What are the leading coefficient and degree of the polynomial?
2+18u^4+9u-u^8
Leading coefficient:
Degree:

[tex] {\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

Here we go ~

The general equation of ellipse is :

[tex]\qquad \sf  \dashrightarrow \: \cfrac{ {x}^{2} }{ {a}^{2} } + \cfrac{ {y}^{2} }{ {b}^{2} } = 1[/tex]

[ because it's a horizontal ellipse with centre at origin ]

so, let's equate given equation with the standard equation ~

[tex]\qquad \sf  \dashrightarrow \: \cfrac{ {x}^{2} }{64} + \cfrac{ {y}^{2} }{36} = 1[/tex]

se get :

As we know, length of minor axis is : 2b = 2 × 6 = 12 units

and, the smaller circle has diameter = 2b = 12 units

so, it's radius = 6 units ~

Now, let's write the equation of circle with origin as centre and radius = 6 units

[tex]\qquad \sf  \dashrightarrow \: {(x - h)}^{2} + (y - k) {}^{2} = {r}^{2} [/tex]

[ h = 0, k = 0, since circle has centre at origin ]

[tex]\qquad \sf  \dashrightarrow \: {x}^{2} + {y}^{2} = 36[/tex]

Answer:

[tex]x^2+y^2=36[/tex]

Step-by-step explanation:

Equation of the red eclipse (taken from your previously posted question):

[tex]\dfrac{x^2}{64}+\dfrac{y^2}{36}=1[/tex]

General equation of an ellipse

[tex]\dfrac{(x-h)^2}{a^2}+\dfrac{(y-k)^2}{b^2}=1[/tex]

where:

As the center of the red ellipse is (0, 0) ⇒ h = 0, k = 0.

[tex]\implies a^2=64 \implies a=\sqrt{64}=\pm8[/tex]

[tex]\implies b^2=36 \implies a=\sqrt{36}=\pm6[/tex]

The Major Axis is the longest diameter of an ellipse.

Therefore, using the formula for the vertices, the vertices of the major axis of the red ellipse are (8, 0) and (-8, 0).

The Minor Axis is the shortest diameter of an ellipse.

Therefore, using the formula for the vertices, the vertices of the minor axis of the red ellipse  (0, 6) and (0, -6).

Therefore, the radius of the larger circle is 8 units and the radius of the smaller circle is 6 units (half the respective axis, since the radius of a circle is half its diameter).

Equation of a circle

[tex](x-a)^2+(y-b)^2=r^2[/tex]

(where (a, b) is the center and r is the radius)

Given:

The equation of the smaller circle is:

[tex]\implies (x-0)^2+(y-0)^2=6^2[/tex]

[tex]\implies x^2+y^2=36[/tex]

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The preparation of a bank reconciliation statement for Mathers Co. for July is as follows:

At July 31

Cash balance per bank statement as at July 31, $21,110

Deposit in transit                                                     3,260

Outstanding checks                                              (4,060)

Balance as per adjusted cash balance             $20,310

A bank reconciliation statement is a summary of banking and business cash transactions so that their balances can agree.

Bank reconciliations help the company to reconcile its bank account as per bank statements with its internal financial records.

The steps for preparing a bank reconciliation include:

Cash balance per Cash Account at July 31 $20,010

Cash balance per bank statement at July 31, $21,110

Checks outstanding, $4,060

Deposit in transit $3,260

Transposed payment $360 ($840 - $480)

Bank service charges $60

Cash balance per Cash Account as at July 31 $20,010

Transposed payment                                               360

Bank service charges                                               (60)

Adjusted cash balance per cash account       $20,310

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Answer: 9 units

Step-by-step explanation: R is at -7 and is at 2. Think of how far away -7 is from 2. -7+9=2.

Answer:

9 units

Step-by-step explanation:

Length of a segment RV is a difference of values of V and R. According to the number line, R is -7 and V is 2.

The difference or change in two values is 2 - (-7) = 2 + 7 = 9 units.

Henceforth, the segment RV is 9 units.

Answer:

A = $11; C = $7 tickets

Step-by-step explanation:

Using the given info, we can create a system of equations to find the price of adult and children tickets.

Thus, we have 5A + 7C = 104 and 7A + 3C = 98

The easiest method to solve would be elimination:

Answer:

Step-by-step explanation:

The sales on the two days can be expressed using equations that can be solved for ticket prices.

Let x and y represent the prices of adult and children's tickets, respectively. Then the sales revenue for the two days can be expressed in the equations ...

One of the easiest solution methods is to use a graphing calculator. The first attachment shows the prices are $11 for an adult ticket; $7 for children tickets.

