Is x+2 a factor of the polynomial f(x)=2x^4-3x^2-4x+1?

a. f(2)=0, so (x+2) is a factor.
b. f(-2)=29, so (x+2) is not a factor.
c. f(-2)=0, so (x+2) is a factor.
d. f(2)=13, so (x+2) is not a factor.

Answer:

corresponding, supplementary, alternate interior, same side interior, vertical, alternate exterior, corresponding, alternate exterior, vertical, and alternate interior

In the figure 10, the pair of angles are alternate interior angles.

Angles in parallel lines are angles that are created when two parallel lines are intersected by another line called a transversal.

From the given figure,

1) corresponding angles

2) Adjacent angles (Supplementary)

3) Alternate interior angles

4) Allied angles (Same side interior)

5) Vertically opposite angles

6) Alternate exterior angles

7) corresponding angles

8) Alternate exterior angles

9) Vertically opposite angles

10) Alternate interior angles

Therefore, in the figure 10, the pair of angles are alternate interior angles.

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Answer:

D. (4,0) and (-4,0)

C. there is one discontinuity at x=3

Step-by-step explanation:

Roots can be found by setting f(x)=0:

f(x)=(x^2-16)/(x^2-2x-3)

0=(x^2-16)/(x^2-2x-3), multiply both sides by x^2-2x-3 to get rid of the denominator

0=x^2-16, use difference of squares to factor it

0=(x+4)(x-4)

x=4,-4

Therefore the roots are (4,0) and (-4,0)

Discontinuities are when f(x) is undefined, and f(x) is undefined when something is divided by 0

Set the denominator equal to 0:

0=x^2-6x+9, use the form a^2 - 2ab + b^2 to factor

0=(x-3)^2

x=3

Therefore, there is a discontinuity at x=3

The perimeter of the contest area on the judo mat will be 32 meters.

For a square with a side length of a unit, we get:

Perimeter of the square = 4a unit

The side length of square is 8 m.

Then the perimeter of the contest area on the judo mat will be

P = 4 x 8

P = 32 m

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Resolviendo un sistema de ecuaciones, veremos que se vendieron 250 boletos de adulto.

Definamos las variables:

Se vendieron un total de 430 boletos, entonces:

x + y = 430

Y se vendieron 70 boletos de estudiante menos que boletos de adulto:

y = x - 70

Tenemos el sistema de ecuaciones:

x + y = 430

y = x - 70

Para resolverlo, podemos reemplazar la segunda ecuación en la primera:

x + y = 430

x + (x - 70) = 430

2x = 430 + 70 = 500

x = 500/2 = 250

Se vendieron 250 boletos de adulto.

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The expressions that have a sum of 6 are Options C and D

In this case, we use the following rules

(-) + (-) = -

(+) + (+) = +

(+) + (-) = -

(-) + (+) = -

From the first case

8 + 2 = 10

(-4) + (-2) = -4 + -2 = -6

(-3) + 9 = -3 + 9 = 6

7 + (-1) = 7 - 1 = 6

Thus, the expressions that have a sum of 6 are Options C and D

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Answer:

multiply x and y coordinates by 2 since its a whole number dilation (make bigger basically) ... (-8,6)

Step-by-step explanation:

Hello, the solution is in this photo.

The correct answer is 300

Answer:

300cm^2

Step-by-step explanation:

Replace pie by 3. 3(10)^2 which equals to 300cm^2. 10 is radius.

Probability that Margie's first serve will be good at least four of the next six times she serves is 0.68

What is Binomial Distribution in Probability?

Assume that n independent replications of a random experiment with exactly two outcomes are performed. Success has a probability of [tex]p[/tex], while failure has a probability of [tex]q[/tex]. Assume that out of these n times, we will experience success [tex]x[/tex] times and failure [tex]n-x[/tex] times. There are [tex]^nC_x[/tex] different ways in which we can succeed. If, [tex]X[/tex] has a binomial distribution, then,

[tex]P(X=x)=p(x)[/tex]

                  [tex]=[/tex] [tex]^nC_xp^xq^{n-x}[/tex]

for [tex]x[/tex] = 0, 1,..., n. Here,  [tex]q=1-p[/tex]. A binomial variate is any such random variable [tex]X[/tex]. A group of n separate Bernoullian trials is known as a binomial trial. Binomial distribution requirements:

For each trial, the odds of success [tex]p[/tex], or failure [tex]q[/tex], remain constant.

