which is the polar form of the parametric equations x=4t and y=t^2?


a. r= 16 tan (theta) sec (theta)

b. r= 16 tan^2 (theta)

c. r= 16 sec^2 (theta)

d. r= 16 sec (theta)

Answer:

[tex]x^{2/3}[/tex]

Step-by-step explanation:

When you have a power then a root like that, you have to divide the power by the root.

So, in this case, you have q square (x²) and a cubic root (³√).

So, you take your square (2) and divide it by the cube (3), to get a new power of 2/3.

Let's verify it with x = 2

[tex]\sqrt[3]{2^{2} } = \sqrt[3]{4} = 1.59\\\\\\2^{2/3} = 1.59[/tex]

So, both expressions equal the same thing, it means they're equivalent.

The purple area is the sum of the circle sector and the triangle:

[tex]A = A_s+A_t[/tex]

Let's compute them one at the time:

The sector is identified by an angle of 260°, because it is the remainder of a 100° angle.

We can build this simple proportion

[tex]\text{total area}\div\text{total angle}=\text{sector area}\div\text{sector angle}[/tex]

The area of the circle is [tex]\pi r^2[/tex], so we have

[tex]\pi 8.35^2\div 360= A_s\div 260[/tex]

Solving for the sector area, we have

[tex]A_s = \dfrac{\pi\cdot8.35^2\cdot260}{360} = \dfrac{8.35^2\cdot 13\pi}{18}[/tex]

The triangle is an isosceles triangle, because two of the sides are radii. This means that the height is also a bisector, so we can cut the triangle in two 90-50-40 triangles.

Using the law of sines, we can deduce that the height is

[tex]8.35\sin(40)[/tex]

And half the base is

[tex]8.35\sin(50)[/tex]

So, the area of the triangle is

[tex]A_t = 8.35^2\sin(40)\sin(50)[/tex]

So, the purple area is

[tex]A = A_s+A_t =\\\dfrac{8.35^2\cdot 13\pi}{18}+8.35^2\sin(40)\sin(50) = 8.35^2\left(\dfrac{13}{18}\pi+\sin(40)\sin(50)\right)\approx 192.5[/tex]

Answer:

A. The ratios of the sine of the angle to the opposite side are the same.

Step-by-step explanation:

The law of sines is ...

sin(A)/a = sin(B)/b = sin(C)/c

Answer:

Option A is correct that is the ratio of the sine of an angle to the length of the opposite side is the same for all part of the triangle.

Step-by-step explanation:

Given:

Three angles of the triangles = ∠A ,  ∠B and ∠C

Three Sides of the triangle = a , b , c

We need to find statement which states the Law of Sines.

We know that Law of Sines is given by,

[tex]\frac{a}{sin\,A}=\frac{b}{sin\,B}=\frac{c}{sin\,C}[/tex]

or

[tex]\frac{sin\,A}{a}=\frac{sin\,B}{b}=\frac{sin\,C}{c}[/tex]

Therefore, Option A is correct that is the ratio of the sine of an angle to the length of the opposite side is the same for all part of the triangle.

Answer:

D 7/24

Step-by-step explanation:

Because on the first choice, there is a total of 24 marbles

if theres 7 black marbles the chance of pulling a black marble is 7/24

Choice D), since Katie went way over the decimals, and Amaya went slightly under to the closest number

Answer:

Amaya's estimate is the closer one.

D. Katie’s estimate will be greater than the actual product, and Amaya’s estimate will be less than the actual product

Step-by-step explanation:

The original expression is 89.1 x 9.3. Katie changed the 89.1 to 99 (difference of 9.9) and the 9.3 to 10 (difference of 0.7). On the other hand, Amaya changed the 89.1 to 89 (0.1 difference) and the 9.3 to 9 (0.3 difference).

Therefore the best comparison would be Amaya's estimate since her numbers are closer to the original expression.

Katie's estimate will be greater than the actual product because she rounded up the numbers and Amaya's estimate will be less than the actual product because she rounded down the numbers.

Answer:

D. 3

Step-by-step explanation:

If the prisms are said to the similar, that means that the ratio/relation between their corresponding sides have to equal, so

[tex]\frac{x}{1} = \frac{9}{3} = \frac{30}{10}[/tex]

We can easily use the part x/1 = 9/3 to make a cross-multiplication that would give us:

x = (1 * 9) / 3 = 9/3 = 3

So, the green prism is a dilated version of the blue one by a dilation/scale factor of 3.

