_C_r=\dfrac{n!}{r!\times (n-r)!}[/tex]

Also, if we are selecting as well as arranging some items from a group of items then that method is known as a method of permutation.

A)

Selecting the best cake and runner up best cake from a cake decorating competition.

In this case we are choosing as well as arranging the best and runner up cake according to their ranks.

Hence, it will be a process of permutation and not combination.

B)

The number of ways 6 people can arrive at a party if no one arrive at the same time.

Again it is a problem of permutation because we have to find the number of ways the people can arrive i.e. arranging people in different orders they may arrive.

C)

Selecting 5 CD's to take with you on a trip from a collection of 30 CD's.

This is a method of combination.

Since we have to select some items from a set of items.

D)

The number of ways triplets can be born.

This is again a process of permutation.

Since there are different order they may come.

Answer:

The function is exponential.

The function increases by a factor of 2.5 for each unit increase in x

The domain of the function is all real numbers

Step-by-step explanation:

The function is exponential.

The function increases by a factor of 2.5 for each unit increase in x

The domain of the function is all real numbers

|x-4| <3

=>. x-4<3 or -(x-4)<3

=>. x-4<3 or x+4>3

=>. x<7 or x>1

So solution is x>1 & x<7. =x€(1,7)

Hope it helps...

Regards,

Leukonov/Olegion.

The solution to the given inequality is:

              [tex]1<x<7[/tex] i.e. in the interval form it is given by: (1,7)

We are given a inequality in term of variable x as follows:

          [tex]|x-4|<3[/tex]

Now, we know that any inequality with modulus function is opened as follows:

If

[tex]|x-a|<b[/tex]

Then we have:

[tex]-b<x-a<b[/tex]

i.e. we may write it as:

[tex]a-b<x<a+b[/tex]

Here in the given expression we have:

a=4 and b=3

Hence, the solution is given by:

[tex]4-3<x<4+3\\\\i.e.\\\\1<x<7[/tex]

Answer:

Step-by-step explanation:

Method 1:

The slope-intercept of an equation of a line:

[tex]y=mx+b[/tex]

m - slope

b - y-intercept

We have the equation of a line in the point-slope form:

[tex]y-4=2(x-6)[/tex]

Convert it the the slope-intercept formula:

[tex]y-4=2(x-6)[/tex]            use the distributive property

[tex]y-4=2x-12[/tex]             add 4 to both sides

[tex]y=2x-8\to b=-8[/tex]

Method 2:

The y-intercept is for x = 0. Put x = 0 to the equation:

[tex]y-4=2(0-6)[/tex]

[tex]y-4=2(-6)[/tex]

[tex]y-4=-12[/tex]           add 4 to both sides

[tex]y=-8[/tex]

[tex]\frac{sin(x+y)}{sin(x-y)} = \frac{tan(x)+tan(y)}{tan(x)-tan(y)}[/tex]

Answer with explanation:

→sin (x+y)=sin x cos y +cos x sin y

→sin (x-y)= sin x cos y - cos x sin y

[tex]\Rightarrow \frac{\sin (x+y)}{\sin (x-y)}\\\\\Rightarrow \frac{\sin x \cos y + \cos x \sin y}{\sin x \cos y - \cos x \sin y}\\\\\rightarrow \text{Dividing numerator and Denominator by} \cos x \cos y\\\\ \Rightarrow \frac{\frac{ \sin x \cos y}{\cos x \cos y} +\frac{ \sin y \cos x}{\cos x \cos y}}{\frac{ \sin x \cos y}{\cos x \cos y} -\frac{ \sin y \cos x}{\cos x \cos y}}\\\\\Rightarrow \frac{\tan x +\tan y}{\tan x -\tan y}[/tex]

Answer:

A, 5n - 300 = 1,500

Step-by-step explanation:

yw gen2020

The equation that could be used is 5n - 300 = 1,500

The DJ charges $200 and decorations cost $100. The team decides to charge each student $5.00 to attend the dance.