Given,

Probability of good serves = Success

⇒ [tex]p=\frac{20}{30}[/tex]

⇒[tex]p=\frac{2}{3}[/tex]

Failure = [tex]q[/tex]

⇒ [tex]q=1-p[/tex]

⇒ [tex]q=1-\frac{2}{3}[/tex]

⇒ [tex]q=\frac{1}{3}[/tex]

Number of trials [tex]= n[/tex]

[tex]n=6[/tex]

Probability of at least four good serve = [tex]P(4 < X < 6)[/tex]

According to the binomial distribution,

Therefore,

[tex]P(4 \leq X \leq 6)=P(X=4)+P(X=5)+P(X=6)[/tex]

                      [tex]=[/tex] [tex]^6C_4(\frac{2}{3}) ^4(\frac{1}{3})^2+ ^6C_5(\frac{2}{3}) ^5(\frac{1}{3})^1+^6C_6(\frac{2}{3}) ^6(\frac{1}{3})^0[/tex]

                      [tex]=[/tex] [tex]15\times\frac{16}{729} +6\times\frac{32}{729} +1\times\frac{64}{729}[/tex]

                      [tex]=[/tex] [tex]\frac{496}{729}[/tex]

                      [tex]= 0.68[/tex]

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The surface area of the composite figure shown in the figure attached is 233.6 cm²

An equation is an expression that shows the relationship between two or more numbers and variables.

The surface area of the composite = (6 * 8) + 2(8 * 3.6) + 2(0.5)(6 + 2 + 6 + 2)(3) + (8)(2 + 6 + 2) = 233.6 cm²

The surface area of the composite figure shown in the figure attached is 233.6 cm²

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The statement 6.05 can be read as "six and five-hundredths" is true and 11.8 can be read as "eleven and eight tens" is false

6.05

6 = ones

0 = tenths

5 = Hundredth

6.05 = six and five-hundredths

11.8

1 = Tens

1 = Ones

8 = tenths

11.8 = eleven and eight tenths

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The value of x is 6 and the measure of ∠C is 86 degrees

The complete question is added as an attachment

Given that:

ABCDE ~ LMNOP

It means that we have the following equivalent ratio

ED : BC = PO : MN

This gives

8 : 6 = 12 : x

Express as fraction

6/8 = x/12

Multiply both sides by 12

12 *  6/8 = x

Evaluate

9 = x

Rewrite as

x = 9

Also

ABCDE ~ LMNOP implies that the corresponding angles are equal

The corresponding angle of C is N

And, we  have:

N = 86

This implies that

C = 86

Hence, the value of x is 6 and the measure of ∠C is 86 degrees

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Answer:

1:3.

Step-by-step explanation:

Probability(getting > 3 on one roll) = 3/6 = 1/2.

So on 2 cubes rolled the probability   of getting > 3 is 1/2 * 1/2 = 1/4.

As a ratio this is 1:3.

x + 3, x > -3 is the piece which will be included in the given function          f(x) = [ x + 3 ]. This can be obtained by removing modulus and finding the value for x.

Given that,  

f(x) = [ x + 3 ] which is an absolute value function.

Therefore,

| x+3 | > 0

By removing the modulus,

x+3 > 0

x > - 3

Hence x + 3, x > -3 is the piece which will be included in the given function          f(x) = [ x + 3 ].

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Disclaimer: The question was given incomplete on the portal. Here is the complete question.

Question: Consider this absolute value function.

f(x) = [ x + 3 ]

If function f is written as a piecewise function, which piece will it include?

A. x + 3, x > 3

B. x + 3, x > -3

C. -x + 3, x < -3

D. -x - 3, x < 3

Answer:

The Answer is C. X+3, x > -3

for edmentum users

Step-by-step explanation:

The slope of diagonal PS is  -1 and the slope of diagonal QR is 1 based on the information about the coordinate plane.

Step 1: Calculate the slope of the diagonals.

The slope of diagonal PS is  -1

The slope of diagonal QR is 1

Step 2: Calculate the midpoint of the diagonals.  

The midpoint of PS is (2,2)

The midpoint of QR is  (2,2)

The diagonals of the square are perpendicular bisectors because the diagonals are perpendicular and share the same midpoint

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Answer:

1. The slope of diagonal PS is -1.

2. The slope of diagonal QR is 1.

3. The midpoint of PS is (2,2).

4. The midpoint of QR is (2,2).

5. The diagonals of the square are perpendicular bisectors because the diagonals are perpendicular and share the same midpoint.