Using the matrix functions of a calculator, the augmented matrix of the equation coefficients can be reduced to row-echelon form. This, too, shows the solution to be (adult price, children price) = ($11, $7). See the second attachment. (The solution is the right-most column of the reduced matrix.)

Yet another solution method can use the coefficients from the equations written in general form:

In this form, we define three products of "cross multiplication":

  Δ1 = (5)(3) -(7)(7) = -34

  Δ2 = (7)(-98) -(3)(-104) = -374

  Δ3 = (-104)(7) -(-98)(5) = -238

Using those, we find the variable values to be ...

  x = Δ2/Δ1 = -374/-34 = 11

  y = Δ3/Δ1 = -238/-34 = 7

(adult price, children price) = ($11, $7)

__

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The standard deviations above the mean that a student have to score to be publicly recognized will be 0.674.

From the information given, it was stated that the students who score in the top 16 percent are recognized publicly for their achievement by the Department of the Treasury.

Based on the information given, it should be noted that the appropriate thing to do is to find the z score for the 75th percentile.

This will be looked up in the distribution table. In this case, the value is 0.674. Therefore, standard deviations above the mean that a student have to score to be publicly recognized will be 0.674.

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The relationship between all pairs of special angles 1, 2, 3, and 4 created by transversal line b and parallel lines d and e include:

These are usually formed when two straight lines meet at a common endpoint or vertex.

Angles 3 and 4 are equal due to them being alternative interior angles and other relationships are mentioned above.

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Answer:

328,233

Step-by-step explanation:

Use the algorithm method.

4 8 9 9

×     6 7

3 6 6 6

3 4 2 9 3

2 5 5 5  

2 9 3 9 4 0

1  1 1  

3 2 8 2 3 3

⇒ 328,233

Answer:

3.36 cm

Step-by-step explanation:

24 - 5 1/2 = 18.5

To find the distance on the map, we can set up a proportion:

1 cm / 5.5 miles = x cm / 18.5 miles

5.5 times 37/11 equals to 18.5; 1 times 37/11 is approximately equals to 3.36 cm (rounded to the nearest hundredths).

A null hypothesis (H₀) can be defined the opposite of an alternate hypothesis (H₁) and it asserts that two (2) possibilities are the same.

The test statistics can be calculated by using this formula:

[tex]t=\frac{x\;-\;u}{\frac{\delta}{\sqrt{n} } }[/tex]

Where:

For this study, we should use t-test and the null and alternative hypotheses would be given by:

H₀: μ = 7

H₁: μ < 7

[tex]t=\frac{6.3\;-\;7}{\frac{1.3}{\sqrt{13} } }\\\\t=\frac{-0.7}{\frac{1.3}{3.6056 } }[/tex]

t = -0.7/0.3606

t = -1.941.

For the p-value, we have:

P-value = P(t < -1.9412)

P-value = 0.0381.

Therefore, the p-value (0.0381) is greater than α = 0.01. Based on this, we should fail to reject the null hypothesis.

Thus, the final conclusion is that the data suggest the population mean is not significantly lower than 7 at α = 0.01, so there is statistically insignificant evidence to conclude that the population mean waiting time to be admitted into the hospital from the emergency room for patients at rural hospitals is equal to 7 hours.

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Answer:

1 +-3i

Step-by-step explanation:

Answer:

answer is 1) x=±3i

Step-by-step explanation:

The age of the younger individual is 3 years, while the age of the older individual is 21 years.

Two distinct individuals' (or things') ages from the present to the past or future are often compared when resolving age-related concerns. The objective of these puzzles is often to ascertain the current age of each subject.

Let the younger person be x years of age.

The answer to the query is:

Age of senior = (4x + 9) years

Their combined ages are 24.

x+4x+9=24

5x=24-9

5x=15

x=15/5

x=3

Younger person's age is equal to x = 3 years.

Age of senior = 4x + 9 = 4(3) + 9 = 21 years

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If the probability of 1 is 0.5; 2 is 0.12; 3 is 0.12; 4 is 0.12; 5 is 0.12 then the graph is somewhat positively skewed and then becomes constant.

Given the probability of 1 is 0.5; 2 is 0.12; 3 is 0.12; 4 is 0.12; 5 is 0.12.

We are required to find whether the graph is constant,symmetric ,negatively skewed or positively skewed.

We can say that the graph is somewhat positively skewed and then it becomes constant.

Positively skewed graph is a graph in which more values exist at the left side of the graph means the tail is started in end.

