Polynomial functions can model situations that change directions multiple times. what is a situation in which a polynomial model might make sense and why?

The equation of the ellipse having foci  (±2,0) and vertices (±5,0) is [tex]x^{2} /4+y^{2} /21=1[/tex].

Given the foci of ellipse is (±2,0) and vertices (±5,0).

We are required to find the equation of ellipse having foci (±2,0) and vertices (±5,0).

Equation is the relationship between two or more variables that are expressed in equal to form. Equation of two variables looks like ax+by=c.

Equation of ellipse is as under:

[tex]x^{2} /a^{2} +y^{2} /b^{2} =1[/tex],where a is the semi major axis.

We have been given that a=5, c=2.

We know that [tex]c^{2} =a^{2} -b^{2}[/tex]

We have to find the value of b.

b=[tex]\sqrt{a^{2} -c^{2} }[/tex]

=[tex]\sqrt{5^{2} -2^{2} }[/tex]

=[tex]\sqrt{25-4}[/tex]

=[tex]\sqrt{21}[/tex]

Using the values of a and b in the equation [tex]x^{2} /a^{2} +y^{2} /b^{2} =1[/tex]

[tex]x^{2} /(2)^{2} +y^{2}/\sqrt{21} ^{2} =1[/tex]

[tex]x^{2} /4+y^{2} /21=1[/tex]

Hence the equation of the ellipse having foci  (±2,0) and vertices (±5,0) is [tex]x^{2} /4+y^{2} /21=1[/tex].

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Answer:

The coordinates of D is (7, 10)

Explanation:

Let the coordinates of endpoint D be (x, y)

Mid-point formula:

[tex]\sf (x_m, y_m) = (\dfrac{x_1+x_2}{2}, \dfrac{y_1+y_2}{2})[/tex]

Applying formula:

[tex]\sf (-1, \:4) = (\dfrac{-9+ x}{2},\: \dfrac{-2+y}{2} )[/tex]

Comparing found:

[tex]\sf -1 =\dfrac{-9+ x}{2} \quad and \quad \: 4 = \dfrac{-2+y}{2}[/tex]

[tex]\sf 2(-1)+9 =x \quad and \quad \: 2(4)+2 =y[/tex]

[tex]\sf x = 7 \quad and \quad \: y = 10[/tex]

So, coordinates of D is (7, 10)

The answer is (7, 10).

Remember the midpoint formula : [tex]\boxed {M = (\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2})}[/tex]

Finding the x coordinate of D

Finding the y coordinate at D

The point that is a solution to the system of inequalities is (5, 0)

The system of inequalities is given as:

y ≤ 2x + 2

y ≥ -5x + 4

Next, we test the given options.

From the list of options, we have

(x, y) = (5, 0)

Substitute (x, y) = (5, 0) in y ≤ 2x + 2 and y ≥ -5x + 4

y ≤ 2x + 2

0 ≤ 2 * 5 + 2

0 ≤ 12 -- this is true

y ≥ -5x + 4

0 ≥ -5 * 5 + 4

0 ≥ -21 -- this is true

Since both results are true, then it means that the point that is a solution to the system of inequalities is (5, 0)

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Complete question

Which point is a solution to the system of inequalities graphed here? y ≤ 2x + 2

y ≥ -5x + 4

A. (1,6)

B. (-6,0)

C. (0,5)

D. (5,0)

The given series is diverges according to the P Test.

According to the statement

we have given that the a series and we have to find that the those series is a converges or diverges.

So, For this purpose, we know that the

P-series test to say whether or not the series converges.

So, The given series is

[tex]1 + 1/\sqrt{32} + 1/\sqrt[3]{243 } + 1/\sqrt[4]{1024} + 1/\sqrt[5]{3125}[/tex]

And then

The value of  P becomes P = 5/6 < 1  when we find it using the p series test.