Step-by-step explanation: I just did it on edge 2023. Hope this helps!

Answer:

B.) 54π units²

Step-by-step explanation:

First, we need to find the height of the cone. We can do this using the Pythagreom Theorem.

a² + b² = c²                              <----- Pythagreom Theorem

3² + b² = 15²                            <----- Insert side lengths

9 + b² = 225                            <----- Solve 3² and 15²

b² = 216                                   <----- Subtract 9 from both sides

b = 14.7 units                          <---- Take square root of 216

Now, we can use the surface area of a right cone equation to find the final answer.

r = 3 units

h = 14.7 units

SA = πr(r + √(h² + r²))                              <----- Surface Area equation

SA = π(3)(3 + √(14.7² + 3²))                     <----- Insert values

SA = π(3)(3 + √(216 + 9))                         <----- Solve 14.7² and 3²

SA = π(3)(3 + √225)                                <----- Add 216 and 9

SA = π(3)(3 + 15)                                     <----- Take square root of 225

SA = π(3)(18)                                            <----- Add 3 and 15

SA = 54π units²                                     <----- Multiply 3 and 18

Answer:

[tex]y = \frac{1}{4} x + 9[/tex]

Step-by-step explanation:

All lines take the form

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

Where m is the gradient (or slope), and c is the y-intercept. To find the gradient if a line perpendicular to another, we must find the negative reciprocal of the other line. The gradient of the line given is -4, so our negative reciprocal is 1/4.

To find our y-intercept, we must find the point where the line crosses the y-axis (in other words, when the X coordinate is 0). Helpfully, the coordinate given is already at this point, so we can simply take the y coordinate from here, and we know our y-intercept is 9. Putting this altogether, our equation is:

[tex]y = \frac{1}{4} x + 9[/tex]

a. Area of A = 20 ft²

Area of B = 16 ft²

Area of C = 12 ft²

Area of A = 24 ft²

b. The surface area of the triangular prism = 96 ft².

The surface area of the triangular prism given in the diagram = area of A + B + C + D.

a.

Area of A (rectangle) = (length)(width) = (10)(2) = 20 ft²

Area of B (rectangle) = (length)(width) = (8)(2) = 16 ft²

Area of C (rectangle) = (length)(width) = (6)(2) = 12 ft²

Area of A (rectangle) = 1/2(base)(height) = 1/2(6)(8) = 24 ft²

b. The surface area of the triangular prism = 20 + 16 + 12 + 2(24) = 96 ft².

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Calculate the total amount invested by summing up all the values of the investment.

Total = 50,000

Calculate the weight of each investment. For WOOPS, weight = 5000 / 50000 = 10% and so on.

Now, Expected Return = sum of weight x Returns = 10% x 0.14 + 20% x 0.16 + ... + 18%x 0.18 = 16.01%

b) Similarly,

Beta of the portfolio = sum of weight x beta = 10% x 0.6 + 20% x 0.8 + ... + 18% x 0.18 = 0.7605

c) Portfolio has less systematic risk as the beta for the average market is 1, which is above the portfolio

d) Using CAPM, Return = Rf + beta x (Rm - Rf) = 4% + 0.7605 x (14% - 4%) = 11.605%

To calculate the expected return of a portfolio, the investor needs to know the expected return of each security in the portfolio and the total weight of each security in the portfolio. This means that investors need to sum the weighted averages of the expected returns (RoRs) of each security.

Investors are based on estimates of the expected rate of return on securities, assuming that what has proven to be true in the past will be true in the future. Investors do not use the structural view of the market to calculate the expected return. Instead, it determines the weight of each security in the portfolio by dividing the value of each security by the total value of the security.

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Answer: The lowest common multiple of 12, 18, and 56 would be 504. Why? Well, see below for an explanation!

Step-by-step explanation: What is the lcm? Well, the lcm of two or more numbers is the lowest possible number that each number has in common as a multiple. Because we are dealing with large numbers, we can tell that the lcm will be a multiple of these numbers times at least 5. I multiplied all the numbers by 10, and it was too large and did not work. However, I backed up and tried 9.

56 x 9 = 504.

Why is this acceptable? Well, this is acceptable because I found that 504 can be divided by 12 and 18 both to get a whole number.

504 divided by 18 equals 28.

504 divided by 12 equals 42.

Using this principle, we will find that 504 is the lowest number that 12, 18, and 56 have in common.

Your final answer: 504 is the lowest common denominator. If you need extra help, let me know and I will gladly assist you.

