PLEASE HELP (20 POINTS)

POLYNOMIAL FUNCTIONS UNIT TEST

Can x3+8 be factored? Explain


Yes, because x3 and 8 both share a common factor.


No, because x3 and 8 do not have any common factors.


No, because a sum of cubes cannot be factored.


Yes, because a sum of cubes can be factored.

The   statement that is true ,congruence of corresponding angles is preserved under rigid Transformations.

If a series of rigid transformations maps ∠F onto ∠C, where ∠F is congruent to ∠C, it implies that the two angles have the same measure or size. Given this information, the following statement is true:

The congruence of corresponding angles is preserved under rigid transformations.

Rigid transformations, such as translation, rotation, and reflection, preserve the size, shape, and angles of geometric figures. When ∠F is congruent to ∠C, it means that the measures of the angles are equal.

By applying a series of rigid transformations that map ∠F onto ∠C, the congruence between the two angles is maintained. This means that the resulting transformed angle, after the series of transformations, will still have the same measure as the original angle.

In other words, if ∠F and ∠C are congruent, the rigid transformations will preserve the equality of their measures. Therefore, the congruence between the corresponding angles is maintained throughout the series of rigid transformations.

It is important to note that congruent angles have equal measures, but their orientations or positions may differ. Rigid transformations do not change the measure of angles but can alter their positions or orientations in space.

Hence, the statement that is true in this context is:

The congruence of corresponding angles is preserved under rigid transformations.

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A stone arch can be twice as wide as a stone lintel because an arch distributes the weight of the structure vertically down its curve to the columns (piers) on either side while a lintel distributes the weight horizontally along the length of the stone.

A stone arch can be twice as wide as a stone lintel because an arch distributes the weight of the structure vertically down its curve to the columns (piers) on either side while a lintel distributes the weight horizontally along the length of the stone.

It requires only a small fraction of the arch's width to support itself while a lintel requires the full width of the structure that it spans. Thus, a stone arch can span a larger gap than a stone lintel and be twice as wide while using the same material.

For example, the Roman Colosseum uses an arch to span the entrances and exits while the walls supporting the upper levels use a series of stone lintels to support the structure.

Moreover, the arc prevents the need for a central support structure, which would be in the way of any events taking place in the structure. The technology of arches made them fundamental to ancient Roman architecture. For example, the arches were used to construct aqueducts, which provided a steady supply of water to the city of Rome.

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The factors of the expression (x³ - 6x² + 3x + 10) are (x + 1), (x - 2), and (x - 5).

We are given a mathematical expression. The expression is cubic in nature. We need to find the factors of the algebraic expression. Let the expression be represented by the variable "E". The expression consists of three terms. Hence, the expression is trinomial. The expression is given below.

E = x³ - 6x² + 3x + 10

One of the factors in the expression is already given. The given factor is (x + 1).

Now we will perform the long division method on the expression to break it into the given factor and a quadratic expression.

E = (x + 1)(x² - 7x + 10)

Now we will factorise the quadratic expression.

E = (x + 1)[x² - 2x - 5x + 10]

E = (x + 1)[x(x - 2) - 5(x - 2)]

E = (x + 1)(x - 2)(x - 5)

We cannot simplify and factorise the expression any further.

Hence, the factors of the expression are (x + 1), (x - 2), and (x - 5).

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Answer:

22.18 = x

Step-by-step explanation:

a^2 + (b)^2 = (x/2)^2

a = sqrt(74)

b = 7

x/2 = ?

(74)[^1/2]^2 = 74            

b^2 = 7^2 = 49

74 + 49 = (x/2)^2       Substitute into a^2 + b^2 = c^2

123 = (x/2)^2              Combine like terms

(123^0.5) = x/2           Take the square root of both sides.

11.09 = x/2                  Multiply both sides by 2

11.09*2 = x

22.18 = x                     The full length of the base of the triangle is 22.18

Answer: C

Step-by-step explanation: We only need to find the value of one of the x so just use Pythagorean theorem but simplified to do it in one step which is sqrt(4^2+6^2) which gives us sqrt(52).

The probability of using a different catalyst for each run is 1.

The given data can be expressed as follows: Six different experimental runs are to be made on the first day of experimentation. If six are randomly selected from among all the possibilities, so that any group of six has the same probability of selection, what is the probability that a different catalyst is used on each run?

We are to determine the probability of using a different catalyst for each run, which is the probability of choosing the six catalysts from six different catalysts. Possible number of ways to select 6 catalysts from 6 = 6C6 = 1

Thus, there is only one way to select 6 different catalysts for 6 different runs. Therefore, the probability of using a different catalyst for each run is 1.