Constant graph is a graph in which all the values are equal to each other.

In our case except the probability of 1 all the values are 0.12 and the probability of 1 is 0.5.

Hence if the probability of 1 is 0.5; 2 is 0.12; 3 is 0.12; 4 is 0.12; 5 is 0.12 then  the graph is somewhat positively skewed and then constant.

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Answer:

constant

Step-by-step explanation:

The features that exist present in this polar graph is that D. Symmetry about the polar axis θ = 0.

A polar curve exists as a form constructed utilizing the polar coordinate system. Polar curves exists determined by points that exist at a variable distance from the origin (the pole) depending on the angle calculated off the positive x-axis.

The polar graph can be said to contain a symmetry about the polar axis which indicates that theta or θ exists equivalent to 0.

This exists because the graph is symmetric about the x-axis. This indicates that all the lines of symmetry can be seen intersecting the graph at x = 0. This demonstrates that there exists indeed symmetry in the polar graph.

Therefore, the correct answer is option D. symmetry about the plane θ = 0

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the coordinates of the vertices of D2(WXYZ) are;

W' ( 2, 3)

X' ( 3, -1)

Y' ( -2, -2)

Z'(−1, −2)

It is important to note that the general formula for finding the transformation of the coordinates is;

M ( h, k) = M' ( k, -h)

Where

For the quadrilateral WXYZ we have to find the transformed coordinates

For W, we have

W(−3, 2)

h = -3

k = 2

Substitute the values

W' ( 2, 3)

For X,

X(1, 3)

h = 1

k = 3

Substitute the values

X' ( 3, -1)

For Y

Y(2, −2)

h = 2

k = -2

Substitute the values

Y' ( -2, -2)

For Z

Z(−1, −2)

h = -1

k = -2

Z'(−1, −2)

Thus, the coordinates of the vertices of D2(WXYZ) are;

W' ( 2, 3)

X' ( 3, -1)

Y' ( -2, -2)

Z'(−1, −2)

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Using the quadratic formula, we solve for [tex]z^2[/tex].

[tex]z^4 - 5(1+2i) z^2 + 24 - 10i = 0 \implies z^2 = \dfrac{5+10i \pm \sqrt{-171+140i}}2[/tex]

Taking square roots on both sides, we end up with

[tex]z = \pm \sqrt{\dfrac{5+10i \pm \sqrt{-171+140i}}2}[/tex]

Compute the square roots of -171 + 140i.

[tex]|-171+140i| = \sqrt{(-171)^2 + 140^2} = 221[/tex]

[tex]\arg(-171+140i) = \pi - \tan^{-1}\left(\dfrac{140}{171}\right)[/tex]

By de Moivre's theorem,

[tex]\sqrt{-171 + 140i} = \sqrt{221} \exp\left(i \left(\dfrac\pi2 - \dfrac12 \tan^{-1}\left(\dfrac{140}{171}\right)\right)\right) \\\\ ~~~~~~~~~~~~~~~~~~~~= \sqrt{221} i \left(\dfrac{14}{\sqrt{221}} + \dfrac5{\sqrt{221}}i\right) \\\\ ~~~~~~~~~~~~~~~~~~~~= 5+14i[/tex]

and the other root is its negative, -5 - 14i. We use the fact that (140, 171, 221) is a Pythagorean triple to quickly find

[tex]t = \tan^{-1}\left(\dfrac{140}{171}\right) \implies \cos(t) = \dfrac{171}{221}[/tex]

as well as the fact that

[tex]0<\tan(t)<1 \implies 0along with the half-angle identities to find

[tex]\cos\left(\dfrac t2\right) = \sqrt{\dfrac{1+\cos(t)}2} = \dfrac{14}{\sqrt{221}}[/tex]

[tex]\sin\left(\dfrac t2\right) = \sqrt{\dfrac{1-\cos(t)}2} = \dfrac5{\sqrt{221}}[/tex]

(whose signs are positive because of the domain of [tex]\frac t2[/tex]).

This leaves us with

[tex]z = \pm \sqrt{\dfrac{5+10i \pm (5 + 14i)}2} \implies z = \pm \sqrt{5 + 12i} \text{ or } z = \pm \sqrt{-2i}[/tex]

Compute the square roots of 5 + 12i.