Hence, the p-series diverges

Because according to the p series test, The series converges if, and only if, the power satisfies p>1.

And diverges if, and only if, the power satisfies p<1.

So, The given series is diverges according to the P Test.

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Disclaimer: This question was incomplete. Please find the full content below.

Question:

Use Theorem 9.11 to determine the convergence or divergence of the p-series. 1 + 1/32 squareroot + 1/243 squareroot 3 + 1/1024 squareroot 4 + 1/3125 squareroot 5.

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Answer:

x = -1

y = 1

Step-by-step explanation:

Given expressions

1) 2x + 3y - 1 = 0

2) 5x + 2y + 3 = 0

Add 1 on both sides of the 1) equation:

2x + 3y - 1 + 1 = 0 + 1

2x + 3y = 1

Subtract 3 on both sides of the 2) equation:

5x + 2y + 3 - 3 = 0 - 3

5x + 2y = -3

Current System

1) 2x + 3y = 1

2) 5x + 2y = -3

Multiply 2.5 on both sides of the 1) equation

(2.5) 2x + (2.5) 3y = (2.5) 1

5x + 7.5y = 2.5

Current System

1) 5x + 7.5y = 2.5

2) 5x + 2y = -3

Subtract 2) equation from 1) equation

(5x + 7.5y) - (5x + 2y) = 2.5 - (-3)

Get rid of the parenthesis

5x + 7.5y - 5x - 2y = 2.5 + 3

Combine like terms

5x - 5x + 7.5y - 2y = 5.5

0 + 5.5y = 5.5

5.5y = 5.5

Divide 5.5 on both sides

5.5y / 5.5 = 5.5 / 5.5

[tex]\boxed{y=1}[/tex]

Substitute the y-value back to one of the equations to find the x-value

2x + 3y - 1 = 0

2x + 3(1) - 1 = 0

Combine like terms

2x + 3 - 1 = 0

2x + 2 = 0

Subtract 2 on both sides

2x + 2 - 2 = 0 - 2

2x = -2

Divide 2 on both sides

2x / 2 = -2 / 2

[tex]\boxed{x=-1}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

The area of a rectangle is the amount of space it would cover on a 2-Dimensional plane. The required value of the width is 25 feet.

A rectangle is a plane shape with equal opposite sides. Its area can be determined by;

Area of a rectangle = length x width

Considering the given question, let the length of the plot be represented by l and its width as w. Given that the width of the plot should be longer than its length by 5, then we have;

w = l + 5

But,

Area of the plot = length x width

500 = l x (l + 5)

       = [tex]l^{2}[/tex] + 5l

This implies that,

500 = [tex]l^{2}[/tex] + 5l

[tex]l^{2}[/tex] + 5l - 500 = 0

Applying the quadratic formula, we have;

l = (-b  ± [tex]\sqrt{b^{2} - 4ac}[/tex]) / 2a

a = 1, b = 5, c = -500

= (-5  ±  [tex]\sqrt{5^{2} - (4*1*-500)}[/tex]/ 2

 = (-5  ± 45) / 2

l =   (40) / 2 OR l =  (-50) / 2

l = 20 OR l = - 25.5

So that,

l = 20

Therefore, the length of the plot is 20 feet.

Thus the width of the plot can be determined as;

w = l + 5

   = 20 + 5

w = 25

The width of the plot is 25 feet.

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The situation described by the distance from Town A is the first graph.

Given that cities A,B and C are on straight line.

We are required to find the graph appropriate the given situation.

Distance is basically the measurement of how far two things,places are located.It can be measurement from one point to another .

On the first hour,they leave town B to town C moving farther from Town A,hence the distance is increasing on the first hour.

On the second hour they stop for lunch,meaning that the distance remains constant at the point, it was at the end of the first hour.

Hence if towns A,B C lie on a straight line and Jack and Arthur start at town B and drive for an hour from Town B to Town C then the distance shown from Town A during these two hours is first graph.