Since n represent the no of students

So, the equation should be

5n - ($200 + $100) = $1500

5n - 300 = 1,500

Learn more about the equation here: https://brainly.com/question/6945567

Answer:

Step-by-step explanation:

It means that you will a 2 or a 3 or a 4 or a 5 or 6.

All of these are permitted.

So the probability of getting at least a 2 is 5/6.

Answer:

434

Step-by-step explanation:

2(wl+hl+hw)

Answer: the surface is 434 square feet.

Step-by-step explanation:

you can use the formula of right rectangular is 2(wl+wh+lh). The rectangular prism has 6 faces. So the surface area is 434 square feet.

Answer:

C.

Step-by-step explanation:

A false negative is when you test negative when you should have tested positive

A false positive is when you test positive on a test you should have been negative on

Testing positive for a disease when you don't really have the disease is option C. False positive.

False positive is defined as the error caused by the false positive of an actual negative condition.

There are mainly two kinds of errors in probability.

One is false positive and the other one is false negative.

False positive error as discussed above is the false positive statement for an actual negative condition.

For example, a test result showing that you are pregnant while you are actually not.

False negative errors are those formed by the false negative for an actual positive statement.

For example, a test result showing that you are not pregnant while you are actually pregnant.

Here, since the test result is positive but actually you don't have the disease is a false positive.

Hence the given statement is false positive.

Learn more about False Positives and False Negatives here :

https://brainly.com/question/18427929

#SPJ7

Answer:

Step-by-step explanation:

f(-4)= 6

f(0)= -6

f(1)= -4

The function values are:

[tex]- \(f(-4) = 22\)\\- \(f(0) = 10\)\\- \(f(1) = 7\)[/tex]

To find the indicated function values, we need to use the function \(f(x) = -3x + 10\).

Let's calculate the values:

1. \(f(-4)\):

  Plug in -4 for \(x\):

 [tex]\[f(-4) = -3(-4) + 10\][/tex]

[tex]\[f(-4) = 12 + 10\][/tex]

 [tex]\[f(-4) = 22\][/tex]

2. \(f(0)\):

  Plug in 0 for \(x\):

 [tex]\[f(0) = -3(0) + 10\][/tex]

 [tex]\[f(0) = 0 + 10\][/tex]

 [tex]\[f(0) = 10\][/tex]

3. \(f(1)\):

  Plug in 1 for \(x\):

[tex]\[f(1) = -3(1) + 10\][/tex]

[tex]\[f(1) = -3 + 10\][/tex]

[tex]\[f(1) = 7\][/tex]

So, the function values are:

[tex]- \(f(-4) = 22\)\\- \(f(0) = 10\)\\- \(f(1) = 7\)[/tex]

Learn more about function  at https://brainly.com/question/29631554

#SPJ3

[tex]1.5+9\times3[/tex]

First multiplication (9 × 3).

[tex]1.5+9\times3=1.5+27[/tex]

Than addition. (1.5 + 27)

[tex]1.5+27=\boxed{28.5}[/tex]

The result is 28.5

Hope this helps.

You can help me by making this answer the brainliest.

To evaluate a numerical expression, one must follow the order of operations and ensure units are consistent, simplify the algebra, and substitute numbers carefully. After calculation, unit consistency and reasonable result checks must be performed.

To evaluate a numerical expression, it is essential to follow the order of operations, often remembered by the acronym PEMDAS: Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right). Before we begin calculations, we must ensure all values are in their correct units. This is particularly important when working with physical quantities that might have units (like meters, seconds, kilograms, etc.), which is a concept known as dimensional analysis. If we are asked to simplify algebraic expressions, we might apply rules involving exponents to make the expression more manageable.

To correctly simplify the algebra, we can combine like terms and reduce expressions where possible. Once we have the simplified form, we can substitute any given numerical values, making sure the substitution is done accurately, respecting the dimensions of each term. After calculating the answer, it is critical to check the units to ensure that they are reasonable and consistent with the problem's context. Additionally, if the evaluation involves significant figures, it's important to apply the rules of significant figures, since calculators by default do not consider these rules.

