Mathematics High School

Determine if the graph is symmetric about the x-axis, the y-axis, or the origin.

r = 5 + 4 cos θ

Answers

Answer 1

Explaining how to determine the symmetry of a polar graph based on the given equation r = 5 + 4 cos θ.

To determine the symmetry of the graph r = 5 + 4 cos θ, we can substitute (-θ) for θ in the equation and check if the resulting polar equation remains the same, indicating symmetry about the origin.

If replacing (-θ) gives us the same equation, the graph is symmetric about the y-axis. If replacing (π - θ) gives the same equation, then the graph is symmetric about the x-axis.

In this case, replacing (-θ) in r = 5 + 4 cos θ gives r = 5 + 4 cos(-θ), which simplifies to r = 5 + 4 cos θ, indicating symmetry about the y-axis.

Related Questions

What is the slip of the line given by the equation y=-1/3 x

Answers

the slip?  I don't think it has any slip, but as far as the slope goes, well, the equation is in slope-intercept form, thus

[tex]\bf y=\stackrel{slope}{-\cfrac{1}{3}}x~~\stackrel{y-intercept}{+0}[/tex]

Factor the trinomial below.

9x2 + 6x + 1

A. (3x + 1)(3x – 1)
B. (9x + 1)(x – 1)
C. (9x + 1)(x + 1)
D. (3x + 1)(3x + 1)

Answers

Answer: D. (3x + 1)(3x+1)

Step-by-step explanation:

9x² + 6x + 1

find two factor of 9 such that its product gives 9 and its sum gives 6 (3 and 3, 3×3 = 9 , also 3+ 3=6)

we are going to replace 6x by 3x + 3x

9x² + 6x + 1

9x² + 3x +3x + 1

3x(3x + 1) + 1(3x+ 1)

(3x + 1)(3x+1)

The correct factorization of the trinomial 9x² + 6x + 1 is (3x + 1)(3x + 1) or (3x + 1)². option D.

How do we identify the correct option when the trinomial is factorized?

The trinomial 9x² + 6x + 1 is a perfect square trinomial, which can be factored as the square of a binomial.

Let's find the correct answer from your options:

(A) (3x + 1)(3x - 1): The difference of squares isn't the correct form for our trinomial.

(B) (9x + 1)(x - 1): Expanding this will not give us the original trinomial.

(C) (9x + 1)(x + 1): Expanding this will not give us the original trinomial.

(D) (3x + 1)(3x + 1): When expanded, this gives us 9x^2 + 3x + 3x + 1, which simplifies to 9x² + 6x + 1.

Therefore option D (3x + 1)(3x + 1) is correct

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Multiply: (2x2 − 5x)(4x2 − 12x + 10)

Answers


The answer is 60x^2 - 138x + 72

Hope this helps!

Answer:

[tex]8x^4-44x^3+80x^2-50x[/tex]

Step-by-step explanation:

The given expression is

[tex](2x^2-5x)(4x^2-12x+10)[/tex]

Using distributive property we get

[tex]2x^2(4x^2-12x+10)-5x(4x^2-12x+10)[/tex]

[tex]2x^2(4x^2)+2x^2(-12x)+2x^2(10)-5x(4x^2)-5x(-12x)-5x(10)[/tex]

On simplification we get

[tex]8x^4-24x^3+20x^2-20x^3+60x^2-50x[/tex]

On combine like terms.

[tex]8x^4+(-24x^3-20x^3)+(20x^2+60x^2)-50x[/tex]

[tex]8x^4-44x^3+80x^2-50x[/tex]

Therefore the product of two polynomials is [tex]8x^4-44x^3+80x^2-50x[/tex].

Which of the following is an undefined term?
Angle
Circle
Plane
Ray

Answers

I think it would be C.plane... I had this question a while ago and I think its right... plz tell me if I am wrong. Thanks.

Answer:

Plane is an undefined plane

Step-by-step explanation:

Hi, there are three undefined terms in geometry: point, line, and plane.

Point: has no size, only location . It can be named with a capital letter.