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The values associated to the exponential function are listed below:

Herein we have the exponential function [tex]g(x) = 1\,296^{x}[/tex], which has to be evaluated, that is, replacing the variable x by constants and make use of algebra properties until result is found.

g(- 1.75) = 3.572 × 10⁻⁶

g(- 1) = 7.716 × 10⁻⁴

g(- 0.25) = 0.167

g(0) = 1

g(0.25) = 6

g(0.50) = 36

g(0.75) = 216

g(1) = 1 296

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Answer: Your answers are

A. 1, 287 ways

B. 154,440 ways

Hope this helped :D

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The amount of cash needed to retire baldwin's bond early based on the brokerage will be $5427896.

It should be noted that from the information given, we are to calculate the amount of cash needed to retire baldwin's bond early based on the brokerage.

This will be:

= 6000 + (5756951 × 94.18/100)

= 6000 + 5421896.45

= 5427896

Therefore, the amount of cash needed to retire baldwin's bond early based on the brokerage will be $5427896.

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Magnitude of the momentum of this system just after the collision = 19.2Kgm/s

Law of conservation of momentum states that the total momentum after the collision must be equal to the total momentum before the collision.

The momentum of each ball is given by:

p = mv

where m is the mass of the ball and v its velocity.

The momentum of ball 1 is:

p = mv

= (3.0 kg)(4.0 m/s)

= 12.0 kg m/s in the eastward direction

The momentum of ball 2 is:

p = mv

= (5.0 kg)(3.0 m/s)

= 15.0 kg m/s in the northward direction

The two momenta are in perpendicular directions, so the magnitude of the total momentum can be found as:

[tex]p = \sqrt{p1^{2} +p2^{2} }[/tex]

[tex]p = \sqrt{12^{2} +15^{2} }\\p = \sqrt{144 + 225} \\p = \sqrt{369}\\ p = 19.2 kgm/s[/tex]

and due to the law of conservation of the momentum, this is also equal to the total momentum after the collision.

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The unit rate of 1/4 book 1/3 hour in books per hour is 3/4 books per hour.

Unit rate is the rate of a quantity in terms of another quantity per unit.

Unit rate(books per hour) = Number of books / Number of hours

= 1/4 ÷ 1/3

= 1/4 × 3/1

= (1×3) / (4×1)

= 3/4 books per hour

Therefore, the unit rate of 1/4 book 1/3 hour in books per hour is 3/4 books per hour.

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Answer:

The answer is x=2 and y=0.

Step-by-step explanation:

The given Equations are:

                    5x-2y=10      ----------------- (i)
                    4y+20=10x   ----------------- (ii)

From equation find the value of x, that is:

         5x=10+2y         (Obtained By adding 2y on both side of Equation (i))

Next divide with 5 on both side to get x:

          x=(10+2y)/5           ------------------ (iii)

Put this value of x in equation (ii):

        4y+20=10((10+2y)/5)

Simplifying the above equation:

         4y+20=2(10+2y)

         4y+20=20+4y

From the above equation the solution of y is not possible.

We can make it 0. So,
         y=0

Put this value of y in equation (iii), to get value of x:

        x=(10+2(0))/5

        x=(10+0)/5

        x=10/5

        x=2

We've got a negative slope, but it doesn't look steep enough to go through 6 on the y-axis.

So, it's the last option:

y = - 1.25x + 5.75

Hope this helps!

Answer:

6

Step-by-step explanation:

Original Equation

(n-1)!

Plug in 4 as n

(4-1)!

Subtract

(3)!

Rewrite using definition of factorial: [tex]a! = a*(a-1)*(a-2)....*1[/tex]

3! = 3*2*1

You don't really have to write the 1, since it doesn't change the value

6

Answer:

13cm

Step-by-step explanation:

Given the map scale:

1cm on the map : 4km actual distance

4km actual distance : 1cm on the map

1km actual distance : [tex]\frac{1}{4} =0.25cm[/tex] on the map

Therefore,

52km actual distance = 0.25 * 52 = 13cm

The number of combinations of balloons that can be chosen is 1716.

