Identify the simplest polynomial function that has the given zeros
-2,4,5
P(x) = x³ - 7x² + 2x + 40
P(x) = x³ + 7x² - 2x - 40
P(x) = x³ - 7x² + 2x - 40
P(x) =x^3+7x² - 2x + 40

Answer:

yes it does represent a function.  

Step-by-step explanation:

Answer:

A. 12.1

Step-by-step explanation:

To find volume using water displacement, you must subtract the final water level from the original.

62.1 - 50 = 12.1

9514 1404 393

Answer:

  A.  12.1 cm³

Step-by-step explanation:

Before the model soldier was added to the graduated cylinder, the volume in it was 50 mL. After the model soldier was immersed in the graduated cylinder, its volume was added to what was already there. That new total volume was 62.1 mL. The amount of volume the model soldier added was ...

  61.2 mL -50 mL = 12.1 mL = 12.1 cm³

_____

Additional comment

The volumes given in the problem statement are in milliliters (mL). The volumes given in the answer choices are cubic centimeters (cm³). These are two different names for the same volume.

__

The density of the soldier is (mass)/(volume) = (137.2 g)/(12.1 cm³) ≈ 11.34 g/cm³. This is equivalent to the density of lead.

Answer:

6x-

7y

=

-11

6x-7y=-11

Using the formula of volume of a sphere and hemisphere, the volume of the figures are given as;

1. 2144.57 m³

2. 696.6 m³

3. 20569.1m³

4. 2637ft³

5. 56.5km³

6. 6381.79 in³

The volume of a sphere is given as 4/3πr³

Where π is a constant whose value is equal to 3.14 approximately. “r” is the radius of the hemisphere.

1. The volume of the sphere is;

v = 4/3 * 3.14 * 8³ = 2144.57m³

2. The volume of the sphere is;

v = 4/3 * 3.14 * (11/2)³ = 696.6m³

3. The volume of the sphere is;

v = 4/3 * 3.14 * 17³ = 20569.1m³

4. The volume of the hemisphere is;

v = 2/3 * 3.14 * 10.8³ = 2637ft³

5. The volume of the hemisphere is;

v = 2/3 * 3.14 * 3³ = 56.5km³

6. The volume of the hemisphere is;

v = 2/3 * 3.14 * (29/2)³ = 6381.79in³

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The measure of the angle ABC given that the bisector is ABP is 12n degrees

From the question, we have the following parameters that can be used in our computation:

Angle measures

The angle measures and the relationships are given as

Using the above as a guide, we have the following:

The above statements mean that

ABC = 2 * ABP

substitute the known values in the above equation, so, we have the following representation

ABC = 2 * 6n

Evaluate the products

ABC = 12n

Hence, the measure is 12n degrees

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Answer:

It’s (-1,0),

Step-by-step explanation:

Matrix A belongs to the permutation and Markov classes. A permutation matrix is a square matrix with exactly one 1 in each row and each column, and 0s everywhere else.

This is the case for matrix A, as it has one 1 in each row and column and 0s everywhere else. Matrix A is also a Markov matrix, which means that all the entries are non-negative and the sum of each row is equal to 1. This can be seen by summing each row, which yields 1+0+0 = 1, 0+1+0 = 1, and 1+0+0 = 1.

Matrix B belongs to the orthogonal, projection, and diagonalizable classes. Matrix B is orthogonal, which means that it is a square matrix whose columns and rows are orthonormal unit vectors (i.e. the dot product of any two columns or rows is 0). This is the case for matrix B, as the dot product of any two columns or rows yields 0. Matrix B is also a projection matrix, which means that it is a square matrix whose columns are all of unit length (i.e. the dot product of any two columns or rows is 1). This can be seen by taking the dot product of any two columns or rows, which yields 1. Finally, matrix B is diagonalizable, which means that it can be transformed into a diagonal matrix using a similarity transformation. This can be seen by calculating the eigenvalues and eigenvectors of matrix B, which yields the same diagonal matrix.

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Answer:

Step-by-step explanation:

4x + 8 = 7x - 4 =

4x - 7x = -8 + (-4)

- 3x = -12

x = 4

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

4 * 4 + 8 = 7 * 4 - 4

24 = 24

the answer is good

Step-by-step explanation:

It has no solution

Answer:

a) $3700

b) $555

Step-by-step explanation:

The length of the loan is 3 years.