If the question involves solving for an unknown using roots such as square roots or cube roots, ensure you know how to perform such operations properly using a calculator. Once you have calculated the final numerical answer, double-check to make sure the answer is reasonable in the context of the original problem.

Answer:

128

Step-by-step explanation:

4*4*8=

Answer:

109.85641

Step-by-step explanation:

A=2AB+(a+b+c)h

A=ah+bh+ch+1/2 squared rooted﹣a4+2(ab)2+2(ac)2﹣b4+2(bc)2﹣c4

=4·8+4·8+4·8+1/2·squared rooted﹣44+2·(4·4)2+2·(4·4)2﹣44+2·(4·4)2﹣44

≈109.85641

Answer:

28.3 Square Feet

Step-by-step explanation:

Diameter of circle=6 feet

then

radius=diameter/2

=6/2

=3 feet

The area of circle is given by  

A = πr^2

where r is the radius of the circle

Putting the values of pi and r

A =(3.14)(3)^2

=3.14*9

=28.26 sq. feet

Rounding off to the nearest tenth

A=28.3 sq. feet

So, 28.3 sq. feet need to be painted for the base circle ..

Answer:

D) L(p(x)) = 2.5(1.04954)x

Step-by-step explanation:

Answer:

1/2

Step-by-step explanation:

Use the slope formula:

[tex] slope = m = \dfrac{y_2 - y_1}{x_2 - x_1} [/tex]

[tex] slope = m = \dfrac{6 - 4}{5 - 1} [/tex]

[tex] slope = m = \dfrac{2}{4} [/tex]

[tex] slope = m = \dfrac{1}{2} [/tex]

[tex] \frac{y2 - y1}{x2 - x1} = \frac{4 - 6}{1 - 5} = - 2 \div - 4 = 1/2

For this case we have that if "and" varies directly proportional to "x", it follows that:

[tex]y = kx[/tex]

Where:

k: It is the constant of proportionality.

Then, we look for the value of "k":

[tex]9 = k (5)\\k = \frac {9} {5}[/tex]

So, now we look for the value of "y" when x = 20.

[tex]y = \frac {9} {5} (20)\\y = \frac {180} {5}\\y = 36[/tex]

Thus, the value of y is 36

Answer:

[tex]y = 36[/tex]

Answer:

Final answer is y=36 and the constant of variation is k=9/5.

Step-by-step explanation:

Given that the variable y varies directly to the variable x.

Then we can write equation as y=kx

Were k is the constant of variation.

Given that If y = 9, then x = 5.

Plug these values into above equation, we get:

y=kx

9=5k

5k=9

k=9/5

Now we need to find the value of y when x = 20. So plug x = 20 and k=9/5 into above formula

y=kx

y=(9/5)(20)

y=180/5

y=36

Hence final answer is y=36 and the constant of variation is k=9/5.

Answer:

C

Step-by-step explanation:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r is the radius

here (h, k) = (- 3, 2), thus

(x + 3)² + (y - 2)² = r²

The radius is the distance from the centre of the circle to a point on the circle.

Calculate r using the distance formula

r = √ (x₂ - x₁ )² + (y₂ - y₁ )²

with (x₁, y₁ ) = (- 3, 2) and (x₂, y₂ ) = (6, 4)

r = [tex]\sqrt{(6+3)^2+(4-2)^2}[/tex]

  = [tex]\sqrt{9^2+2^2}[/tex] = [tex]\sqrt{85}[/tex]

Hence

(x + 3)² + (y - 2)² = ([tex]\sqrt{85}[/tex] )², that is

(x + 3)² + (y - 2)² = 85 → C

The circumference of a circle is found by multiplying the diameter by PI.

Since the answer are in the form of PI, the answer is 140π ft.

Answer:

112.98

Step-by-step explanation:

37.68/2π = 5.9969

5.9969²π = 112.98

ANSWER

The area is 112.9 square units to the nearest tenth.