[tex]|5 + 12i| = \sqrt{5^2 + 12^2} = 13[/tex]

[tex]\arg(5+12i) = \tan^{-1}\left(\dfrac{12}5\right)[/tex]

By de Moivre,

[tex]\sqrt{5 + 12i} = \sqrt{13} \exp\left(i \dfrac12 \tan^{-1}\left(\dfrac{12}5\right)\right) \\\\ ~~~~~~~~~~~~~= \sqrt{13} \left(\dfrac3{\sqrt{13}} + \dfrac2{\sqrt{13}}i\right) \\\\ ~~~~~~~~~~~~~= 3+2i[/tex]

and its negative, -3 - 2i. We use similar reasoning as before:

[tex]t = \tan^{-1}\left(\dfrac{12}5\right) \implies \cos(t) = \dfrac5{13}[/tex]

[tex]1 < \tan(t) < \infty \implies \dfrac\pi4 < t < \dfrac\pi2 \implies \dfrac\pi8 < \dfrac t2 < \dfrac\pi4[/tex]

[tex]\cos\left(\dfrac t2\right) = \dfrac3{\sqrt{13}}[/tex]

[tex]\sin\left(\dfrac t2\right) = \dfrac2{\sqrt{13}}[/tex]

Lastly, compute the roots of -2i.

[tex]|-2i| = 2[/tex]

[tex]\arg(-2i) = -\dfrac\pi2[/tex]

[tex]\implies \sqrt{-2i} = \sqrt2 \, \exp\left(-i\dfrac\pi4\right) = \sqrt2 \left(\dfrac1{\sqrt2} - \dfrac1{\sqrt2}i\right) = 1 - i[/tex]

as well as -1 + i.

So our simplified solutions to the quartic are

[tex]\boxed{z = 3+2i} \text{ or } \boxed{z = -3-2i} \text{ or } \boxed{z = 1-i} \text{ or } \boxed{z = -1+i}[/tex]

The simplification of a³ - 1000b³ and 64a³ - 125b³ is (a - 10b) × (a² + 10ab + 100b²) and 4a - 5b) • (16a² + 20ab + 25b²) respectively.

Question 1: a³ - 1000b³

a³ - b³

= (a-b) × (a² +ab +b²)

So,

(a - 10b) × (a² + 10ab + 100b²)

Question 2: 64a³ - 125b³

a³ - b³

= (a-b) × (a² +ab +b²)

So,

(4a - 5b) • (16a² + 20ab + 25b²)

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Answer:

-25

Step-by-step explanation:

[tex] \dfrac{(20 - 5^2)(16 + 2^2)}{-2^3 + (3 \times 2^2)} = [/tex]

First, do all exponents.

[tex] = \dfrac{(20 - 25)(16 + 4)}{-8 + (3 \times 4)} [/tex]

Now do each operation in parentheses.

[tex] = \dfrac{(-5)(20)}{-8 + 12} [/tex]

Multiply in the numerator. Add in the denominator.

[tex] = \dfrac{-100}{4} [/tex]

Divide the numerator by the denominator.

[tex] = -25 [/tex]

Answer:

-25

Step-by-step explanation:

PEMDAS

The PEMDAS rule is an acronym representing the order of operations in math:

Given expression:

[tex]\sf \dfrac{(20-5^2)(16+2^2)}{-2^3+(3 \times 2^2)}[/tex]

As the given expression is a fraction, carry out the operations in the numerator and denominator first before finally dividing them.

Following PEMDAS, carry out the calculations inside the parentheses first, then carry out the rest of the calculations following the order of operations:

Parentheses

Calculate the exponents inside the parentheses:

[tex]\implies \sf \dfrac{(20-25)(16+4)}{-2^3+(3 \times 4)}[/tex]

Multiply:

[tex]\implies \sf \dfrac{(20-25)(16+4)}{-2^3+(12)}[/tex]

Add and subtract:

[tex]\implies \sf \dfrac{(-5)(20)}{-2^3+(12)}[/tex]

Exponents

Calculate the exponent:

[tex]\implies \sf \dfrac{(-5)(20)}{-8+(12)}[/tex]

Multiply and Divide

Multiply:

[tex]\implies \sf \dfrac{-100}{-8+(12)}[/tex]

Add and Subtract

Add:

[tex]\implies \sf \dfrac{-100}{4}[/tex]

Finally, divide the numerator by the denominator:

[tex]\implies \sf -25[/tex]

Answer: -2

Step-by-step explanation:

The graph passes through (-2, 3) and (4, -9).

So, the average rate of change is [tex]\frac{-9-3}{4-(-2)}=\boxed{-2}[/tex]

The value of Quotient from the given terms is 9.6* 10^8

According to the statement

we have given that the two terms and we have to find the quotient of the these terms.

So, we know that the

Quotient is a the number resulting from the division of one number by another.

And for find the quotient we have to divide the terms with each other.