The interest after 3 years is $444.

The rate of the Simple Interest is 4%.

Simple Interest is given as:

I = (P * R * T) / 100

where P = principal (amount borrowed)

R = rate

T = length of years

Therefore:

\(444 = (P * 3 * 4) / 100\\\\444 = 12P / 100\\\\12P = 444 * 100\\\\12P = 44400\\\\P = 44400 / 12\\\)

P = $3700

She borrowed $3700

b) If the simple interest was 5%, then:

I = (3700 * 5 * 3) / 100 = $555

The interest would be $555.

Answer:

I believe that the answers are:

a= 65 degrees

b= 80 degrees

Step-by-step explanation:

Purple 80 and b should be the same so 80 degrees

180 - 80 is 100 which is A so a equals 100-35 whis is 65.

Answer:

a=65°, b=100°

Step-by-step explanation:

Hope the answers help! I got confused at first, but take a last look at line BE. Angle EAF is vertically opposite to this line. This means that angle BAF equals 80°. b=100°. a is just 180-80-35, so a=65°.

The concept of isosceles triangle is presented in this answer.

An isosceles triangle is a type of triangle in which two sides are of equal length. These two sides are known as the legs of the triangle, and the third side is called the base. The angles opposite to the legs are also equal in measure. This makes the isosceles triangle a symmetrical shape, with two congruent sides and angles.

In an isosceles triangle, the height is perpendicular to the base and bisects it, dividing the base into two equal parts. The height is also an axis of symmetry of the triangle, which means that if the triangle is folded along the height, the two halves will be congruent.

The problem is incomplete, hence concepts of isosceles triangles are presentd.

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Answer:

11

Step-by-step explanation:

Opposite sides of a trapezoid are parallel. So, by the same-side interior angles theorem,

\(-16x+10x+86=180 \\ \\ 10x+70=180 \\ \\ 10x=110 \\ \\ x=11\)

The system of equations are parallel lines and they do not intersect. Thus, the system has no solution.

Parallel lines are any two or more lines that all lie in the same plane and never cross one another. They are equally spaced apart and have the same incline.

No matter how far we extend a parallel line, it will never meet another parallel line.

Given that,

y=x-2

y=x-1

For x = 1:

y = x - 2 = 1 -2 = -1

y = x - 1 = 1 - 1 = 0

For x = 2:

y = 2- 2 = 0

y = 2 -1 = 1

Plot the graph using the points.

The two lines have the same slope hence they are parallel lines.

Since, the two lines are parallel the system has no solutions.

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we are allowed to change the vertical axis on a line chart.

suppose we have a large range of value needed to plot along the vertical and horizontal axis, but the current line chart cannot meet this demand. in such cases, we can customize the scales to provide more vertical and horizontal spaces.

dramatic slopes are the steep slopes of a straight line calculated by vertical and horizontal coordinate of two points laying on it. By changing the vertical axis as well as the horizontal axis we can plot a graph of a straight line more properly and finally more dramatic slope is visible there.

hence, we can change the scale values on a line chart to meet the requirement of the plot.

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Answer:

6 + 7/10x + 2/y

Step-by-step explanation:

Hope this helps :)

Answer:

36 units

Step-by-step explanation:

The actual probability histogram of how frequently we win will roughly follow the normal curve as both the number of games we play and the number of simulations we run increase.

The central limit theorem states that under certain conditions, the probability distribution of the sum (or average) of a large number of independent and identically distributed random variables will approach a normal distribution.

In the case of roulette, if we bet $5 on even numbers and count the number of times we win after a large number of bets, this corresponds to a sum of a large number of independent Bernoulli trials, each with probability p of success (winning on an even number). Therefore, if we want the true probability histogram of the number of times we win to approximately follow the normal curve, we need to ensure that the conditions of the central limit theorem are met.

One way to do this is to increase the number of times we play (i.e., the number of independent Bernoulli trials). As the sample size increases, the distribution of the sample mean (i.e., the proportion of wins) will become more normal.

Another way to achieve this is to increase the number of simulations used to approximate the probability histogram. The more simulations we run, the closer the probability histogram will be to the true underlying distribution. Moreover, as the number of simulations increases, the central limit theorem ensures that the distribution of the sample mean will converge to a normal distribution.