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9514 1404 393

Answer:

  A.  -(1 4/6 +2 1/6)

  B.  -3 5/6

Step-by-step explanation:

A. Real number properties let us factor out a factor of -1, and they let us rewrite 2/3 as 4/6. Using these, an equivalent expression is ...

  -(1 2/3 +2 1/6) = -(1 4/6 +2 1/6)

__

B. The sum is ...

  -((1+2) +(4/6 +1/6)) = -(3 +(4+1)/6) = -3 5/6

Answer:

a=8

b=⅛

c= 2.6

d= 0.26

that's all the answers

Answer:

\(\tt{ \green{P} \orange{s} \red{y} \blue{x} \pink{c} \purple{h} \green{i} e}\)

The expected return on James's portfolio is 18%.

The expected return on Siebling Manufacturing Company's common stock is 8.4%.

To calculate the expected return on James's portfolio, we need to take the weighted average of the expected returns of MSFT and AAPL based on their respective investments.

Let's assume James invests x% in MSFT and (100 - x)% in AAPL.

The expected return on James's portfolio can be calculated as:

Expected Return = (x * Expected Return of MSFT) + ((100 - x) * Expected Return of AAPL)

Substituting the given values:

Expected Return = (x * 12%) + ((100 - x) * 24%)

To find the value of x that makes James's investments equal, we set the weights equal:

x = 100 - x

Solving this equation gives us x = 50.

Now we can substitute this value back into the expected return equation:

Expected Return = (50% * 12%) + (50% * 24%)

Expected Return = 6% + 12%

Expected Return = 18%

Therefore, the expected return on James's portfolio is 18%.

To calculate the expected return on Siebling Manufacturing Company's common stock, we can use the Capital Asset Pricing Model (CAPM).

The CAPM formula is:

Expected Return = Risk-Free Rate + Beta * Market Premium

Risk-Free Rate = 2%

Market Premium = 8%

Beta = 0.8

Expected Return = 2% + 0.8 * 8%

Expected Return = 2% + 6.4%

Expected Return = 8.4%

Therefore, the expected return on Siebling Manufacturing Company's common stock is 8.4%.

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Answer:

21 and 34.

Step-by-step explanation:

21 is 13 less than 34 and the sum of them is 55.

Answer:

(0,-3)

Step-by-step explanation:

x = 3

y = -3

(3, -3)

Step-by-step explanation:

Choose one of the equations and isolate y. I will use the first one.

2x + y = 3

Y = 3 - 2x

Now sub the solution for y into the equation below.

3x - y = 3

3x - (3 - 2x) = 12

3x - 3 + 2x = 12

5x - 3 = 12

5x = 15

x = 3

To get y, sub the answer for x into one of the equations.

2(3) + y = 3

6 + y = 3

y = 3 - 6

y = -3

Answer:

(x,)y) =(3,-3)

Step-by-step explanation:

add the equations vertically to eliminate one variable

2x +y = 3

3x -y = 12

5x =15    divide both sides by 5

x  = 3       now substitute the given value of x into the equation  2x+y=3

2 x 3 + y = 3  multiply 2x3

6 +y =3           move constant to the right

y = 3-6

y = -3  

Answer:

0.13 cm per second

Step-by-step explanation:

Lets convert the minutes to seconds:

3/4 minutes = 3/4(60) = 45 seconds

The snail traveled 5.85 cm in 45 seconds

To find out the speed per second, we set up a proportion:

\(\frac{5.85}{45} = \frac{x}{1}\)      where 45 and 1 represent the number of seconds, and 5.85 and x represent the distance in that set of time

Let's solve for x, or the distance in 1 second:

\(\frac{5.85}{45}=\frac{x}{1}\\\\\\\frac{5.85*1}{45x}\\\\\\x = \frac{5.85}{45}\\\\\\\\\\x = 0.13\)

The snail travels 0.13 cm per second.

-Chetan K

Answer:

32

Step-by-step explanation:

\(\begin{array}{ccll} Trains&Planes\\ \cline{1-2} 3 & 8\\ 12& x \end{array} \implies \cfrac{3}{12}~~=~~\cfrac{8}{x} \implies \cfrac{ 1 }{ 4 } ~~=~~ \cfrac{ 8 }{ x }\implies x=32\)

Answer:

A.g, a.f ,a.b

Step-by-step explanation:

Answer:

358

Step-by-step explanation:

Please let me know if you want me to add an explanation as to why this is the answer/how I got this answer. I can definitely do that, I just wouldn’t want to write it if you don’t want me to :)

Answer: (a) 2³ ˣ 3 ˣ 5², 2 ˣ 3 ˣ 5² = 150

Step-by-step explanation:

This is problems on common factors.