Plane: a flat surface that has no thickness, that extends infinitely n every direction.  Is named  by a single letter or by three coplanar, but non-collinear, points.

Line: Set of points extending in either direction infinitely.

Angle, circle, and ray are not undefined terms.  are not Plane.

Please help me, if you'd be so kind.

A right rectangular prism is shown.

What is the length of DH¯¯¯¯¯¯ to the nearest tenth of an inch?

Drag and drop the answer into the box.

Answers

[tex]\overline{DH}=\sqrt{3^2+1.5^2+1^2}=\sqrt{9+2.25+1}=\sqrt{12.25}=\boxed{3.5}[/tex]

which transformation can verify congruence by flipping a triangle over the y-axis?

A. Dilation
B. Translation
C. Reflection
D. Rotation

Answers

Reflection. Reflection is when you flip an object over an axis. Flipping the triangle over axis wouldn't change the triangles properties.

Answer:  C.  Reflection

Step-by-step explanation:

There are three rigid transformations which create congruent figures :  

a)reflections, b) rotations, c) translations

A reflection is a transformation that flips a figure on the coordinate plane across a given line without changing the shape or size of the figure.

A translation moves a shapes by a particular distance.

A rotation rotates a shape around a fix point by an angle .

Therefore, the transformation can verify congruence by flipping a triangle over the y-axis is reflection.

HELP!!!!!!What is the equation of the graph below?

Answers

The answer to your question is y = sin(x + 90) as we have a sine graph phase shifted 90 units left

In this triangle, side AT = 24. Please give the value for the sine, cosine, and tangent for this diagram (Which is the marked angle?). Give the value as a ratio ONLY. Make sure all ratios are in the lowest form.

Be sure to explain IN WRITING how you find sine, cosine, and tangent! If you are not sure, check the directions in this problem!

Question 1 options:

Answers

The value  of the sine, cosine and tangent of the figure will be found as follows:
a] Sine
sin x=(opposite)/(hypotenuse)
opposite=7
hypotenuse=25
thus:
sin x=  7/25  

 b] Cosine
cos x=adjacent/hypotensue
adjacent=24
hypotenuse=25
cos x=24/25

Tangent
Tan x=opposite/adajcent
opposite=7
adjacent=24
thus
tan x=7/24

Find the surface area of the cylinder in terms of π.

See picture

a) 1008π in.2

b) 522π in.2

c) 360π in.2

d) 396π in.2

Answers

[tex]\bf \textit{total surface area of a cylinder}\\\\ SA=2\pi r(h+r)~~ \begin{cases} r=radius\\ h=height\\ -----\\ r=9\\ h=20 \end{cases}\implies SA=2\pi (9)(20+9) \\\\\\ SA=18\pi (29)\implies SA=522\pi [/tex]

what is the sum of the geometric series E (-2)(-3)^n-1

Answers

Sum of the geometric series: S=?
S=(-2)(-3)^(1-1)+(-2)(-3)^(2-1)+(-2)(-3)^(3-1)+(-2)(-3)^(4-1)
S=(-2)[(-3)^0+(-3)^1+(-3)^2+(-3)^3]
S=(-2)[1+(-3)+9+(-27)]
S=(-2)(1-3+9-27)
S=(-2)(-20)
S=40

Answer: Third option 40

Answer:

The sum is 40.

Step-by-step explanation:

Given,

[tex]\sum_{n=1}^{4} (-2)(-3)^{n-1}[/tex]

We know that,

[tex]\sum_{n=1}^{4} (-2)(-3)^{n-1}=(-2)(-3)^{1-1}+(-2)(-3)^{2-1}+(-2)(-3)^{3-1}+(-2)(-3)^{4-1}[/tex]

[tex]=(-2)(-3)^{0}+(-2)(-3)^1+(-2)(-3)^2+(-2)(-3)^3[/tex]

[tex]=-2\times 1 - 2\times - 3 - 2\times 9-2\times -27[/tex]

[tex]=-2+6-18+54[/tex]

[tex]=40[/tex]

Hence,

[tex]\sum_{n=1}^{4} (-2)(-3)^{n-1}=40[/tex]

Which of the following types of equations have you learned to solve using algebraic methods?
[]Quadratic[]Exponential[]Radical[]Linear[]Rational

Answers

The following types of equations have you learned to solve using algebraic methods is Linear.