Therefore, both increasing the number of times we play and increasing the number of simulations will have the effect of making the true probability histogram of the number of times we win approximately follow the normal curve.

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Answer:

g

Step-by-step explanation:

Answer:

C)  Domain:  all real numbers x except x = ±2

E)  f(x) → ∞ as x → -2⁻ and as x → 2⁺, f(x) → -∞ as x → -2⁺ and as x → 2⁻

Step-by-step explanation:

Given function:

\(f(x)=\dfrac{3x^2}{x^2-4}\)

The domain of a function is the set of all possible input values (x-values).

A rational function is undefined when the denominator is equal to zero.

The denominator of the given function is zero when:

\(\implies x^2-4=0\)

\(\implies x^2=4\)

\(\implies \sqrt{x^2}=\sqrt{4}\)

\(\implies x= \pm 2\)

Therefore the domain of the function is:

The excluded x-values are x = -2 and x = 2.

To find the behaviour of the function near the excluded x-values, input values of x that are very near either side of excluded values:

\(x \rightarrow -2^-: \quad f(-2.001)=\dfrac{3(-2.001)^2}{(-2.001)^2-4}=3002.250...\)

\(x \rightarrow -2^+: \quad f(-1.999)=\dfrac{3(-1.999)^2}{(-1.999)^2-4}=-2997,750...\)

\(x \rightarrow 2^-: \quad f(1.999)=\dfrac{3(1.999)^2}{(1.999)^2-4}=-2997.750...\)

\(x \rightarrow -2^+: \quad f(2.001)=\dfrac{3(2.001)^2}{(2.001)^2-4}=3002.250...\)

Therefore, the behaviour of the function near the excluded x-values:

Standard form looks like this: Ax + By = C.

y - (-1) = 3(x - 4)

y + 1 = 3x - 12

y = 3x - 12 - 1

y = 3x + 13

Move 13 to left side and y to right side.

-13 = 3x - y

Done!

Answer:

8 years

Step-by-step explanation:

Answer:

A.

Step-by-step explanation:

that signs means that the value is not equal to the given value. So any number that q is, is not equal to 3.

Do you need to create an algebraic expression? In that case, the answer would be 6x.

Based on the NPV, project 2 should be chosen.

When the NPV is adjusted for unequal lives using the equivalent annual annuity, the decision does not change.

The net present value of a project is the cost of an asset or project less the sum of the discounted cash flows from the project.

NPV of Project 1

Cost of the project: -2,090,000

Discounted year 1 cash flow: 580,000 / (1.097) = 528,714.68

Discounted year 2 cash flow: 580,000 / (1.097)^2 = 481,964.15

Discounted year 3 cash flow:  580,000 / (1.097)^3 = 439,347.45

Discounted year 4 cash flow:  580,000 / (1.097)^4 = 400,499.04

Discounted year 5 cash flow:  580,000 / (1.097)^5 = 365,085.73

Sum of discounted cash flows = 2,215,611.05

NPV =  2,215,611.05  -2,090,000 = $125,611.05

NPV of Project 2

Cost of the project: -2,090,000

Discounted year 1 cash flow: 500,000 / (1.09) = 458,715.60

Discounted year 2 cash flow: 500,000 / (1.09)^2 = 420,840

Discounted year 3 cash flow:  500,000 / (1.09)^3 = 838,550.06

Discounted year 4 cash flow:  500,000 / (1.09)^4 = 354,212.61

Discounted year 5 cash flow:  500,000 / (1.09)^5 = 324,965.69

Discounted year 6 cash flow:  500,000 / (1.09)^6 = 298,133.66

Sum of discounted cash flows = 2,242,959.30

NPV = 2,242,959.30 - -2,090,000 = $152,959.30

Based on the NPV, project 2 should be chosen because it has a higher NPV.

Equivalent annual annuity = \(\frac{r(NPV)}{1 - \frac{1}{(1 + r)^{n} } }\)

Equivalent annual annuity for project 1:

\(\frac{0.097 (125,611.05)}{1 - \frac{1}{1.097^{5} } }\) = $32,882.31

Equivalent annual annuity for project 2:

\(\frac{0.09 (152,959.30)}{1 - \frac{1}{1.09^{6} } }\) = $34,079.65

Project 2 would be chosen because the equivalent annual annuity is higher.

