Find the area of the following region The region inside the inner loop of the limaçon r=6 + 12 cos θ The area of the region is square units.(Type an exact answer, using π as needed.)

Answer:

The path of the soccer ball can be modeled by a parabolic equation, which can be represented as y = ax^2 + bx + c.

In this equation, y represents the height of the soccer ball, x represents the horizontal distance traveled, a represents the parabolic shape of the path, b represents the horizontal direction and c represents the initial position.

To find the equation that models the path of the soccer ball, you would need to know the values of a, b, and c. These values can be found using the information given in the problem, which is the horizontal distance traveled (80 feet) and the highest point reached (30 feet).

It can be represented as y = -(1/240)x^2 + (1/2)x + 30

In this equation, -(1/240) is the value of a, (1/2) is the value of b and 30 is the value of c.

Step-by-step explanation:

The domain of the given function would be all real numbers such that x is not equal to 0 comma negative five halves comma -3/2.

Option (A) is correct.

What is the domain of the function?

The domain of a function is the set of all input values (also known as the independent variable) for which the function produces a valid output (also known as the dependent variable). In other words, it is the set of all input values for which the function is defined.

The domain of the rational function f(x) = 3x/(2x^3 - x^2 - 15x) is all real numbers except for x = 0 and x = -3/2, -5/2 (the values that make the denominator equal to zero).

Hence, the domain of the given function would be all real numbers such that x is not equal to 0 comma negative five halves comma -3/2.

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Answer:

A

Step-by-step explanation:

The equation in point-slope form for the line passing through (3, -8) with a slope of -3 is y = -3x + 1

What is the slope?

The slope of a line is a measure of its steepness. Mathematically, the slope is calculated as "rise over run" (change in y divided by change in x).

The point-slope form of the equation of a line is:

y - y1 = m(x - x1)

where (x1, y1) is a point on the line and m is the slope.

We are given that the line passes through the point (3, -8) and has a slope of -3, so we can substitute these values into the point-slope form:

y - (-8) = -3(x - 3)

Simplifying the equation, we get:

y + 8 = -3x + 9

Subtracting 8 from both sides, we get:

y = -3x + 1

Therefore, the equation in point-slope form for the line passing through (3, -8) with a slope of -3 is:

y - (-8) = -3(x - 3)

which simplifies to:

y + 8 = -3x + 9

or in slope-intercept form:

y = -3x + 1

Hence, the equation in point-slope form for the line passing through (3, -8) with a slope of -3 is y = -3x + 1

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Answer:

I assumed that the square roots were not nested for this problem, which means I put √125 beside √20 - (-3).

Step-by-step explanation:

Start this problem off by applying an inversive rule: x - (-y) = x + y

[tex]=14\sqrt{20+3}\sqrt{125}[/tex]

Now, simplify √125 into a radical.

[tex]= \sqrt[5]{5}[/tex]

Now that the previous number is a radical, this is what the expression should look like:

[tex]=14\sqrt{20+3}\times 5\sqrt{5}[/tex]

Next, we multiply the numbers together. Borrow the ^5 from the radical, then regroup like terms.

[tex]14\times 5 = 70\\=70\sqrt{20+3}\sqrt{5}\\=70\sqrt{5}\:\times \sqrt{20+3}[/tex]

Last of all, we must apply the radical rule, which states that if there are two radicals, radical X and radical Y, these radicals will combine into one, and then will be multiplied by each other. However, note that the radicals cannot equal 0.

[tex]\sqrt{5}\sqrt{23}=\sqrt{5\times 23}[/tex]

Now, since the radicals are combined, multiply them together. 5 times 23 is 115, so combine the square root, and that will be your final answer. :)

Hope this helps!

A straight line is a boundless one-dimensional figure that has no breadth. It is a combination of boundless points joined on both sides of a point. A straight line does not have any loop in it. If we draw an angle between any two points on a straight line, we always get 180°.

A straight line can be formed between two points but both ends extend to infinity. A straight line is a figure created when two points A ([tex]x_{1} , y_{1}[/tex]) and B ([tex]x_{2} , y_{2}[/tex],) are connected with the shortest distance between them, and the line ends are extended to infinity.

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No, it depends upon the size of the bottle but it's not enough for a normal bottle to make 6 frozen juice bars.

