Which of the following represents the polar equation r = (tan 2θ)(csc θ) as a rectangular equation?

Answer:

Explanation:

Here, we want to get the dimensions of the rectangle

Let us represent the length by l and the width by w

From the question:

The length of the rectangle is 3 m less than double the width

Mathematically:

The product of the two represents the area

Now, let us substitute the first equation with the second:

Solving the quadratic equation, we have:

Recall:

These are the solutions of all the questions

Answer:

[tex]5 \times 107 = 535[/tex]

This is equivailent to the following

Answer: slope is -3

Step-by-step explanation: (-5,6) and (-9,-6)

Take your Y values and subtract them -6-6=-12

Take your X values and subtract them -9-(-5) or -9+5= -4

Then your -12 will be your numerator and your -4 will be your denominator

Then Divide

-12/-4= -3

I hope this helps!  

4x² - 18x - 5 cannot be factored by grouping.

Factoring a polynomial involves writing it as a product of two or more polynomials.

In other words, it is a process of finding the factor.

Therefore, let's factor the quadratic equation as follows:

4x² - 18x - 5

Factorization by grouping means that we need to group the terms with common factors before factoring.

The grouping method can be used to factor polynomials whenever a common factor exists between the groupings.

Hence,

4x² - 18x - 5 cannot be factorise by grouping because it has no common factor.

in other word, we cannot, however, use the grouping method to factor 4x² - 18x - 5 because factoring out the GCF from both groupings does not yield a common factor.

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Hello!

First, let's write the possible options:

Dice: 6 different results.

• 1, 2, , 4, 5, 6.

Spinner: 4 different results.

• A, B, C, D.

Knowing it, let's solve each alternative of your exercise:

In the dic, we have 6 possible results and we want a specific number. SOo, we can write it as 1/6.

In the spinner, we have 4 possible results and we want a specific one too. So, we have 1/4.

Now, remember he r"and" rule: when we consider two events happening simultaneously, we must multiply their probabilities.

Solving:

We'll solve it in a similar way.

We have three possible odd numbers (1, 3, 5) in a total of 6 options. So, 3/6 = 1/2.

For the spinner, the reasoning will be the same: 1/.

Let's calculate:

In a dice, we have four numbers less than 5: 1, 2, 3,4.

In the spinner, there are 3 consonants (B, C, D).

Let's calculate:

Step 1:

Draw the table for the input x and output y.

Step 2:

From the table, we can see that the function is an exponential function.

Step 2:

Find the inverse of the function.

Step 3:

The two graphs below, show the graph of the inverse for both negative and positive square roots of x.

Final answer

The blue graph is the inverse of the red graph.

The new point is (-2, -9).

What happens when a point is reflected about an axis?
The x-coordinate remains constant when a point is reflected across the x-axis, but the y-coordinate is assumed to be the additive inverse. Point (x, y) is reflected across the x-axis as (x, -y).
The y-coordinate stays the same when a point is reflected across the y-axis, but the x-coordinate is assumed to be the additive inverse. Point (x, y) is reflected across the y-axis as (-x, y).

Given, the point to be reflected is : A : (2, -9)
Also, the axis through which the point is to be reflected is y-axis.
Following the statement established in the literature, we have:
The point (2, -9) when reflected over the y-axis,  the x-coordinate is assumed to be the additive inverse, thus the new co-ordinate is (-2, -9).
The new point is (-2, -9).

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The height of the tree is approximately 2.11 meters if Kayla is 1.85 meters tall. At 12 noon, she measures the length of a tree's shadow to be 28.15 meters.

It is defined as the law to prove that two triangles have the same shape, but it is not compulsory to have the same size. The ratio of the corresponding sides is in the same proportions and the corresponding angles are congruent.

It is given that:

Kayla is 1.85 meters tall. At 12 noon, she measures the length of a tree's shadow to be 28.15 meters.

D = 39.75 m

d = 34.9 m

H:h = D:d

H/1.85 = 39.75/34.9

H = 2.11 m

Thus, the height of the tree is approximately 2.11 meters if Kayla is 1.85 meters tall. At 12 noon, she measures the length of a tree's shadow to be 28.15 meters.

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Answer:

A, 61.

Step-by-step explanation:

(2x+24). If we sub in 61 for x, we get (2(61)+24). Follow order of operations.

2 times 61= 122. Add 24 and you get 146. We can know this is correct because we are given the other angle and it's degrees, whch is also 146 degrees. Therefore, the answer is A, 61.

Answer:

24° , 60° , 96°

Step-by-step explanation:

sum the parts of the ratio, 2 + 8 + 5 = 15 parts

divide the sum of the angles in a triangle by 15 to find the value of one part of the ratio.

