Consider the following polynomial.
X^3 -6x^2 + 49x -294
Write the equivalent factored form of the polynomial. Fill in the expression with the values of a, b and where a is an integer and band
care complex numbers.

Answer: 8.4

Step-by-step explanation: 5.25 divided by 5 is 1.05. So 1.05 x 8 is 8.4

Answer:

C

Step-by-step explanation:

Use the pythagorean theorem.

32^2+b^2=48^2

1024+b^2=2304

Subtract 1024

b^2=1280

Square root

b=sqrt(1280)

Now simplify sqrt(1280)

sqrt(1280) = sqrt(256*5)

You can take the square root of 256 since it is a perfect square so take it out of the radical.

sqrt(256*5)=16sqrt(5)

So the answer is c, 16\(\sqrt{5}\)

Answer:

C. 16/5

Step-by-step explanation:

pythagorean theorem

a^2 + b^2 = c^2

divide 48 and 32 by 16

a= 2 c= 3

4 + b^2 = 9

b^2 = 5

b = √5

then multiply 16 with √5

which =

16√5

The elimination of dominated strategies is an iterative technique in which any alternative that is dominated by another alternative is deleted from further consideration.

The correct answer is  {(D,Y)}

It is important to recognize that a strategy is said to be dominated by another strategy if it performs worse than the other strategy for all possible responses from the other player(s), regardless of what the other player does. the elimination of dominated strategies is given figure can be represented as: This game is solved through the elimination of dominated strategies. We solve this by using the following iterative steps: Dominated Strategy Elimination In this step, we eliminate all the strategies which are dominated by another strategy.

The payoffs in the lower-right corner are (-1, -1) in (B,Y) and (-2, -1) in (C,Y). Therefore, strategy (C,Y) dominates (B,Y) and hence we eliminate (B,Y) from our list of strategies. This leads to a new matrix as shown below: Therefore, strategy (D,X) dominates (D,Y) and hence we eliminate (D,Y) from our list of strategies. This leads to the following matrix as shown below:  Step 3: Final Decision We are now left with only one strategy, (D, Y). Hence, it is the only dominant strategy in this game and the solution to the game is (D, Y). Therefore, the solution to the game in Figure 2 by the elimination of dominated strategies is (D, Y).

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Answer:

Mary have £ 0.7

and Eleanor 1.05

because

Mary 10/ 10 +15 × 1.75= .7

Eleanor 15 /10+15× 1.75 =1.05

That we added a real number (2/3) and subtracted a real number (3), but the imaginary part of the result is still (5/3)i.

First, let me clarify what 1ị represents. In mathematics, the imaginary unit i is defined as the square root of -1. Therefore, 1ị means 1 times the imaginary unit i.

To write three more equations for 1ị that are all true and all different, we can use the fact that i satisfies the equation i^2 = -1. We can also use the fact that any multiple of i, such as 2i, 3i, and so on, is also an imaginary number. Finally, we can use the fact that adding or subtracting real numbers to or from an imaginary number does not affect the imaginary part of the number.

Here are three possible equations for 1ị:

(2 + 1/3)i = 1ị + 2i

Explanation: We can add 2 times the imaginary unit i to 1 times the imaginary unit i to get 3 times the imaginary unit i, which is equal to (2 + 1/3) times the imaginary unit i.

(-1/3)i = 1ị - 4/3i

Explanation: We can subtract 4/3 times the imaginary unit i from 1 times the imaginary unit i to get -1/3 times the imaginary unit i.

(5/3)i = 1ị + 2/3 + 3i - 3

Explanation: We can add 2/3 and 3i - 3 to 1 times the imaginary unit i to get (5/3) times the imaginary unit i. Notice that we added a real number (2/3) and subtracted a real number (3), but the imaginary part of the result is still (5/3)i.

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The missing parts for both triangles to be congruent are:

1. AE ≅ BD.

2. ∠CAB ≅ FED.

3. ∠BA ≅ DA.

Two triangles can be proven to be congruent by the following criteria:

Therefore, the following are the missing parts in the pair of triangles:

1. The missing parts that weren't shown for both triangles to be congruent by SAS is: AE ≅ BD.

2.  The missing parts that weren't shown for both triangles to be congruent by ASA is: ∠CAB ≅ FED.

3. The missing parts that weren't shown for both triangles to be congruent by SSS is: ∠BA ≅ DA.

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3) \(\angle ADB\) and \(\angle BDE\) are supplementary (if two angles form a linear pair, they are supplementary)

4) \(\angle ADC\) and \(\angle CDE\) are supplementary (if two angles form a linear pair, they are supplementary)

5) \(\angle ADB \cong \angle ADC\) (supplements of congruent angles are congruent)

6) \(\triangle ADB \cong \triangle ADC\) (SAS)

7) \(\angle ABD \cong \angle ACD\) (CPCTC)

The side AE and side CD are parallel to each other because they will never intersect to each other.

A polygon is a two-dimensional geometric figure having a finite number of sides. Straight-line segments are linked end to end to make a closed shape on the sides or edges of a polygon. The vertices or corners are the spots where two line segments intersect, resulting in an angle.