As a math teacher, I would guide you through solving the problem of finding the value of \( x \) for two similar prisms. However, without specific information about the measurements of the prisms, we can't calculate this value. Similarity in prisms implies that corresponding lengths are proportional, but without knowing these lengths or their ratios, we can't determine \( x \).
However, let's assume you have provided the dimensions for both prisms. For similar prisms, the ratio of any two corresponding linear measurements (such as the height, width, or depth) is the same. If we were given that the ratio of a pair of corresponding dimensions is 1:3, for example, then all other pairs of corresponding dimensions would also have a 1:3 ratio.
Here's a typical process to follow if you had the dimenions:
1. Determine the ratio of corresponding lengths:
Suppose for the smaller prism, a certain length is given as 'a', and for the corresponding length on the larger prism, the length is given as '3a' (implying a 1:3 ratio for the sides).
2. Apply the ratio to unknown lengths:
If 'x' is an unknown length on the larger prism and its corresponding length on the smaller prism is given as some value 'b', then we set up the proportion \( \frac{b}{x} = \frac{1}{3} \).
3. Solve for 'x':
To find 'x', you would solve the proportion by cross-multiplying and dividing as necessary, \( x = 3b \).
However, since we don't have actual numbers here, we can't follow these steps. To answer this question, I would need specific lengths for the corresponding sides of the prisms. Once provided, I can demonstrate the mathematical process to find \( x \). For now, there is not enough information to solve for \( x \), and none of the options A, B, C, or D can be verified as correct.

Answer:

The measures of the angles of the rhombus are 72° , 108° , 72° , 108°

Step-by-step explanation:

* Lets revise the properties of the rhombus

- It has 4 equal sides

- Each two opposite angles are equal

- Each two adjacent angles are supplementary (their sum = 180°)

- The diagonals are perpendicular to each other

- The diagonals bisect the vertices angles (divide each vertex into two

 equal parts)

* Now lets solve the problem

- Let the name of the rhombus is ABCD

- The two diagonals are AC and BD

- Let the diagonals AC and BD make the angles BAC and ABD with

 side AB

∵ The diagonals of the rhombus bisect the vertex angles

∴ m∠BAC is half m∠A

∴ m∠ABD is half m∠B

- There is a ratio between the measures of the angles BAC and ABD

∵ m∠BAC : m∠ABD = 6 : 9

∵ m∠A + m∠B = 180° ⇒ consecutive angles

∴ m∠BAC + m∠ABD = 1/2 × 180° = 90°

∵ m∠BAC : m∠ABD : their sum

         6     :       9      : 15⇒(6 + 9)

          ?    :        ?      : 90° ⇒(the sum of the angles)

∴ m∠BAC = 6/15 × 90° = 36°

∴ m∠ABD = 9/15 × 90° = 54°

∵ m∠BAC is half m∠A

∴ m∠A = 36° × 2 = 72°

∵ m∠ABD is half m∠B

∴ m∠B = 54° × 2 = 108°

* The measures of the angles of the rhombus are 72° , 108° , 72° , 108°

Answer:

72°, 108°, 72°, and 108°

Notes:

You should probably give the other person Brainliest, the answered first and they have a better explanation.

Answer:

[tex]4,000 ml = 4 liters[/tex]

Hope this helps!

Answer:

y=-2x+3

Step-by-step explanation:

Slope intercept form is y = mx + b where m is the slope, b is the y-intercept, and y and x are their respective coordinates.

The questions gives us a coordinate pair and a slope so all we need to find is the y-intercept to find the equation.

Begin by plugging in what we know.

(3) = (-2)(0) + b

3 = 0 + b

3 = b

Plug in the y-intercept (b) and slope (m)

y=-2x+3

Answer:

 The line x=6.

Step-by-step explanation:

The usual translations between polar and rectangular coordinates are ...

If we multiply the given equation by cos(θ), we get ...

  r·cos(θ) = 6

Using the above translation, this becomes ...

 x = 6

Answer:

The answer would be 56.

Answer:

56 will be your answer

Step-by-step explanation:

20 23 26 29 32 35 38 41 44 47 50 53 56

Please mark Brainiest.

I believe it is section 3 because it is the closest to 0.

Final answer:

The domain of f(x) = (1/6)x + 2 is all real numbers and the range is y > 2.

Explanation:

The domain of the function f(x) = (1/6)x + 2 is {x | x is a real number} because there are no restrictions on the input values. The range of the function is {y | y > 2} because any value of x will give a y-value greater than 2. To find the range, you can consider that the slope of the function is positive, meaning that as x increases, y will also increase, but it will never go below 2.