To obtain the least common multiple (lcm) we must do it by simultaneous decomposition.

This method consist of extracting the common and uncommon prime factors, then

[tex]\large\displaystyle\text{$\begin{gathered}\sf \left.\begin{matrix} \blue{12 \ \ \ 18 \ \ \ 56}\\ \ 6 \ \ \ \ 9 \ \ \ \ 28\\ \ 3 \ \ \ \ 9 \ \ \ \ 14\\ \ 3 \ \ \ \ 9 \ \ \ \ \ 7 \\ \ 1 \ \ \ \ 3 \ \ \ \ \ 7 \\ \ 1 \ \ \ \ 1 \ \ \ \ \ 7\\ \ 1 \ \ \ \ 1 \ \ \ \ \ 1 \end{matrix}\right|\begin{matrix} 2\\ 2\\ 2\\ 3\\ 3\\ 7\\ \: \end{matrix} \end{gathered}$}[/tex]

                        [tex]\sf{L.c.m.(12,18,56)=2\times2\times2\times3\times3\times7}[/tex]

                                        [tex]\sf{L.c.m.(12,18,56)=2^{3}\times3^{2}\times7 }[/tex]

                                            [tex]\boxed{\boxed{\sf{L.c.m.(12,18,56)=504}}}[/tex]

The lowest common multiple of 12, 18, and 56 is 504.

Answer: 15x-2

Step-by-step explanation: ?

Answer:

15x - 10

Step-by-step explanation:

[tex]5(3x-2)=5(3x)+5(-2)=15x-10[/tex]

Hope this helps

A significant problem is her sample will not be representative for her survey when she needed a large number of responses for her survey about taste preferences so she chose to do an internet survey.

what is internet survey ?

An Internet survey is a structured questionnaire that your target audience fills out over the internet, typically by filling out a form. The length and format of online surveys can vary. The data is saved in a database, and the survey tool usually includes some level of data analysis in addition to review by a trained expert.

Survey Advantages:

Unlike traditional surveys, internet surveys allow businesses to collect information from a large number of people at a low cost. When you conduct an internet survey, you will have the opportunity to learn:

Who are your customers?

What your users want to achieve?

What information are your users looking for?

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The table represents an exponential function:

[tex]f(x) = 3^x[/tex]

Then the correct option is B.

Here we have the table:

x       y

1       3

2      9

3      27

4      81

5      243

You can see that each time that x increases by one unit, the value of is multiplied by 3. This is clearly an exponential function.

The function actually is:

[tex]f(x) = 3^x[/tex]

Evaluating it we get:

[tex]f(1) = 3^1 = 3\\\\f(2) = 3^2 = 9\\\\f(3) = 3^3 = 27\\...[/tex]

So the correct option is B, exponential.

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The value of the expression 9w + 5x when w= 5 and x =9 is 90

9w + 5x

When

w = 5 and x = 9

9w + 5x

= 9(5) + 5(9)

= 45 + 45

= 90

Complete question:

What is the value of the expression below when w = 5 and x = 9? 9w + 5x

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The probability in all given conditions is 1/4.

According to the statement

Number of coin tossed = 3

Total outcomes = 8

Now, we have to find the probabilities on different conditions.

Probability = A head on each of the last two tosses/ total outcomes

Probability = 2/8

Probability = 1/4.

Probability = alternating tale and head / total outcomes

Probability = 2/8

Probability = 1/4.

Probability = A No tails on each of the last two tosses/ total outcomes

Probability = 2/8

Probability = 1/4.

So, The probability in all given conditions is 1/4.

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The slope of both lines is mathematically equivalent to

[tex]Slope=\frac{(z - v)}{ (x - w)}[/tex]i

Generally, the equation for Slope is  mathematically given as

[tex]S= dy / dx[/tex]

Therefore

[tex]Slope of PQ = \frac{(z - v)}{(x - w)}[/tex]

[tex]S of P'Q' =\frac{ (z + b - (v + b))}{((x + a) - (w + a))}\\\\S of P'Q' =\frac{ (z - v)}{(x - w)}[/tex]

The slopes of both lines are equivalent to

[tex]Slope=\frac{(z - v)}{ (x - w)}[/tex]

In conclusion, The slope of both lines is equivalent to

[tex]Slope=\frac{(z - v)}{ (x - w)}[/tex]

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Answer:

A: z - v | x - w

Step-by-step explanation:

Answer:15000

Step-by-step explanation:50,000 x 0.12=6,000 X 2=12,000

6000 divided by 2= 3,000

12 + 12=24+6=30

The probability of getting someone in the 22-29 age bracket or someone who agreed to respond is 0.96.