As we know, the parallel lines never intersect to each other, they go infinitely without crossing each other.

As we can see in the figure (refer to the attached picture)

Line AE and CD are parallel to each.

Thus, the side AE and side CD are parallel to each other because they will never intersect to each other.

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Answer:c

Step-by-step explanation:a. 30.9, b. 32.9

Answer:

the third distribution

Answer:

18

Step-by-step explanation:

Answer:

d is the answer

Step-by-step explanation:

The sine of angle V is 97/72. The length of side VW is 65 units.

To find the sine of angle V, we need to use the ratio of the length of the side opposite angle V to the length of the hypotenuse. In this case, side VU is opposite angle V, and hypotenuse UW is the longest side of the right triangle.

Using the Pythagorean Theorem, we can find the length of side VW:

VW² = UW² - VU²

VW² = 72² - 97²

VW² = 5184 - 9409

VW² = 4225

VW = 65

Now we can use the sine ratio:

sin(V) = opposite/hypotenuse = VU/UW

sin(V) = 97/72

Therefore, the ratio that represents the sine of ∠V is 97/72.

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The slope of a line is determined by the formula:

(y2 - y1) / (x2 - x1)

So for the points (9, 5) and (21, -5), the slope would be:

(-5 - 5) / (21 - 9) = -10 / 12 = -5/6

So the slope of the line that passes through the points (9, 5) and (21, -5) is -5/6 in simplest form.

The angle formed by this intersection point and the corresponding point on LMNO is congruent to ZH.

In this case, we have two figures, LMNO and HIJK, and we know that LMNO is a reflection of HIJK. This means that there is an axis of reflection that maps HIJK onto LMNO.

When a shape is reflected across a line of symmetry, its angles are preserved. That is, if two angles in the original shape are congruent, then their images in the reflected shape are also congruent.

In this case, ZH is an angle in HIJK, and we want to find the angle in LMNO that corresponds to it. To do this, we need to find the line of symmetry that maps HIJK onto LMNO.

Once we have identified this line, we can draw the perpendicular bisector of ZH and find where it intersects the line of symmetry. The angle formed by this intersection point and the corresponding point on LMNO is congruent to ZH.

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Answer: -4096

Step-by-step explanation:

I just did the lesson

The total amount of interest paid on the loan when it is repaid is $93,255.08. This is the difference between the total amount paid in loan payments and the loan amount of $100,000.

What is the interest?

Interest is the price you pay to borrow money or the cost you charge to lend money. Interest is most often reflected as an annual percentage of the amount of a loan. This percentage is known as the interest rate on the loan.

To calculate the amounts the Bainters would pay on their loan, we need to know the loan amount, the interest rate, and the loan term. Without this information, we cannot provide exact amounts, but we can illustrate how to calculate them using a hypothetical loan amount and interest rate.

For example, suppose the Bainters borrow $100,000 at an annual interest rate of 5% for a 30-year term. Using an amortization calculator, we can calculate the loan payments and total interest paid as follows:

The total amount paid in loan payments after 1 year is $6,158.54. This includes both principal and interest payments.

The total amount paid in loan payments after 5 years is $33,786.39. This includes both principal and interest payments.

The total amount paid in loan payments after 10 years is $69,267.75. This includes both principal and interest payments.

The total amount paid in loan payments after 15 years is $107,212.01. This includes both principal and interest payments.

The total amount paid in loan payments after 30 years is $193,255.08. This includes both principal and interest payments.

The total amount of interest paid on the loan when it is repaid is $93,255.08. This is the difference between the total amount paid in loan payments and the loan amount of $100,000.

These amounts are based on the assumption of a fixed interest rate and a fixed loan term. If the interest rate or the loan term changes, the amounts paid on the loan will also change.

Hence, The total amount of interest paid on the loan when it is repaid is $93,255.08. This is the difference between the total amount paid in loan payments and the loan amount of $100,000.

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The equation whose graph is a line perpendicular to the graph of y=4 and which passes through the point (2, 5)​ is x = 2

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

Perpendicular to the graph of y = 4

The above means that

The equation is a vertical line that passes through the x-axis

In the point (2, 5), we have

x = 2

This means that

The equation of the line is x = 2

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Answer: The number of game cards that Parvin gave to Ryan is 195. The number of game cards that Parvin gave to Ryan is 195.

\((52y + 3a) = 1.5(13x - a)(52y + 3a) \\= 19.5x - 1.5a54y + 3a = 19.5x - 1.5a54y + 3a + 1.5a \\= 19.5x1.8a = 19.5x - 54y = (39x - 108y)/2\\39x - 108y = 2k\)

Now, \((52y + 3a\\ = 1.5(13x - a)(52y + 3a) \\= 19.5x - 1.5a(52y + 3a)\\ = 19.5x - 1.5a(52y + 3a + 1.5a) \\= 19.5x + a(50y + 13x) = 19.5x + 2k50y + 13x\\= (19.5x + 2k)/a\)…..(iii)

Solving this equation, we get: y = 16 and x = 20

Parvin had 260 game cards and Ryan had 1352 game cards after Parvin and Christina gave some game cards to Ryan. Parvin gave (1352 - 676)/4 = 195 game cards to Ryan.