180° ÷ 15 = 12° , then

2 parts = 2 × 12° = 24°

5 parts = 5 × 12° = 60°

8 parts = 8 × 12° = 96°

the 3 angles in the triangle are 24° , 60° , 96°

When two lines and a transversal form comparable angles that are congruent, the lines are parallel, which is the converse of the corresponding angles theorem's flow proof. Which means that line c ║ to line d.

The two different lines that meet at an angle of 90 degrees are called perpendicular lines. Do your walls' connecting corners—or the letter "L"—share any similarities? They are the straight lines, referred to as perpendicular lines, that intersect at the proper angle. An angle of 90 degrees between two straight lines is known as a perpendicular. The illustration depicts a little square in between two perpendicular lines to indicate the 90° angle, which is also known as a right angle. Here, a right angle between the two lines Two lines that cross each other at a 90° angle are referred to as perpendicular lines in mathematics. I

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Depending on the particular isotope, this process can take a variety of times. While for some it will take years and decades, it will just take a microsecond for individuals. Usually, the isotope will decay into a different element or isotope.

Isotopes are two or more different atom types that share the same atomic number and place in the periodic table but have different quantities of neutrons in their nuclei, resulting in various nucleon numbers.

If we start with 180 g of the isotope, after one half-life the quantity will diminish to  180 g/2 = 90 g which exists half the original quantity.

This can be written mathematically as: [tex]$180 g\left(\frac{1}{2}\right)^1$[/tex]

After the second half life: [tex]$\frac{90 g}{2}=45 g=\frac{180 g}{4}=(180 g)\left(\frac{1}{2}\right)^2$[/tex]

After the third half life: [tex]$\frac{45 g}{2}= 22.5 g=\frac{180 g}{8}=(180 g)\left(\frac{1}{2}\right)^3$[/tex]

But now that we are dividing the amount by 2 to a power that grows as the number of half-lives, we can start to notice a pattern.

The original quantity can then be rapidly computed for six half-lives using the formula below:

[tex]$(180 g)\left(\frac{1}{2}\right)^6=(180 g)\left(\frac{1}{64}\right)=\frac{180 g}{64}=2.8 g$$[/tex]

Depending on the particular isotope, this process can take a variety of times. While for some it will take years and decades, it will just take a microsecond for individuals. Usually, the isotope will decay into a different element or isotope.

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The given statement "Sal earns $480 per week. Lidia earns $300 per week. Are their salaries proportional if Sal works 40 hours per week and Lidia works 25 hours per week" is true.

As given in the question,

If one amount is proportional to another, the two amounts increase and decrease at the same rate so there is always the same relationship between them

a:b = c:d

a ÷b = c ÷d

ad = bc

let Sal earns $480 per week and he works 40hours per week

  480÷40 = 12

Lidia earn $300 per week and she works 25 hours per week

   300÷25 = 12

Cross product of their salaries is  

480×25=1200

300×40=1200

The ratio of their salaries and their product are equal.

Hence, The given statement "Sal earns $480 per week. Lidia earns $300 per week. Are their salaries proportional if Sal works 40 hours per week and Lidia works 25 hours per week" is true

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Answer:

See below.  I added words tro the first question "Is a" so that I could answer it.

Step-by-step explanation:

f(x) = -3x³ + 9x² - 5x + 15

f(x) = -(x-3)(3x² + 5)

x((9-3x)x-5)+15

-3(x-1)[tex]x^{3}[/tex] + 4(x-1) + 16

=======

a) Is a [ghost happy]?

O Yes  Yes, as long as it can haunt.

O No

b) Is x + 1 a factor of f(x)?

O Yes  Yes

No

1 a factor of f(x)?  

Always

c) Is a 3 a factor of f(x)?

O Yes

O No    No, as far as I can see.

The probability that a randomly selected band member is a senior given that he or she plays the trumpet is 34.78%.

Probability is defined as the likeliness of an event to happen. It can be calculated by dividing the total desired outcomes by the total outcomes.

P = desired outcomes / total outcomes

Of the 108 band members, if 23 play the trumpet, and 8 are seniors who play the trumpet, then the probability that a randomly selected band member is a senior given that he or she plays the trumpet is 8 divided by 23.

P = 8/23 x 100

P = 34.78%

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The probability a selected person is both tall and fat is 0.341

From the question, the given parameters are

People = 100

Fat = 55

Tall = 62

So, the individual probabilities are

P(Fat) = 55/100

P(Tall) = 62/100

Evaluate

P(Fat) = 0.55

P(Tall) = 0.62

The probability a person is both tall and fat is

P(Fat and Tall) = P(Fat) * P(Tall)

So, we have

P(Fat and Tall) = 0.55 *  0.62

Evaluate

P(Fat and Tall) = 0.341

Hence, the probability is 0.341

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If covariance between two variables is near 0, it implies that the variables are not linearly related.