Quadratic equations involve a variable raised to the power of 2, and algebraic methods like factoring or using the quadratic formula are used for solving.

Exponential equations involve variables in the exponent, and logarithmic methods are employed to solve them.

Radical equations involve roots, and solving them often involves isolating the radical and squaring both sides or other methods based on the root's degree.

Linear equations involve variables raised to the power of 1, and solving them uses standard algebraic techniques like isolating the variable.

Rational equations involve ratios of polynomials and are solved by methods such as clearing denominators and factoring.

There are five red marbles eight blue marbles and 12 Green marbles in a bag. What is the theoretical probability of randomly drawing a red marble and then a green marble

Answers

you do add den you get30

I really need help

What is the equation of a circle with its center at(10,−4) and a radius of 4?

(x−10)2+(y+4)2=4

(x+10)2+(y−4)2=16

(x−10)2+(y+4)2=16

(x+10)2+(y−4)2=2

(x−10)2+(y+4)2=2

(x−10)2+(y+4)2=8

(x+10)2+(y−4)2=8

(x+10)2+(y−4)2=4

Answers

The answer should be
(x-10)²+(y+4)²=16


The equation of any circle is
(x – h)² + (y – k)² = r²

(h,k) is the center point and r is the radius

What is the value of b?

Answers

Look at the picture.

d° + c° = 2 · 68° = 136°

b° = 360° - (136° + 104°) = 360° - 240° = 120°

Circle J has center J (4,-3) and radius 5 What is the measure, in degrees, of the arc with endpoints A (9,-3) and B (4,2)?
Explain the process you used (in words) and include the work you did to find this answer.

Answers

This would be a 90° arc.

To find this, we can find the measure of the central angle that intercepts the arc.

The endpoints of the arc are at (9, -3) and (4, 2).
The slope of the line that passes through the endpoint (9, -3) and the center (4, -3) is given by 
m=(-3--3)/(9-4) = 0/5 = 0.

Since the slope is 0, this tells us it is a horizontal line.

The line that passes through the endpoint (4, 2) and the center (4, -3) has a slope that is undefined; it is a vertical line at x=4.  Numerically the slope is given by 
m=(2--3)/(4-4) = 5/0, which is undefined.

These slopes are negative reciprocals of one another; 5/0 and 0/5 (0 has no sign).  This means that these two lines would form a right angle, so the central angle of the circle is a right angle.  

The intercepted arc has a measure equal to that of the central angle, so the arc is also 90°.

The unt informs club has 16 members. they need to elect a president, a vice president, a secretary and a treasurer. how many different ways can this group of 4 officers be formed? (order is important)

Answers

If they needed to elect just the president there could be 16 possible combination. If they needed to elect the president and the vice there could be 16×15 possible combination, because each president could have 15 possible vice. So the possible combination are 16×15×14×13=43 680.

Hope this helped!

Help needed soon. please

Answers

For this case we first define variables:
 x = daisies flowers
 y = roses flowers
 We write the system of equations:
 x + 2y = 33
 x = y + 3
 Solving the system we have:
 x = 13
 y = 10
 Therefore, the cost of roses is:
 2 * y = 2 * 10 = 20 $
 Answer:
 Roses = $ 20

Solve each of the following right triangles. Round angle measures to the nearest degree and segment lengths to the nearest tenth. Angle C is the right angle of the triangle

Answers

6. C=67
AC=23.
BA=55.2

The frequency of F3 is 174.61 Hz. What is the frequency of the note that is a perfect fifth below f3?
A) 43.6525 Hz
B) 87.305 Hz
C) 116.407 Hz
D) 261.915 Hz

Answers

Notes separated by a perfect 5th have a frequency ratio of 3:2. The note a perfect 5th below f3 will have a frequency of
  174.61 Hz × 2/3 = 116.407 Hz

The appropriate choice is ...
  C) 116.407 Hz

Suppose that a small town has seven burger shops whose respective shares of the local hamburger market are (as percent- ages of all hamburgers sold): 23 percent, 22 percent, 18 percent, 12 percent, 11 percent, 8 percent, and 6 percent. what is the four-firm concentration ratio of the hamburger industry in this town

Answers

SSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSS

what is the value of the expression?