The rate of possible outcomes to the total outcomes is said to be the probability.

P(E) = n(E)/n(S)

E - event and S -sample space

we have,

P(A or B) = P(A) + P(B) - P(A and B)

It is given that,

Pollsters are concerned about declining levels of cooperation among persons contacted in surveys.

The data is listed below:

(Age group)                Response - agreed         Response - refused   Total

18-21                            76                                     14                                 90

22-29                          240                                   23                                263

Total                            316                                    37                                353

So, consider the required events

Age group (22-29) as A and someone who agreed to respond as B

Thus, the probabilities are calculated as below:

P(A) = n(A)/n(S) = 263/353

P(B) = n(B)/n(S) = 316/353

P(A and B) = n(A and B)/n(S) = 240/353

Substituting all these in the formula we get,

P(A or B) = P(A) + P(B) - P(A and B)

               = 263/353 + 316/353 - 240/353

               = 339/353

               = 0.96

Therefore, the required probability is 0.96.

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The exponential  equation that matches the coordinate is 3(2)^x while the linear equation is y = 6x

The standard exponential equation is expressed as y= ab^x

where

a is the base

x is the exponent

Given the coordinates (2, 12) and (4, 48)

12 = ab^2

48 = ab^4

Find the ratio

4 = b^2

b = 2

Sice ab^2 = 12

4a = 12

a = 3

The exponential  equation that matches the coordinate is 3(2)^x

For the linear equation

The standard form is y = mx + b

m is the slope = 48-12/4-2
Slope = 12/2

Slope = 6

For the y-intercept

12 = 6(2) + b

b = 0

Hence the required linear equation is. y = 6x

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Answer:

60 degrees

Step-by-step explanation:

The sum of the interior angles of a triangle are 180.  The bottom triangle give you two of the angle measurements (43 and 35)  Take 180 - 43 -35 = 102.  Angle E is 102.  Vertical angles are congruent so that mean that we can use that to find angle a.  Again, the sum of the interior angles adds up to 180.  180 - 102 - 18 gives us the measurement of angle a (60)

Answer:

[tex]x=-1,\frac{5}{7}[/tex]

Step-by-step explanation:

1) Split the second term in [tex]7{x}^{2}+2x-5[/tex] into two terms.

1 - Multiply the coefficient of the first term by the constant term.

[tex]7\times -5=-35[/tex]

2 - Ask: Which two numbers add up to 2 and multiply to -35?

7 and -5.

3 - Split 2x as the sum of 7x and -5x.

[tex]7x^2+7x-5x-5[/tex]

2)  Factor out common terms in the first two terms, then in the last two terms.

[tex]7x(x+1)-5(x+1)=0[/tex]

3) Factor out the common term x+1.

[tex](x+1)(7x-5)=0[/tex]

4) Solve for x.

1 - Ask: When will (x+1)(7x-5) equal zero?

When x + 1 0 or 7x-5=0

2 - Solve each of the 2 equations above.

[tex]x=-1,\frac{5}{7}[/tex]

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textbf{What are the quadratic formulas?}[/tex]

[tex]\bullet\rm{\ \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}}[/tex]

[tex]\bullet\rm{\ ax^2 + bx + c = 0}[/tex]

[tex]\huge\textbf{What are we solving for?}[/tex]

[tex]\rm{7x^2 + 2x - 5 = 0}[/tex]

[tex]\huge\textbf{What do we have to do?}[/tex]

[tex]\rm{7x^2 + 2x - 5 = 0}[/tex]

[tex]\huge\textbf{Factor the LEFT side of the given}\\\\\huge\textbf{equation:}[/tex]

[tex]\rm{(7x - 5)(x + 1) = 0}[/tex]

[tex]\rm{(7x - 5) \times (x + 1) = 0}[/tex]

[tex]\huge\textbf{Set 0 to the factors:}[/tex]

[tex]\rm{7x - 5 = 0\ or\ x + 1 = 0}[/tex]

[tex]\huge\textbf{Simplify it:}[/tex]

[tex]\rm{x = \dfrac{5}{7}\ or\ x = -1}[/tex]

[tex]\huge\textbf{Therefore, your answer should be:}[/tex]

[tex]\huge\boxed{\frak{\mathsf x = \dfrac{5}{7}\ or\ \mathsf{x} = -1}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]