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Answer:

\(\boxed{\sf{-30}}\)

Step-by-step explanation:

To solve this problem, all you have to do is solve by order of operations.

PEMDAS stands for:

First, remove parenthesis.

Multiply.

-3*10

Solve.

\(\sf{-3*10=\boxed{\sf{-30}}\)

-30

I hope this helps you! Let me know if my answer is wrong or not.

Answer:

-30

Step-by-step explanation:

it is adding 10 three times, but then you add the negative after

so it is 10+10+10 because you are multiplying it by 3

you could also add 3 ten times because the communitive property

so 3+3+3+3+3+3+3+3+3+3

you would do the same whether the -3 was in parentheses or not

Answer:

Intersecting (fourth answer choice)

Step-by-step explanation:

First, let's convert both lines to slope-intercept form, whose general equation is y = mx + b, where

Converting y - 3x = 4x to slope-intercept form:

(y - 3x = 4x) + 3x

y = 7x

Thus, the slope of this line is 7 and the y-intercept is 0.

Converting 6 - 2y = 8x to slope-intercept form:

(6 - 2y = 8x) - 6

(-2y = 8x - 6) / -2

y = -4x + 3

Thus, the slope of this line is -4 and the y-intercept is 3.

Checking if y = 7x and y = -4x + 3 are perpendicular lines:

We can show this in the following formula:

m2 = -1 / m1, where

Thus, we only have to plug in one of the slopes for m1.  Let's do -4.  

m2 = -1 / -4

m2 = 1/4

Thus, the slopes 7 and -4 are not negative reciprocals of each other so the two lines are not perpendicular.

 Checking if y = 7x and y = -4x + 3 are parallel lines:

The slopes of parallel lines are equal to each other.

Because 7 and -4 are not equal, the two lines are not parallel.

Checking if the lines intersect:

Method to solve the system:  Elimination:

We can multiply the first equation by -1 and keep the second equation the same, which will allow us to:

-1 (y = 7x)

-y = -7x

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

    -y = -7x

+

    y = -4x + 3

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

(0 = -11x + 3) - 3

(-3 = -11x) / 11

3/11 = x

Now we can plug in 3/11 for x in y = 7x to find y:

y = 7(3/11)

y = 21/11

Thus, x = 3/11 and y = 21/11

We can check our answers by plugging in 3/11 for x 21/11 for y in both y = 7x and y = -4x + 3.  If we get the same answer on both sides of the equation for both equations, the lines intersect:

Checking solutions (x = 3/11 and y = 21/11) for y = 7x:

21/11 = 7(3/11)

21/11 = 21/11

Checking solutions (x = 3/11 and y = 21/11) for y = -4x + 3:

21/11 = -4(3/11) + 3

21/11 = -12/11 + (3 * 11/11)

21/11 = -12/11 + 33/11

21/11 = 21/11

Thus, the lines y = 3x = 4x and 6 - 2y = 8x are intersecting lines (the first answer choice).

This also means that lines are not skew since lines had to be neither perpendicular nor parallel nor intersecting to be skew.

The turning points of the function y = x³ - 3x² - 9x + 4 are (3, -23) and (-1, 9).

To determine the turning points of the given function y = x³ - 3x² - 9x + 4, we need to find the critical points where the derivative of the function is equal to zero.

1. Find the derivative of the function:

  y' = 3x² - 6x - 9

2. Set the derivative equal to zero and solve for x:

  3x² - 6x - 9 = 0

3. Factorize the quadratic equation:

  3(x² - 2x - 3) = 0

4. Solve the quadratic equation by factoring or using the quadratic formula:

  (x - 3)(x + 1) = 0

  This gives us two possible values for x: x = 3 and x = -1.

5. Substitute these critical points back into the original function to find the corresponding y-values:

  For x = 3:

  y = (3)³ - 3(3)² - 9(3) + 4

    = 27 - 27 - 27 + 4

    = -23

  For x = -1:

  y = (-1)³ - 3(-1)² - 9(-1) + 4

    = -1 - 3 + 9 + 4

    = 9

6. Therefore, the turning points are (3, -23) and (-1, 9).

Note: It appears that there was a typo in the original equation, where the term "-9x" should have been "-3x²". The above solution assumes the corrected equation.

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