Answer:

0.15x=x-30

Step-by-step explanation:

Let

x-----> the regular price

we know that

15%=15/100=0.15

so

0.15x=30

x=30/0.15=$200

Verify each case

case a) 0.15x=30

x=30/0.15=$200

therefore

The equation could be used to determine x

case b) 0.85x=x-30

x-0.85x=30

0.15x=30

x=30/0.15=$200

therefore

The equation could be used to determine x

case c) 0.15x=x-30

x-0.15x=30

0.85x=30

x=30/0.85=$35.29

therefore

The equation could not be used to determine x

case d) x-0.15x=x-30

-0.15x=-30

0.15x=30

x=30/0.15=$200

therefore

The equation could be used to determine x

Answer:

Step-by-step explanation:

find the percentage of the people who want the store open longer. of the 40 customers that were surveyed, 12 would want that. 12 divided by 40 is .30, so 30 percent of the customers want it open.

100 more customers are surveyed, so you take 30 percent of 100, which is 30. your answer is "B"

Ask: Which two numbers add up to -12 and multiply to 32?

-8 and -4

Rewrite the expression using the above

= (y - 4)(y - 8)

Answer:

The correct answer is option B.

Step-by-step explanation:

Given quadratic equation : [tex]y^2-12y+32[/tex]

Using middle term splitting theorem:

=[tex]y^2-12y+32[/tex]

=[tex]y^2-8y-4y+32[/tex]

=[tex]y(y-8)-4(y-8)[/tex]

=[tex](y-8)(y-4)[/tex]

y = 8, 4

The factors of given quadratic equation is (y-8)(y-4).

Answer:

3. 415926535

Step-by-step explanation:

Answer:

One solution. A system of linear equations has one solution when the graphs intersect at a point.

1\small{1}

1

2\small{2}

2

3\small{3}

3

-1\small{\llap{-}1}

-

1

1\small{1}

1

2\small{2}

2

3\small{3}

3

-1\small{\llap{-}1}

-

1

yy

y

xx

x

No solution. A system of linear equations has no solution when the graphs are parallel.

1\small{1}

1

2\small{2}

2

3\small{3}

3

-1\small{\llap{-}1}

-

1

1\small{1}

1

2\small{2}

2

3\small{3}

3

-1\small{\llap{-}1}

-

1

yy

y

xx

x

Infinite solutions. A system of linear equations has infinite solutions when the graphs are the exact same line.

Step-by-step explanation:

Answer:

2π

Step-by-step explanation:

This is a little something you have to memorize, but you could derive it from the equation pb = 2π. In the parent function, the b value is 1, so the period, p, is equal to 2π/1 or just 2π.

What is the period of the parent cosine function, y = cos(x)?

360 degrees

What is the period of the cosine function shown in the graph?

1080 degrees

Which type of transformation of the parent function is shown by the graph?

horizontal stretch

A function is a relation where each input is related to exactly one output. In mapping diagrams, if an 'x' value is associated with multiple 'y' values, the relation is not a function. Make sure to check the mapping to determine this.

In mathematics, specifically in the area of functions and relations, a function is a type of relation where each input (or 'x' value) is related to exactly one output (or 'y' value). If a relation has an 'x' value that is associated with more than one 'y' value, we say that this relation is not a function. When examining mapping diagrams, you can tell if it's a function or not by checking this rule.

For example, if you have a mapping diagram where the number 1 (the 'x' value) is mapped to both 2 and 3 (the 'y' values), this would not be a function because one input is associated with more than one output. On the other hand, if you have a mapping where every 'x' value is mapped to one 'y' value, such as 1 to 2, 2 to 3 and 3 to 4, this is a function.

https://brainly.com/question/2253924

#SPJ12

Answer:

91

Step-by-step explanation:

The lines that are parallel are parallel and because of that 89+91=180 for two angles of the square on the same side.

Answer:

[tex]5.x=5x\\x^{2} =4, x=2\\x=2[/tex]

Step-by-step explanation:

hope its right

Answer:

The plane would have been going the amount as it supposed to g.

Step-by-step explanation:

The plane flying against the wind is going 90 mph and the plane flying with the wind is traveling at 130 mph. Your welcome

Answer:

Step-by-step explanation:

Here y = -x^2 + 36.

We can choose x values pretty much at random and then calculate the associated y values:

x    y = -x^2 + 36

----  --------------------

0                      36

2                 -2^2 + 36 =  32

-2                  -4 + 36 = 32

3                  -9 + 36 = 27

You did not share the equation of the slanted line.  Let's assume that the equation of this line is y = mx + b.  The first two points in the table above are (0, 36) and (2, 32).  We could find the equation of this line as follows:

Slope:  as we move from (0, 36) to (2, 32), x increases by 2 and y decreases by 4.  Thus, the slope is m = rise / run = -4/2, or -2.  Using info from the point (0, 36), we find the y-intercept of this straight line:

y = mx + b becomes 36 = m(0) + b, so b = 36, and the line is y = -2x + 36.