(a) 600 = 2 × 2 × 2 × 3 × 5 × 5

       = 2³ˣ 3 ˣ 5²

(b)   The highest common factors could be calculated using factors methods and the divisional methods.

Here we go.

(i)   600  = 2³ ˣ 3 ˣ 5²

     1050 = 2 ˣ 3 ˣ 5² ˣ 7, the highest common factor HCF will be

      HCT = 2 ˣ 3 ˣ 5²

               = 150.

The divisional methods.

     600) 1050 ( 1

            -  600

                ------

                450 ) 600 ( 1

                       -  450

                          ------

                           150 ) 450 ( 3

                                  - 450

                                    ------

                                     000

     So the answer is 150, the principle is that you continue to divide and subtract until you arrive at zero.

Answer = 150

k = 0 to 399 By calculating this summation, we will obtain the probability that Paul goes broke. To find the probability that Paul goes broke when Peter has a 2/3 probability of winning each game, we can use the concept of probability, game, and bet in our explanation.

First, we need to determine the probability of Paul winning a game, which can be found by subtracting Peter's winning probability from 1:

Probability of Paul winning = 1 - Probability of Peter winning = 1 - 2/3 = 1/3

Now, let's denote the number of games required for one of them to go broke as 'n'. Since they each start with $400, the total number of games would be n = 400 + 400 = 800.

We will use the binomial probability formula to calculate the probability of Paul going broke after 'n' games:

P(Paul goes broke) = (n! / (k!(n-k)!)) * (p^k) * (q^(n-k))

Here, n is the total number of games (800), k is the number of games Paul wins, p is the probability of Paul winning (1/3), and q is the probability of Peter winning (2/3).

To find the probability of Paul going broke, we need to calculate the probability of Paul winning fewer than 400 games out of 800:

P(Paul goes broke) = Σ [P(Paul wins 'k' games)] for k = 0 to 399

By calculating this summation, we will obtain the probability that Paul goes broke.

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Answer:

In algebra, setting an equation equal to zero is a common technique used to solve for the unknown variable. The reason for this is that when we set an equation equal to zero, we can often use factoring or the quadratic formula to solve for the variable.

In the example you gave, x^2-4x=-4, we can set the equation equal to zero by adding 4 to both sides of the equation, which gives us x^2-4x+4=0. Notice that the left side of this equation can be factored into (x-2)^2, so we have (x-2)^2=0.

At this point, we can use the zero product property, which states that if the product of two or more factors is zero, then at least one of the factors must be zero. In this case, the only factor is (x-2)^2, which means that (x-2)^2=0 if and only if x-2=0. Solving for x gives us x=2, which is the solution to the original equation x^2-4x=-4.

So, setting an equation equal to zero allows us to use factoring and the zero product property to solve for the unknown variable. It is a useful technique that is often used in algebra, especially when solving quadratic equations.

Step-by-step explanation:

Setting an equation equal to zero is a technique used in algebra to help us solve equations. When we set an equation equal to zero, we are essentially looking for the points on the graph where the function crosses the x-axis. In other words, we are looking for the roots or solutions of the equation, which are the values of x that make the equation true.

In your example, x^2-4x=-4, we want to solve for x. By adding 4 to both sides, we get x^2-4x+4=0. This is equivalent to (x-2)^2=0, which can be simplified to x-2=0. Therefore, x=2 is the solution to the equation.

Setting the equation equal to zero allows us to use factoring or the quadratic formula to solve for x, which can be more straightforward than trying to solve the original equation.

Answer:

$90

Step-by-step explanation:

First you find the total area of the shape:

9ft times 6 ft times 5 ft= 270 ft

divide 270 ft by 3 to get the amount of money that Maya will pay.

270 divided by 3 is 90

so the answ er is $90

a) the population cannot be negative, the limiting population is 4300.

b)the population is increasing when 0 < p < 4300 and decreases when p > 4300.

c)the equilibrium solutions are p = 0 and p = 4300.

(a) To determine when the population is increasing or decreasing, we need to look at the sign of dp/dt.

\(\frac{dp}{dt} = 1.2p(1 - \frac{p}{4300})\)

For dp/dt to be positive (i.e. population is increasing),

we need\(1 - \frac{p}{4300} > 0, or \ p < 4300.\)

For dp/dt to be negative (i.e. population is decreasing),

we need\(1 - \frac{p}{4300} < 0, or p > 4300.\)

Therefore, the population is increasing when 0 < p < 4300 and decreases when p > 4300.