Answers

To solve this we are going to use the unitary circle and the fact that [tex]tan \alpha = \frac{sin \alpha }{cos \alpha } [/tex]

From our circle we can infer that [tex]sin\frac{5 \pi }{3}= \frac{- \sqrt{3} }{2} [/tex] and [tex]cos\frac{5 \pi }{3}= \frac{1}{2} [/tex].

Since [tex]tan \alpha = \frac{sin \alpha }{cos \alpha } [/tex], [tex]tan\frac{5 \pi }{3}= \frac{\frac{- \sqrt{3} }{2}}{\frac{1}{2} } [/tex]
[tex]tan\frac{5 \pi }{3}=- \sqrt{3} [/tex]

We can conclude that [tex]tan\frac{5 \pi }{3}=- \sqrt{3} [/tex].

A license plate has 3 letters and 3 digits in that order. a witness to a hit-and-run accident saw the first 2 letters and the last digit. if the letters and digits can be repeated, how many license plates must be checked by the police to find the culprit?

Answers

26×10×10=2600

Hope this helped!

The police must check 2600 possible license plates, calculated by multiplying 26 possibilities for the third letter not seen by the witness with 100 possibilities for the two digits also not seen.

To determine how many license plates the police must check to find the culprit, we consider the information that the witness saw the first two letters and the last digit. Since letters can be repeated, there are 26 possibilities for each of the two letters the witness saw. For the last digit, which the witness also saw, there are 10 possibilities (0 through 9). The third letter and the other two digits, which the witness did not see, each have the following number of possibilities: 26 for the third letter, and 10 for each of the two remaining digits.

Calculating the number of possible combinations:

First two letters (seen by the witness): 26 * 26 = 676 possibilitiesLast digit (seen by the witness): 10 possibilitiesThird letter (not seen by the witness): 26 possibilitiesThe two remaining digits (not seen by the witness): 10 * 10 = 100 possibilities

Therefore, the total number of license plates the police must check is the product of the possibilities for the parts the witness did not see:

26 (third letter) * 100 (two remaining digits) = 2600 possible license plates.

Tina can paint a room 1.5 times faster than Joey can. If they work together, they can paint a room in 6 hours. How long would it take the slower person working alone to paint the room?

Answers

So, the rate is 1 job / hours, so:
1/n + 1/1.5n = 1/6
We'll make the denominator 3n:
3/3n + 2/3n = 1/6
5/3n = 1/6
Cross multiply:
3n = 30
n = 10
It will take the slower person 10 hours to complete the room.

How many arrangements are possible using the letters in the word fuzzy if each letter "z" is distinctly different than the other? how many arrangements are possible if the letter "z" is interchangeable with the other? explain your reasoning?

Answers

If the letter z's are distinctly different, there are P(5,5) arrangements. That is 
    [tex]P\left(5,5\right)=5!=5\cdot 4\cdot 3\cdot 2\cdot 1=120[/tex]

If the z's are interchangeable, the number of different arrangements is given by 
     [tex]\frac{5!}{2!}=5\cdot 4\cdot 3=60[/tex]

When each letter "z" is distinctly different, there are 60 possible arrangements.
When the letter "z" is interchangeable with the others, there are 24 possible arrangements.

1. When each letter "z" is distinctly different from the others:
- The word "fuzzy" has 5 letters in total, including 2 "z" letters.
- To calculate the number of arrangements, we use the formula for permutations with repeated elements:
- The formula is: n! / (n1! n2! ... * nk!)
- n is the total number of letters in the word (5 in this case).
- n1, n2, ... are the number of repetitions of each distinct letter.
- Calculating: 5! / (1! 2! 1! * 1!) = 120 / 2 = 60 arrangements.