No, 2 cups of orange juice is not enough to make 6 frozen juice bars. Each frozen juice bar typically requires a certain amount of juice, and it is likely that 6 bars would require more than 2 cups of juice. To be sure, you would need to check the recipe or packaging for the frozen juice bars to determine the exact amount of juice required per bar.

It is also important to note that even if the juice is enough to make 6 bars, it might not yield the same taste as desired because of the lack of enough juice, also the freezing process might not work as well as it should because of the small quantity of juice.

Therefore, It is not enough as it depends upon the size of the bottle but it's not enough for a normal bottle to make 6 frozen juice bars.

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The steps to bisect the line segment are as detailed below.

The steps to bisect a line segment are as follows;

Step 1: Place the compass at one end of line segment.

Step 2: Adjust the compass to slightly longer than half the line segment length

Step 3: Draw arcs above and below the line.

Step 4: Keeping the same compass width, draw arcs from other end of line.

Step 5: Place ruler where the arcs cross, and draw the line segment.

Looking at the given image that was used to bisect a line segment, the steps above are the steps that were taken to bisect it.

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The range of the data on the boxplot is 12

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

The box plot

The range is calcilated as

Range = Maximum - Minimum

From the plot, we have

Maximum = 12

Minimum = 0

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

Range = 12 - 0

Evaluate

Range = 12

Hence, the range is 12

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Answer:6c+2y=4.5i

Step-by-step explanation:

i am pretty sure it that answer is because you cant add 2 variables in a problem well 2 different variable

hope its right

The required equation of transformation from figure V to figure W is (-x, y+3).

Transform the shapes on a coordinate plane by rotating, reflecting, or translating them. Felix Klein introduced transformational geometry, a fresh viewpoint on geometry, in the 19th century.

Here,
From the figure, it is clearly seen that first the figure gets mirrored on the y-axis, so the translation in the horizontal direction is given as -x. Now after forming the image across the y-axis the figure is translated up by 3 units so vertical translation is given as y +3.
Combine translation is given as {-x, y+3}

Thus, the required equation of transformation from figure V to figure W is (-x, y+3).

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The number of images formed by two mirrors kept at an angle of 72° are;

5 images, If the object is positioned symmetrically between the mirrors

4 images if the object is placed asymmetrically between the mirrors

The formula that can be used to find the number of images formed, n, when two mirrors are placed at a specified angle, θ, to each other is presented as follows;

If [tex]\dfrac{360^{\circ}}{\theta}[/tex] is an even number, the number of images formed is obtained using the formula;

If [tex]\dfrac{360^{\circ}}{\theta}[/tex] is an odd number, the number of images formed is obtained using the formula;

If [tex]\dfrac{360^{\circ}}{\theta}[/tex] is an odd number, and the position of the object is asymmetric, the number of images formed is obtained using the formula;

When θ = 72°, we get;

[tex]n = \dfrac{360^{\circ}}{72^{\circ}} = 5[/tex], which is an odd number, therefore;

If the object is placed symmetrically between the two mirrors, the number of images formed is therefore;

[tex]n = \dfrac{360^{\circ}}{72^{\circ}}-1 = 4[/tex]

If the object is placed asymmetrically between the two mirrors, the number of images formed is [tex]n = \dfrac{360^{\circ}}{72^{\circ}} = 5[/tex]

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Answer:

x=25

Step-by-step explanation:

Vertical angles are congruent

37+45=82

180-82=98

Liner pairs=180

82+123=155

180-155=25

x=25

Answer:

Hence, your answer will be:

P  ≈  $54900

Step-by-step explanation:

Owen is going to invest in an account paying an interest rate of 5.7% compounded continuously. How much would Owen need to invest, to the nearest hundred dollars, for the value of the account to reach $122,000 in 14 years?

Compounded Continuously:

A  =  Pe^rt

Given Values:

A = 122000     t = 14    r = 0.057

Plug In:

122000 = Pe^0.057(14)

Plug In:

122000 = Pe^0.798

Evaluate In Calculator Using e Button:

122000 = P(2.221094295)

Divide By: 2.221094295

122000 / 2.221094295  =  P(2.221094295) / 2.221094295  

Use Calculator:

54927.87959894 = P

Round to The Nearest Hundred Dollars:

P  ≈  $54900

The right triangle in question 3 have the value of m = 10√2 and n = 10 using the trigonometric ratio of sine and cosine of the angle 45°.

The trigonometric ratios involves the relationship of an angle of a right-angled triangle to ratios of two side lengths. Basic trigonometric ratios includes; sine cosine and tangent.