(b) To find the limiting population, we need to find the value of p as t approaches infinity.

As t approaches infinity,\(\frac{dp}{dt}\)approaches 0. Therefore, we can set \(\frac{dp}{dt}\) = 0 and solve for p.

0 = 1.2p(1 - p/4300)

Simplifying, we get:

0 = p(1 - p/4300)

So, either p = 0 or 1 - p/4300 = 0.

Solving for p, we get:

p = 0 or p = 4300.

Since the population cannot be negative, the limiting population is 4300.

(c) Equilibrium solutions occur when\(dp/dt = 0.\)We already found the equilibrium solutions in part (b): p = 0 and p = 4300.

Therefore, the equilibrium solutions are p = 0 and p = 4300.

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a)  The population is increasing when 0 < p < 4300, and  decreasing when p > 4300.

b)  The population cannot be negative, the limiting population is 4300.

c)  these are the equilibrium solutions.  At p = 0, the population is not

increasing or decreasing, and at p = 4300,  the population is decreasing

but not changing in size.

(a) To determine when the population is increasing or decreasing, we

need to find the sign of dp/dt. We have:

dp/dt = 1.2p(1 - p/4300)

This expression is positive when 1 - p/4300 > 0, i.e., when p < 4300, and

negative when 1 - p/4300 < 0, i.e., when p > 4300.

Therefore, the population is increasing when 0 < p < 4300, and

decreasing when p > 4300.

(b) To find the limiting population, we need to solve for p as t approaches infinity. To do this, we set dp/dt = 0 and solve for p:

1.2p(1 - p/4300) = 0

This equation has two solutions: p = 0 and p = 4300. Since the population cannot be negative, the limiting population is 4300.

(c) To find the equilibrium solutions, we need to solve for p when dp/dt = 0. We already found that the only solutions to dp/dt = 0 are p = 0 and

p = 4300.

Therefore, these are the equilibrium solutions.

At p = 0, the population is not increasing or decreasing, and at p = 4300,

the population is decreasing but not changing in size.

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The evaluation of the fraction, \(\dfrac{x^3-5\cdot x^2+ 2\cdot x-6}{x - 1}\), using the long division method is the option;

The expression can be presented as follows;

\(\dfrac{x^3-5\cdot x^2+ 2\cdot x-6}{x - 1}\)

The numerator x³ - 5·x² + 2·x - 6  does not have (x - 1) as a factor
However, dividing x³ - 5·x² + 2·x - 6 by (x - 1), gives;

        x² - 4·x -2

(x - 1)|x³ - 5·x² + 2·x - 6

  \({}\)      x³ - x²

\({}\)             -4·x² + 2·x - 6

\({}\)             -4·x² + 4·x

\({}\)                        -2·x - 6

\({}\)                      -2·x  + 2

\({}\)                                 -8

The quotient from the division is x² -4·x  -2, the remainder is -8, therefore, the result from the division x³ - 5·x² + 2·x - 6 by (x - 1) is the option;

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I attached an image of it filled out, please give me brainliest if this helped!

Answer:

Step-by-step explanation:

x^2 -4x - 9 = 29

x^2 - 4x = 37

x = 2 ±\(\sqrt{42}\)

Answer:

x = 2 ± \(\sqrt{42}\)

Step-by-step explanation:

x^2 -4x - 9 = 29

x^2 - 4x = 37

x = 2 ± \(\sqrt{42}\)

Answer:

6.63 pounds

Step-by-step explanation:

Total pounds of mixture = 20

The contents of the mixture are; peanuts and almonds. Of which;

Peanuts cost = $2.95 per pound

Almonds cost = $5.95 per pound

The mixture cost = $4.00 per pound

Total cost of contents of the mixture = $8.90

The pounds of peanuts = \(\frac{2.95}{8.90}\) x 20

                     = 6.63

Therefore, 6.63 pounds of peanuts was used in producing 20 pounds of the mixture.

The measurement of altitude BE is 4 unit.

As the average level of the sea's surface, sea level is used to measure altitude. A high altitude is defined as being significantly higher than sea level, such as Mount Everest. It is referred to as having a low altitude when something is closer to the ground, like a plane coming in to land.

As ABCD is rectangle

AD = BC = 12

ΔABC = ΔBCD

BE = FD

5² = 3²+BE²

AE = 3

BE = √(5²-3²)

BE = 4

Thus, The measurement of altitude BE is 4 unit.

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