So, The given terms are [tex]7.536*10^7[/tex]and [tex]7.85*10^2[/tex]

divide both terms with each other.

Quotient = [tex]\frac{7.536*10^7}{7.85*10^2}[/tex]

Then

The value of quotient becomes

Quotient = [tex]0.96 * 10^9[/tex]

After removing the decimal from the answer it will become

Quotient = [tex]9.6* 10^8[/tex].

So, The value of Quotient from the given terms is 9.6* 10^8

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Answer: its 7.85x10^-9

Step-by-step explanation:

Answer: 16

Step-by-step explanation:

Answer:

(4,8)

hi hi hi hi hi hi hi hi

The rectangular representation of the polar point of (4 , 300) is (2,- 2√3)

According to the statement

we have given a coordinates of the rectangle and we have to find the polar coordinates.

So, For this purpose, we know that the

We Use the conversion formulas to convert from polar coordinates to rectangular coordinates which are

x = rcosθ

y = rsinθ

Substitute the given values in it then

x=(4)cos(300)

y=(4)sin(300)

Apply the reference angle by finding the angle with equivalent trig values in the first quadrant.

x=(4)cos(60) -(1)

y= - (4)sin(60) -(2)

And then

x=(4)cos(60)  

x=(4)(1/2)

x = 2 -(3)

and

y= - (4)sin(60)

y= - (4)(√3/2)

y= - 2√3 -(4)

Replace (3) with (1) and (4) with (2)

then it becomes

x = 2 and y= - 2√3

The rectangular representation of the polar point of (4 , 300) is (2,- 2√3)

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Answer:

98-54+12-36

110-54-36

56-36

20Ans

The ratio of grenadine syrup to 7-Up will be 1:8.

From the information given, we are told that Shirley Temple" drink is made by a 5 mixing 2 cups of 7-Up with 4 tablespoons of grenadine syrup.

The ratio of grenadine syrup to 7-Up will be:

4 tablespoon : 2 cups

Note that 1 cup = 16 teaspoon

4 : (2 × 16)

= 4:32

= 1:8

Therefore, the ratio of grenadine syrup to 7-Up will be 1:8.

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The area of the shaded region is 8.1838. The area of the shaded region is calculated by subtracting the area of the triangle from the area of the sector of the circle.

The area of the sector of a circle with a radius 'r' and an angle of sector 'θ' is

A = (θ/360) πr² sq. units

The area of the triangle with measures of two sides and an angle between them is

A = 1/2 × a × b × sinC sq. units

Where a and b are the lengths of sides and ∠C is the angle between those sides.

It is given that,

The area of the sector shown in the diagram is 78.6794 cm² and the area of the triangle is 70.4956 cm².

Then to calculate the area of the shaded region, subtract the area of the sector and the area of the triangle. I.e.,

Area of the shaded region = Area of the sector - Area of the triangle

⇒ 78.6794 - 70.4956

⇒ 8.1838 cm²

Therefore, the required area of the shaded region is 8.1838 sq. cm.

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Answer:

2500

Step-by-step explanation:

5000 ÷ 2 = 2500

Answer:

5% of 15 is 0.75 i think

Step-by-step explanation:

15/5% is 0.75

a) The probability is P = 1/9

b) The probability is P = 1/3.

First, we need to count the total number of outcomes (different cars that can be made with the given options):

Then there are 2*3*3 = 18 different cars.

a) Picking a blue hybrid car with an interior that is not leather.

There are 2 cars that meet that condition:

2 out of the 18 cars meet the condition, then the probability is:

P = 2/18 = 1/9

b) picking an electric car in a color other than blue is

The cars that meet the condition are:

So 6 out of the 18 cars meet the condition, then the probability is:

P = 6/18 = 1/3

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Answer:

$ 296 732 .10

Step-by-step explanation:

FV = PV ( 1 + i)^n      FV = future value = 531402     PV = ?

                                 i = decimal interest per period = .06

                                 n = periods = 10

531 402 = PV ( 1.06)^10         Solve for PV = 296 732 .10

The answers to the questions are:

1. The confidence level is 99 percent.

2. We have to conclude that there is no sufficient evidence available to support this claim because the Confidence interval contains 75 sec.

1. The confidence level here should be

1- 0.01 = 0.99

= 99 percent

Given that, 99% confidence interval for population mean (μ) is (-34.1 sec u< u < 264.1 ) seconds.

We are to test  the claim that the population mean is greater than 75 sec.

2.

The given confidence interval contains the value of 75 sec, so there is not sufficient evidence to support the claim that the mean is greater than 75 sec.

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