We need to find the points of intersection of y = -2x + 36 and y = -x^2 + 36.  We can equate these equations to eliminate y:  -2x + 36 = -x^2 + 36, or

-2x = -x^2.  Equivalently, 2x - x^2 = 0, or (x)(2 - x) = 0.  Then x = 0 and x = 2.

This says that the line and the parabola intersect in at least two places:

(0, 36) and (2, 32).

Answer:

Observational study, survey, experiment

Step-by-step explanation:

The first is an observational study.  The children make the choices and the choices are observed.

The second one is a survey.  The employees are given questionnaires to answer.

The third one is an experiment.  The nurse selects random samples to compare the effects of different ointments.

Answer:

48

Step-by-step explanation:

central angle with arc of <y is 96

so circumference angle 48

Answer:

y = 48°

Step-by-step explanation:

The angle on the circle ( the inscribed angle ) y is half of the central angle subtended by the same arc on the circle, hence

y = 0.5 × 96° = 48°

Answer:

i believe Tonya will be at least 26 years old or 34 years old.

Step-by-step explanation:

17+17=34

Answer:

x= 36.2

Step-by-step explanation:

Because that's a right triangle and the reference angle and adjacent side measures are given to us, we can use the trig ratio for cosine.  Cosine relates the side adjacent to (next to...NOT ever the hypotenuse!) the angle to the hypotenuse.  Therefore, our equation will look like this:

[tex]cos(28)=\frac{32}{x}[/tex]

Solving for x we have

[tex]x=\frac{32}{cos(28)}[/tex]

Perform that operation on your calculator in degree mode and you'll get that the length of the hypotenuse is 36.2.  If for some reason, your math gave you the length of the hypotenuse and it was shorter than one of the other sides, you did something wrong.  The hypotenuse will ALWAYS be the longest side in a right triangle.

Answer:

The area of the scale drawing is [tex]67.5\ cm^{2}[/tex]

Step-by-step explanation:

The scale drawing is

[tex](1\frac{1}{2})/2\ \frac{cm}{ft}[/tex]

Convert to an improper fraction

[tex](1\frac{1}{2})=3/2[/tex]

substitute

[tex](1\frac{1}{2})/2=(3/4)=0.75\ \frac{cm}{ft}[/tex]

The area is equal to

[tex]120\ ft^{2}[/tex]

substitute

[tex]120*(0.75)^{2}=67.5\ cm^{2}[/tex]

The area of the scale drawing of Charlene's swimming pool is [tex]\( 67.5} \)[/tex] square feet.

To find the area of the scale drawing of Charlene's swimming pool, we need to understand the scale given and how it applies to the dimensions and area.

Given:

Actual area of the swimming pool: [tex]\( 120 \) ft\(^2\)[/tex]

Scale of the drawing: [tex]\( 1 \frac{1}{2} \) centimeters = 2 feet[/tex]

First, convert the scale to centimeters:

[tex]\[ 1 \frac{1}{2} \text{ centimeters} = 1.5 \text{ centimeters} \][/tex]

Now, determine the scale factor for the dimensions:

[tex]\[ \text{Scale factor} = \frac{1.5 \text{ cm}}{2 \text{ ft}} \][/tex]

To find the area of the scale drawing, we need to square the scale factor, because area is two-dimensional:

[tex]\[ \text{Area scale factor} = \left(\frac{1.5}{2}\right)^2 \][/tex]

[tex]\[ \text{Area scale factor} = \left(0.75\right)^2 \][/tex]

[tex]\[ \text{Area scale factor} = 0.5625 \][/tex]

Now, calculate the area of the scale drawing:

[tex]\[ \text{Area of scale drawing} = 0.5625 \times 120 \text{ ft}^2 \][/tex]

[tex]\[ \text{Area of scale drawing} = 67.5 \text{ ft}^2 \][/tex]

Answer:

Step-by-step explanation:

1000 = 10³ is a perfect cube.

27r^21 can be re-written as (3r^7)³ and is a perfect cube.

343p can be rewritten as (7)³·∛p.  (7)³ is a perfect cube, but ∛p is not.

g³h^30 can be rewritten as (g·h^10)³ and is a perfect cube.

1 is a perfect cube:  1³ = 1

Answer:

A, B, D, E

Step-by-step explanation:

A = 1,000

B = [tex]27r^{21}[/tex]

D= [tex]g^{3}h^{30}[/tex]

E = 1

(just took it on edge)