2. When the letter "z" is interchangeable with the other letters:
- In this case, there are 4 distinct letters in the word "fuzzy" (f, u, z, y).
- The total number of arrangements can be calculated using the formula for permutations of distinct items.
- Calculating: 4! = 24 arrangements.
In summary:
- When each letter "z" is distinctly different, there are 60 possible arrangements.
- When the letter "z" is interchangeable with the others, there are 24 possible arrangements.

Compute the stock turnover in dollars for a product that has sales of $6,000 and an average value of inventory investment of $1,500.

Answers

Question: It should be inventory turnover.

Solution:
Inventory turnover = Cost of goods sold/Average inventory

Substituting the values given for cost of goods and average inventory;
 Inventory turnover = 6,000/1,500 = 4

Answer: 4

Step-by-step explanation:

Given: Cost of product sold = $6,000

Average value of inventory= $1,500

We know that the inventory turnover formula is given by :-

[tex]\text{Inventory turnover}=\frac{\text{ Cost of product sold}}{\text{Average value of inventory}}[/tex]

[tex]\\\Rightarrow\ \text{Inventory turnover}=\frac{\$6,000 }{\$1500}\\\\\Rightarrow\ \text{Inventory turnover}=4[/tex]

Therefore, the stock turnover for a product that has sales of $6,000 and an average value of inventory investment of $1,500 = 4

WILL GIVE BRAINLIEST PLZ HURRY!!!!!!!!Woodland High School recently won the state Academic Bowl Championship. The medal counts for the 7 members of the team are listed in the table. Which statement is true about the data shown in the table?
A) The range is less than the mode.
B) The mode is greater than the median.
C) The mean is greater than the median.
D) The median is greater than the mode.

Answers

Answer: B = The range is greater than the mean.

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

The mean is greater than the median

Calculate the total cost of the order: Veggiburger with cola and soup, sales tax 4%, tip 15.

Veggiburger: $3.25
Cola: $1.50
Soup: $2.25

A $8.33
B $7.28
C $7.00
D $5.50

Answers

Add the prices of the food together to get $7. Then you calculate the sales tax, which is 1.04 * $7 = $7.28. The tip is 15% I am assuming, and not 15, so it would be $7 * 0.15 = $1.05. Add $1.05 with $7.28 to get $8.33, so the answer is A.
Final answer:

The cost of the order, including the sales tax of 4%, comes out to be $7.28. However, the tip is unclear in the question. If it's 15%, the cost rises to $8.37, but none of the provided options match this result.

Explanation:

The first step is to calculate the total cost of the Veggiburger, cola, and soup by adding them together. So, $3.25 (Veggiburger) + $1.50 (cola) + $2.25 (soup) = $7.00. Next, apply the 4% sales tax on this amount which is $7.00 * 4/100 = $0.28. So the subtotal now is $7.28 ($7.00 + $0.28). Finally, the tip mentioned in the problem is not clear whether it is a percentage or a fixed amount. If it is a 15% tip, then calculate 15% of the subtotal, i.e $7.28 * 15/100 = $1.09 (Approx). Adding this to the subtotal we get $8.37 which is not an option in the given answers. If $15 is a fixed tip amount, the total cost would be substantially larger. Please ensure the tip amount is correct.

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Four golf balls are packaged in a cylindrical container as shown below. The balls just touch the top, bottom, and sides of the cylinder. The diameter of each ball is 4cm.

What is the volume of the cylinder rounded to the nearest cubic centimeter?

What is the total volume of the four balls rounded to the nearest cubic centimeter?

What percent of the volume of the container is occupied by the four balls?

Answers

Hello,
Please, see the attached files.
Thanks. 

A train travels at a constant speed. What is the train's speed between checkpoints, expressed as a unit rate? Use the information given in the picture to help you.