Considering the angle 45° for the right triangle, recall that sin 45° and cos 45° are both equal to √2/2

sin 45° = 10/m {opposite/hypotenuse}

√2/2 = 10/m

m = 20/√2 {cross multiplication}

m = 20/√2 × √2/√2 {rationalize}

m = 20√2/2

m = 10√2

cos 45° = n/m {adjacent/hypotenuse}

√2/2 = n/10√2

n = 10(√2)²/2

n = 10 × 2/2

n = 10

Therefore, the value of m is equal to 10√2 and that of n is equal to 10, using the trigonometric ratio of sine and cosine of the angle 45° for the right triangle.

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A representative sample is one that is drawn at random from the population and is large enough to provide accurate data.

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Answer:

x - 1 is inside a cubic root.

The cubic root of a positive number is positive.

The cubic root of zero is zero.

The cubic root of a negative number is negative.

That means that the cubic root of any real number is also a real number.

The domain is all real numbers.

The required equation that represents the relationship between b and e exists m<b + m<e = 180.

Two angles are called supplementary when their measures add up to 180 degrees.

If the sum of two angles is 180 degrees then they are said to be supplementary angles, which form a linear angle together. Whereas if the sum of two angles is 90 degrees, then they are said to be complementary angles, and they form a right angle together.

The required equation that represents the relationship between b and e exists m<b + m<e = 180

From the given diagram, we can see that the line x and y are cut by a transversal. This shows that the following statements exists true;

m<b and m<g exists supplementary

i.e m<b + m<g = 180

Also m<b and m<f are equal (alternate interior angle)

m<b = m<d (vertically opposite angle)

Also, since m<d and m<e are supplementary angles (angle on a straight line), then m<b and m<e are also supplementary.

Therefore, the required equation that represents the relationship between b and e exists m<b + m<e = 180.

The complete question is:

Lines x and y are parallel. Write an equation that represents the relationship between b and e. Explain how you know this equation is always true. Your explanation should use AT LEAST TWO of the following terms: vertical angles, corresponding angles, congruent, supplementary.

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Answer: It seems that the missing step in this proof would be option "OB" ZBDE ZDEB ZADE ZDEC,

Step-by-step explanation:  

It's showing that the angles are equal and the angles are congruent. The reason is that by definition, congruent angles have the same degree measure and by using the Angle-Angle Similarity Criterion we can prove that if two angles of one triangle are congruent to two angles of another triangle, the two triangles are similar.

It is important to note that this statement can only be used when the two figures are similar and it is not sufficient for congruency. Therefore, a missing step in this proof would be to prove that the figures are similar before using the Angle-Angle Similarity Criterion.

The statement given is "AABC with = CB" and the conclusion is "DE AC." The question is asking for the missing step in the proof that shows how these two statements are related.

There are 2,848 calories in two pounds of a certain ice cream.

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

We have to given that;

There are 623 calories in seven ounces of a certain ice cream.

Since, We know that;

⇒ 1 pound = 16 ounces

Hence, We get;

⇒ 2 pounds = 32 ounces

Here, Amount of ice cream in 7 ounces = 623 calories

Hence, Amount of ice cream in 32 ounces = 623 × 32 / 7

                                                                   = 2,848 calories

Thus, Amount of ice cream in 1 pounds = 2,848 calories

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[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{(3^3)^2}[/tex]

[tex]\mathsf{= (3 \times 3 \times 3)^2}[/tex]

[tex]\mathsf{= (9 \times 3)^2}[/tex]

[tex]\mathsf{= (27)^2}[/tex]

[tex]\mathsf{= 27^2}[/tex]

[tex]\mathsf{= 27 \times 27}[/tex]

[tex]\mathsf{= 729}[/tex]

[tex]\huge\text{Therefore, your answer should be: }[/tex]

[tex]\huge\boxed{\mathsf{729}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

Let's assume that the reaction is taking place between alkyl bromide and the nucleophile is OH- , then the formula for substitution reaction will be , R-Br + OH− => R-OH + Br− .

Nucleophiles are known as organisms that are strongly linked to an area of positive charge in the form of an ion or a molecule. These are believed to be fully charged or to have negative ions on a molecule. Cyanide ions, water, hydroxide ions, and ammonia are common examples of nucleophiles.