Selections and combinations are synonyms. Combinations represent the choosing of items from a predetermined group of items. We're not trying to arrange anything here. We're going to pick them.

Utilizing the combinations formula, it is simple to determine how many distinct groups of r objects each may be created from the provided n unique objects.

Number of red balloons = 12

Number of blue balloons = 8

First, we figure out how to choose from 13 red and 9 blue balloons.

There are 7 balloons left out of the 29 total (i.e. 29 - 13 - 9)

So, n = 7+7-1

n = 13

r = 7

Number of combinations of balloons = [tex]_{13} C_{7}[/tex]

                                                               = 13!/(13-7)!7!

                                                               = 13!/6!7!

                                                               = 1716

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It will take 585 billion years to solve the puzzle tower of Hanoi puzzle.

What is hanoi of tower?

The Tower of Hanoi is a mathematical game or puzzle that uses three rods and a number of disks that can slide onto any rod. It is also known as The Problem of the Benares Temple, the Tower of Brahma, Lucas' Tower, or simply the pyramid puzzle. The disks are stacked on one rod at the start of the problem, the smallest at the top and roughly forming a conical shape.

Using the Tower of Hanoi as little as possible

In one version of the problem, 64 golden disks are being used by Brahmin priests to solve it.

Minimum moves required if you had 64 golden disks [tex]=2^{64}-1[/tex]

The problem would take around 585 billion years to solve if every move took a single second.

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The inequality to describe the possible temperature in Bismarck, North Dakota given that t represent temperature is t < 4°F

The inequality signs are;

Let

So

t < 4°F in Bismarck, North Dakota

This means, temperature in Bismarck, North Dakota is less than 4°F

Therefore, t < 4°F is the inequality to represent temperature in Bismarck, North Dakota.

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Answer: C

Step-by-step explanation:

[tex]\frac{3x+1}{x+8} \div \frac{x-7}{5x}\\\\=\frac{3x+1}{x+8} \times \frac{5x}{x-7}\\\\=\frac{5x(3x+1)}{(x+8)(x-7)}\\\\=\frac{15x^2 +5x}{x^2 +x-56}[/tex]

Answer:

C

Step-by-step explanation:

y is greater or equal to 0

x is also greater or equal to 0

you can see that only one answer choice can be the answer

the line is x-y = 2

the upper side is x-y <= 2

proves that c is the answer

x-y ≤ 2

y ≥ 0

x ≥ 0 satisfies this graph. Thus option C is correct.

A schematic or visual presentation that organizes the depiction of data or quantities is known as a graph. The relationships connecting two or more objects are frequently represented by the spots on a graph. They are employed to arrange data in order to highlight correlations and patterns. This data is presented as a pattern on a graph.

When y is bigger than 0 and x is also.

The equation is 2x-y.

x-y ≤ 2 on the upper side of the graph is represented in this same way.

x-y ≤ 2; y ≥ 0 and x ≥ 0 will be the correct represented points in the graph. Therefore, option C is the correct option.

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The probability of getting exactly one face card is 0.72.

According to the questions two cards are drawn from a deck.

Since, we know that

Total number of cards in a deck = 52

Total number of face cards =  3 × 4 = 12

So, the number of ways of selecting 2 cards from a deck = [tex]^{52} C_{2}[/tex]

And, the total number of ways of  getting exactly one face cards

= [tex]^{12} C_{1} \times ^{40} C_{1}[/tex]  + [tex]^{40} C_{1} \times ^{12} C_{1}[/tex]

= 2[tex]^{40} C_{1} \times ^{12} C_{1}[/tex]

Therefore, the probability of getting exactly one face card

= [tex]\frac{2(^{40} C_{1} \times ^{12} C_{1})}{^{52C_{2} } }[/tex]

[tex]= \frac{2(\frac{40 \times 39!}{1!\times 39!} \frac{12\times 11!}{11!}) }{\frac{52\times 51\times 50!}{2!\times50!} }[/tex]

[tex]= \frac{2(40\times 12)}{26\times 51}[/tex]

[tex]=\frac{2\times 480}{1326}[/tex]

= 0.72

Hence, the probability of getting exactly one face card is 0.72.