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Answer:

Find the total number of oranges.

Total oranges = 90 × 5

= 450

Since 1/5 were rotten oranges,

Fraction of oranges that were not rotten

= Fraction of total oranges - Fraction of rotten oranges

= 5/5 - 1/5

= 4/5

Number of oranges not rotten = 4/5 × 450

= 360

First convert the angle measure from radians to degrees using the formula

Were θ represents the angle of interest

So for this exercise the angle is pi, so:

Now using the calculator you can determine tha tangent of negative 180º

tan(-180º)=0

So the tangent of negative pi should also be zero

ANSWER

(-4, 2)

(Option D)

EXPLANATION

The triangle in the picture is dilated with scale factor 2.

This simply means that the size of the triangle was increased by 2.

To do this, first, let us write out the cordinates of the vertices of the original triangle:

M(-2, 1)

P(2, -2)

A(3, 5)

To dilate this, we will multiply the cordinates by 2, they become:

M' (-4, 2)

P' (4, -4)

A' (6, 10)

Therefore, the vertex M on the image after the dilation is (-4, 2).

(Option D)

Answer: 5 3/5

Step-by-step explanation:

3 + 2 = 5

2/5 + 1/5 = 3/5

5 + 3/5 = 5 3/5

Hope this helps!

An inequality that represents the number of minutes m you need to practice on the seventh day is m≤70.

Given that, You have a goal to practice the piano for an average of at least 45 minutes per day for one week.

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

Let m be the number of minutes you need to practice on the seventh day

The inequality for the given situation is

245+m≤315

⇒ m≤315-245

⇒ m≤70

Therefore, an inequality that represents the number of minutes m you need to practice on the seventh day is m≤70.

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"Your question is incomplete, probably the complete question/missing part is:"

You have a goal to practice the piano for an average of at least 45 minutes per day for one week. The first six days you practice a total of 245 minutes.

Write and solve an inequality that represents the number of minutes m you need to practice on the seventh day.

1) The x-intercept lies at (1, 14), and the y-intercept lies at (3, 42).

2) This means that after 3 cuts, the length of the string is 33 inches.

3) Therefore, the 42-inch string can be cut into 14 pieces of 3 inches each.

The x-intercept is the point on the graph where a line crosses the x-axis.

The y-intercept is the point on the graph where a line crosses the y-axis.

The x- and y-intercepts are the coordinate points for graphing data.

Thus, the x- and y-intercepts are coordinate points where the graph of a function or an equation touches the two axes.

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The conservationist expects to be in the lake would be; 142 trouts.

An equation is an expression that shows the relationship between two or more numbers and variables.

Given, that determine the number of trout in a lake, a conservationist catches 200 trout, tags them, and throws them back into the lake.  

We have to find conservationists who expect to be in the lake.

Now, initially, trout count = 200

Then, again 56 trouts caught then, trout count = 200 + 56

But 14 of them are tagged that means; they are part of 200 trouts so we should not count again in 56 trouts.

So, trout count = 200 + 56 – 14  = 142.

Hence, the conservationist expects would be; 142 trouts.

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Answer:

Your answer would be

(a) FPUGT.

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. The equation 9 x 5 = 45 consists of the two equations are separated by the 'equal' sign.

Assume that a team has N players.

Each squad may have anywhere from 3 to 5 players, so

3 ≤ 5 ...(i)

Let P represent a player's total points in a single game round.

Each round of the game allows for a maximum of 10 points for each player, so

0 ≤ p ≤ 10 ....( i)

(1) Elena assembled a team of five people.

As a result, 5 players' points in 1 round equal 5P.

Equation (ii) yields the range of

0 ≤ 5p ≤ 50.

As a result, Elena's team's points total ranges from 0 to 50.

(2) If each shot is off by one point, then

One player's points in one round are equal to 10-1=9.

So, 9 x 5 = 45 points were collected by 5 players in 1 round.

(3) Assume that R represents the number of teams as an integer.

the game involves at least three teams, therefore

R ≥ 3 ...( iii)

Given that N players make up one team,

R team has NR players, where R is 3, 4, or more.

Next, using equation (i)

3R ≤ 5R

Therefore, the number of players ranges from 3R to 5R if there are at least 3 teams.

The game can have anywhere from 3x3=9 to 5x3=15 players when R=3.

Answer:

(I) Between 0 and 50.

(ii) Between 3 and 5.

(iii) Between 3R and 5R, where R = 3,4,5,...

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Simplify the expression and express in standard form.

So answer is,

Answer:

a) 1.6×10∧-6

b)2×10∧7