Electrophiles are compounds which are involved in the electrophilic substitution process. They are the molecules that transfer a pair of electrons during the creation of a covalent bond.

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The additive inverse of 3/2 is -3/2 as the sum of both value is 0 which is additive identity.

An additive inverse of a number is the number that when added to the original number, results in a sum of zero. In other words, it is the opposite of the original number on the number line. In the case of a fraction, the additive inverse is found by multiplying the numerator and denominator by -1. The additive inverse of 3/2 is -3/2 because 3/2 + (-3/2) = 0. This is true for any number in any form, whether it be an integer, a decimal, or a fraction.

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Complete question:

what is additive inverse of 3/2?

r represents the sample correlation coefficient.

p represents the population correlation coefficient.

A statistical concept known as the correlation coefficient helps in establishing a relationship between expected and actual values gained through statistical experimentation.

The estimated correlation coefficient's value explains how much the expected and actual values match.

The correct answers are

r represents the sample correlation coefficient

The interpretation of sample correlation coefficient (r) depends on how the sample data are collected.

A statistical concept known as the correlation coefficient helps in establishing a relationship between expected and actual values gained through statistical experimentation.

p represents the population correlation coefficient.

With a large simple random sample, the sample correlation coefficient is an unbiased estimate of the population correlation coefficient (p)

A correlation coefficient of 1 is perfect positive correlation

A correlation coefficient of -1 is perfect negative correlation

A correlation coefficient of 0 indicated the variables do not have any direct relationship.

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Discuss the difference between r and p. Choose the correct answers below.

r represents the _____

1. sample correlation coefficient thing

2. critical value for the correlation coefficient.

3. population correlation coefficient.

p represents the _____

1. critical value for the correlation coefficient.

2. population correlation coefficient.

3. sample correlation coefficient.

The absolute value of real number is 0 and the absolute value of complex number is z=a+bi.

So, the complete value of a complex number represents the distance between the starting and the point in the complex plane. On the other hand, the absolute value of a real number means only how far a number is from zero without all in all any direction.

A number system is a way of showing numbers by writing, which is a mathematical way of act for the numbers of a given set, by using the numbers or symbols in a mathematical means.

Both all the negative and positive integers, decimal and fractional numbers without imaginary numbers are called real numbers. Real numbers are act for by the “R” symbol.

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Her checking account balance at every given time is represented by the linear function 175 + 8.75t

In this situation, the checking account offers simple interest at a rate of 5% annually. Her account has $175 in it.

The amount of money in the account at anytime will be:

= 175 + (PRT/100)

P = principal

R = rate

T = time

= 175 + [(175 × 5 × t)/100]

= 175 + 8.75t

The function is 175 + 8.75t

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The length of DM is 38 cm.

We know that,

Triangles DEF and OEN are similar by the AAA Similarity Postulate.

According to the Angle-Angle-Angle (AAA) criteria, "if in two triangles, corresponding angles are equal, then their corresponding sides are in the same ratio (or proportion), and hence the two triangles are identical."

If two triangles are similar, then the ratio of its corresponding sides is proportional,

Hence,

DE/OE = DF/ON

Substituting the values given,

44/22 = DF /38

DF = 2*38 = 74 cm

Since, DF = 2DM

76 = 2 DM

DM = 38 cm

Therefore, The length of DM is 38 cm.

(Refer to the image attached for the diagram of the triangle)

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Answer:

7

Step-by-step explanation:

42$ total ÷ 6$ per keychain = 7

7 is the most amount of keychains Hailey can buy.

let's firstly convert the mixed fractions to improper fractions.

[tex]\stackrel{mixed}{3\frac{1}{2}}\implies \cfrac{3\cdot 2+1}{2}\implies \stackrel{improper}{\cfrac{7}{2}} ~\hfill \stackrel{mixed}{1\frac{4}{8}} \implies \cfrac{1\cdot 8+4}{8} \implies \stackrel{improper}{\cfrac{12}{8}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{7}{2}+\cfrac{12}{8}\implies \cfrac{(4)7~~ + ~~(1)12}{\underset{\textit{using this LCD}}{8}}\implies \cfrac{28+12}{8}\implies \cfrac{30}{8}\implies \cfrac{15}{4}\implies 3\frac{3}{4}[/tex]

Answer: 5

Step-by-step explanation:

3 1/2 + 1 4/8

= 7/2 + 12/8

= 28/8 + 12/8

= 40/8

= 5