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Given a triangle ABC at points A = (-6, 3) B=(-4,7) C = (-2, 3), and a first transformation of up 2 and right 3, and a second transformation of down 1 and left 6, the final point B" is located at (-7, 8), which is option (a).

In mathematics, a transformation refers to a change or mapping of one set of values to another set. In geometry, a transformation involves changing the position, size, or orientation of a geometric object.

To find the location of the final point B", we need to apply the two transformations given to the initial point B (-4, 7).

First transformation: up 2 and right 3

This means we add 2 to the y-coordinate (to move the point up) and add 3 to the x-coordinate (to move the point right).

So, the new location of B after the first transformation is: (-4 + 3, 7 + 2) = (-1, 9)

Second transformation: down 1 and left 6

This means we subtract 1 from the y-coordinate (to move the point down) and subtract 6 from the x-coordinate (to move the point left).

So, the new location of B" after the second transformation is: (-1 - 6, 9 - 1) = (-7, 8)

Therefore, the final point B" is located at (-7, 8), the correct option is a.

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[tex]\huge\boxed{18\ \text{points}}[/tex]

We'll represent Louise's, Tammy's, Delores's, and Sheryl's point values with [tex]x[/tex], [tex]x+1[/tex], [tex]x+2[/tex], and [tex]x+3[/tex] respectively since each one is 1 point more than the last.

Add all of these values up and set it all equal to [tex]78[/tex].

[tex]x+x+1+x+2+x+3=78[/tex]

Now, simplify.

[tex]4x+6=78[/tex]

Subtract [tex]6[/tex] on both sides.

[tex]\begin{aligned}4x+6-6&=78-6\\4x&=72\end{aligned}[/tex]

Divide both sides by [tex]4[/tex].

[tex]\begin{aligned}\frac{4x}{4}&=\frac{72}{4}\\x&=\boxed{18}\end{aligned}[/tex]

Since Louise's score is [tex]x[/tex], the answer is [tex]18[/tex].

To verify our answer, add the point totals [tex]18[/tex], [tex]19[/tex], [tex]20[/tex], and [tex]21[/tex].

This equals [tex]78[/tex], so we can be sure the answer is correct.

The correct answers to the sample space illustrated will be:

S = {I, L, L, M, P, T, U, Y}.

S = {g, r, b, y, o}.

S = {W, X, Y, Z}.

Flipping a fair, two-sided coin.

Sample space = lemon-lime, lemon-lime, watermelon, watermelon, watermelon, grape, grape, grape, grape, grape.

S = {Joy, Bob, Ben, Peter, John}

A paper bag has five colored marbles. The marbles are red, green, blue, yellow, and orange. The sample space when choosing one marble will be S = {g, r, b, y, o}.

A four-part spinner is spun once and the spinner with four parts labeled W, X, Y, and Z. The sample space for the experiment is S = {W, X, Y, Z}.

The event will have a sample space of S = {h, t} is the flipping a fair, two-sided coin.

The correct sample space for the gumballs in her bag will be sample space = lemon-lime, lemon-lime, watermelon, watermelon, watermelon, grape, grape, grape, grape, grape.

My experiment with 5 or more possible outcomes will be that a teacher wants to randomly give one of his give students a pack of chocolate.

The sample space for the experiment will be based on their names. This will be S = (Joy, Bob, Ben, Peter, John).