EXPLANATION

The circumference is given by:

[tex]C=2\pi \: r[/tex]

This implies that,

[tex]37.68 = 2 \: \pi \: r[/tex]

[tex] \frac{37.68}{2\pi} = r[/tex]

[tex]r = 5.997[/tex]

The area of a circle is

[tex]\pi \: {r}^{2} [/tex]

We substitute the radius to get;

[tex]3.14 \times 5.997 ^{2} = 112.93 \: sq. \: units[/tex]

To the nearest tenth, the area of the circle is 112.9 square units.

Answer:

Step-by-step explanation:

We have:

two rectangles 2 × 3

two rectangles 3 × 5

two rectangles 2 × 5

Calculate the areas:

A₁ = (2)(3) = 6

A₂ = (3)(5) = 15

A₃ = (2)(5) = 10

The Surface Area:

S.A. = 2A₁ + 2A₂ + 2A₃

S.A. = (2)(6) + (2)(15) + (2)(10) = 12 + 30 + 20 = 62

The function f(x) = (x^2 - 4x - 12) / (x + 2) is a rational function, which is a ratio of two polynomials. To find its discontinuity, we identify values of x which makes the denominator zero, in this case x = -2, making this the function's discontinuity.

The function given is f(x) = (x^2 - 4x - 12) / (x + 2). This is a rational function, which is a ratio of two polynomial functions - in this case, a quadratic function (x^2 - 4x - 12) and a linear function (x + 2).

To find the discontinuity of a rational function, we need to identify the values of x that make the denominator zero since division by zero is undefined. In this case, that's when x = -2. Thus, this function has a discontinuity at x = -2.

Note that this does not factor into the asymptote of the function as some might believe, but it's instead a point at which the function is undefined. "Graphing this function would show a hole at x = -2".

https://brainly.com/question/28914808

#SPJ3

Answer: Slope of the line is -9/7

Step-by-step explanation:

Given :

Points : (10,9) and (3,18)

Now slope of line when two points are given

m=[tex]\frac{y2-y1}{x2-x1}[/tex]

Slope = [tex]\frac{18-9}{3-10}[/tex]

m=[tex]\frac{9}{-7}[/tex]

m=[tex]\frac{-9}{7}[/tex]

This is an improper fraction since numerator is greater than the denominator

Hence slope of the line is -9/7

Answer: 1/4

Explanation: Because there is a 1/2 chance that a female will get the first job, and a half chance that a lady will get a second job. So (1/2)*(1/2)=(1/4)

Answer:

a=5, s=3

Step-by-step explanation:

a=adult s=student

then write 2 equations to represent the amount of people and money

a+s=8

7.25a+5.5s=52.75

• To solve a pair of equations using substitution, first solve one of the equations for one of the variables. Then substitute the result for that variable in the other equation.

{a+s=8, 7.25a+5.5s=52.75}

• Choose one of the equations and solve it for a by isolating a on the left hand side of the equal sign.

a+s=8

• Subtract s from both sides of the equation.

a=−s+8

• Substitute −s+8 for a in the other equation, 7.25a+5.5s=52.75.

7.25(−s+8)+5.5s=52.75

• Multiply 7.25 times −s+8.

−7.25s+58+5.5s=52.75

• Add −29s/4  to 11s/2.

−1.75s+58=52.75

• Subtract 58 from both sides of the equation.

−1.75s=−5.25

• Divide both sides of the equation by −1.75, which is the same as multiplying both sides by the reciprocal of the fraction.

s=3

• Substitute 3 for s in a=−s+8. Because the resulting equation contains only one variable, you can solve for a directly.

a=−3+8

• Add 8 to −3.

a=5  

Answer:

1/2 + 1/4 + 1/12 + 8333/10000

Answer:

C & D

Step-by-step explanation:

Change all the test scores so they have common denominators.

Unit 1 91/100

Unit 2 45/50 * 2/2 = 90/100

Unit 3 18/20 * 5/5 = 90/100

Unit 4 23/25* 4/4 = 92/100

As you can see, Unit 2 and 3 are equivalent.

I believe the answers are C and D. You have to change the test scores so they have common denominators. Correct me if I'm wrong. Hope this helps!