Answers

Remember that the speed is the rate of change of the position with respect to time, so to solve this we are going to use the kinematic equation: [tex]S= \frac{d_{f}-d_{i}}{t_{f}-t_{i}} [/tex]
where 
[tex]S[/tex] is the speed of the train
[tex]d_{i}[/tex] is the initial distance
[tex]d_{f}[/tex] is the final distance 
[tex]t_{i}[/tex] is the initial time 
[tex]t_{f}[/tex] is the final time 

Since checkpoint A is the initial checkpoint, we can infer that [tex]d_{i}=105[/tex] and [tex]t_{i}=2[/tex]. Similarly, since checkpoint B is the final checkpoint, we can infer that [tex]d_{f}=285[/tex] and [tex]t_{f}=5[/tex]. Lets replace the values in our kinematic euation:
[tex]S= \frac{d_{f}-d_{i}}{t_{f}-t_{i}} [/tex]
[tex]S= \frac{285-105}{5-2} [/tex]
[tex]S= \frac{180}{3} [/tex]
[tex]S=60[/tex] mph

We can conclude that the train's speed between checkpoints is 60 mph.
the checkpoints is 60 mph if you have any questions just ask:)

If 7 is subtracted from the product of 3 and a number, the result is 5 more than the number.

Answers

If you subtract 3-7 and add 9 to it the result is 5. 3-7+9=5
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What is the preposition in this sentence After the movie, we will grab a pizza to take home? Which value of h makes 10/8+h=9/3-2 a true statement? The major division of the nervous system that make up the brain and spinal cord is called: Which of the following best illustrates the concept of total war in World War I?A. Artillery shells caused high casualty rates along the Western Front.b. Millions of young men volunteered to serve when war was declared.c. Propaganda campaigns encouraged people to grow their own food.d.The alliance system drew almost every major European power into the war.Please help me! I am struggling. I am not good with history:( What is the complete factorization of r2 - 6r - 9s2 + 9? A) (r - 3 + 3s)(r - 3 - 3s) B) (r + 3 + 3s)(r - 3 - 3s) C) (r - 3 + 3s)(r - 3 + 3s) chose the pair of words that is the correct analogy for the following depreciate : reduce :a.condone : agree b. discern : misunderstand c acquiesce : violent How does the structure of paragraph 2 help the writer make an effective argument What do you need to clean a knight,s armor? 1. Who was the power to begin the impeachment process against a U.S. official?A- any state governor B- Supreme CourtC- SenateD- House of RepresentativesPLEASE HELP!!!! China was to have received the shandong province from Germany following world war 1. Which nation did the treaty of Versailles give it to instead cheryl went on a 3-hour train traveled at an average speed of 75 miles per hour.what was the total distance in miles that cheryl traveled? If the diameter of a penny is 19.05 millimeters and the width of each penny is 1.52 millimeters, what is the approximate volume of the roll of pennies? Use 3.14 for and round your answer to the nearest tenth. The function f(x) is given by the set of ordered pairs. {(1,0), (-10,2), (0,6), (3,17), (-2,-1)} which equation is true? f(-10)=1f(2)=-10f(0)=6f(1)=-10 Some chemical reactions can proceed in just one direction . True or False ? one number is 2 larger than another number. the sum of their squares is 100. find the numbers what does 1/2x+30=55 equals? Before world war one, people in western europe and the united states expected the conflict to be ____________ g Use unit multipliers to convert 123 pounds per mile to ounces per centimeter. There are 5,280 feet in 1 mile. There are 16 ounces in 1 pound. There are approximately 2.54 cm in 1 inch. Enter your answer as a decimal rounded to the nearest hundredth. Just enter the number. Which sentence is the best example of personification? A."Watch out!" Walter cried, waving his arms frantically. B.The pines shed their needles and seemed to shiver in the cold. C.In the 105-degree weather, the city became a vast microwave oven. D.The lazy cats lay like discarded laundry on the thick rug. What about uranium room temperature is it "SOLID LIQUID or GAS)?