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The equation of the given parabola is y2=−20(x+3)

A parabola is a symmetrical open plane curve formed by the intersection of a cone with a plane parallel to its side. The path of a projectile under the influence of gravity ideally follows a curve of this shape.

In general in a parabola, if we have

(y−n)2=4p(x−m),

then the vertex is (m,n)

The axis of symmetry is y=m

The focus is (p+m,n)

The directrix is x=m−p.

Hence, for the given case

p+m=−8

n=0

m−p=2

⇒n=0

m=−3

p=−5

So, the answer will be y2=−20(x+3)

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The range of possible values should be (7,34), i.e 7 < x < 34.

The answer must be more noteworthy than 7, else the two sides are less than or rise to to the third. That triangle is outlandish. The reply must moreover be less than 34, since at that point the two other sides would rise to the third, making an impossible triangle.

By the property of triangle, Sum of the lengths of any two sides of a triangle is always greater than the length of the third side.

To prove above propert, let us assume a  ΔABC

extend AB to D in such a way that AD=AC.

In ΔDBC, as the angles opposite to equal sides are always equal, so,

∠ADC=∠ACD

so,

∠BCD>∠BDC

As the sides opposite to the greater angle is longer, so,

BD>BC

AB+AD>BC

Since AD=AC, then,

AB+AC>BC

Hence, sum of two sides of a triangle is always greater than the third side.

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Answer:

7 < x < 34

Step-by-step explanation:

The correct option is: (b)

                                =432.

By employing multiple processes, simplification refers to reducing the expression to a simpler form. Approximation is the process of making something less complicated and hence easier to accomplish or understand, or the object that arises from this process. The mathematical formula is simplified to its nearest value but is not exactly correct.

Therefore, we must follow the order listed above when simplifying expressions. In the example before, we divide 8 by 4 and then add the result to 12 because, according to BODMAS, division (D) comes before multiples (M).

[tex]$3 \cdot 2^{3} \cdot 2 \cdot 3^{2}Calculate exponents $2^{3}: 8$$$=3 \cdot 8 \cdot 2 \cdot 3^{2}$$Calculate exponents $3^{2}: 9$$$=3 \cdot 8 \cdot 2 \cdot 9$$ $3 \cdot 8 \cdot 2 \cdot 9= 432$$$=432$$[/tex]

So. the value will be = 432

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I understand that the question you are looking for is :

Simplify the expression to a single numerical value.

3*2^3*2*3^2

(a)144

(b)432

(c)900

(d)5,184

Answer: The answer is 87. when you look at the picture each number is one number apart from each other like look at

86, 87, 88, 89, 90, 91

85 + 1  = 86

86 + 1 = 87

87 + 1 = 88

89 + 1 = 90

90 + 1 = 91

Step-by-step explanation:

The statements that are true regarding the angles formed by the transversal and parallel lines are:

A. m∠1 = 70°.

B. m∠2 = 110°

C. m∠6 = 70°.

E. m∠9 = 50°

H. m∠16 = 130°

Given the following angle measures formed when two parallel lines ( being cut by two transversals:

Using relevant theorems, let's determine which of the statements are true:

Angles 4 and 1 are vertical angles, therefore they are congruent based on the vertical angles theorem.

m∠4 = m∠1

m∠1 = 70°.

m∠2 = 180 - m∠4 [linear angles theorem]

m∠2 = 180 - 70

m∠2 = 110°

m∠6 = m∠4 [base on the alternate interior angles theorem]

m∠6 = 70°.

m∠9 = 180 - m∠12 [based on the linear angles theorem]

m∠9 = 180 - 130

m∠9 = 50°

m∠16 = m∠12 [based on the corresponding angles theorem]

m∠16 = 130°

The statements that are true are:

A. m∠1 = 70°.

B. m∠2 = 110°

C. m∠6 = 70°.

E. m∠9 = 50°

H. m∠16 = 130°

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