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Step-by-step explanation:

The amplitude is the value that the cosine is being multiplied by.

The general equation of a sinusoid is

\( a \cos(b(x + c) ) + d\)

where a is the amplitude

\( \frac{2\pi}{ |b| } \)

is the period

-c is the phase shift

d is the midline(vertical shift)

Here the amplitude is -1/2 so b is the correct answer.

Answer:

the amplitude of the function that is y= -1/2 cos x, is 1/2.

Step-by-step explanation:

Given:

44 cu. cm of wire is drawn into a wire of diameter 2 mm.

To find:

The length of the wire.

Solution:

We know that,

1 cm = 10 mm

1 cu. cm = 1000 cu. mm

We have, a wire of cylindrical shape.

Volume of the wire = 44 cu. cm

                                = 44000 cu. mm

Radius of the wire = 2 mm

Volume of a cylinder is:

\(V=\pi r^2h\)

Where, r is the radius and h is the height.

Putting V=44000, \(\pi=\dfrac{22}{7}\) and r=2, we get

\(44000=\dfrac{22}{7}\times 2^2\times h\)

\(44000\times \dfrac{7}{22}=4h\)

\(14000=4h\)

Divide both sides by 4.

\(\dfrac{14000}{4}=h\)

\(3500=h\)

Therefore, the length of the wire is 3500 mm or 350 cm.

The shortest length of fence is thus equal to P1 = x + 1,300,000/x.

Let the width of the rectangular field be "x" feet and the length be "y" feet, then the area of the field, A = x y square feet. The area of the field is given as 1,300,000 square feet, so we can write; x  y = 1,300,000 Therefore, y = 1,300,000/x feet. Now, if we divide the rectangular field into two halves parallel to one side, we can write the new dimensions of each half as follows: Half 1: Length = x, Width = y/2 = 1,300,000/2x = 650,000/x Half 2: Length = x, Width = y/2 = 1,300,000/2x = 650,000/x

The total length of fence needed to enclose the rectangular field is given by; P = 2x + 2y = 2x + 2(1,300,000/x)P = 2x + 2(1,300,000/x)The total length of fence needed to divide the rectangular field into two halves is given by;P1 = x + 2(650,000/x)P1 = x + 1,300,000/x Thus, the shortest length of fence that the rancher can use is the length of the fence needed to divide the field into two halves. Therefore;P1 = x + 1,300,000/x.

The shortest length of fence is thus equal to P1 = x + 1,300,000/x.

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As per the Leading Coefficient Test, If a polynomial is of an odd degree and the leading coefficient is positive then polynomial, then it Rises to the right and falls to the left.

Leading Coefficient Test:

The leading coefficient test defined that the graph rises or falls depending on whether the leading terms are positive or negative, so for left-hand behavior (negative numbers), by the use of both the coefficient and the degree of the component together.

Given,

Here we have to determine If a polynomial is of an odd degree and the leading coefficient is positive then polynomial will fall in which place.

By using the Leading Coefficient Test we have to determine the end behavior of the graph of the polynomial function.

Here we know that the behavior of the polynomial function is odd degree and the leading coefficient is positive.

Therefore, as per the leading coefficient test, the resulting graph will rises to  the right and falls to the left.

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Answer:

2

Step-by-step explanation:

0.55 rounded is 1,

2.2 rounded is 2.

1×2=2

have a great day

Answer:

$17.33

Step-by-step explanation:

3.5×4.95

=17.325

= $17.33

The matrix A that transforms the letter 'n' in regular 12-point font to the italicized 'n' in 16-point font can be determined by scaling and shearing operations.

To achieve the desired transformation, we can apply a combination of scaling and shearing operations using a 2x2 matrix. Let's denote this matrix as A.

To find the specific values of the matrix A, we need to consider the differences between the regular 'n' and the italicized 'n' in terms of scaling and shearing.

The italicized 'n' is slanted compared to the regular 'n'. This slant can be achieved by applying a shear transformation along the x-axis.

We can determine the values of A by examining the specific slant and size changes of the italicized 'n' compared to the regular 'n'.

The matrix A will consist of scaling factors and shear coefficients that capture the desired transformation. The exact values of the matrix elements will depend on the specific slant and size adjustments required for the italicized 'n'.

To obtain the matrix A, we would need to analyze the italicized 'n' in 16-point font and compare it to the regular 'n' in 12-point font to determine the necessary scaling and shearing parameters.

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Answer:

2.54 units²

Step-by-step explanation:

To find the area first find the radius from 2πr since the cricumference, C was given

C = 2πr

6.28 = 2 x 22/7 x r

6.28 = 44r/7

r = (7 x 6.28)/44

r = 0.9

So now the area = πr^2

22/7 x 0.9^2

=2.54 units²