Transform each polar equation to an equation in rectangular coordinates and identify its shape.
(a) r=6
(b) r= 2 cos theta

please show ur work

Supplementary angles are angles that add up to 180 degrees, aka one straight line. The supplementary angles here are:

1 and 2, 1 and 3, 2 and 4, 3 and 4, 5 and 6, 6 and 8, 7 and 8, and 6 and 7. Well, those are the more obvious ones. 1 and 7 are supplementary because if you envision them next to each other, you’ll see that they create a straight line. So, with that logic, 3 and 5 are supplementary because when you put them together, they create a straight line

Angle ∠5 and angle ∠3 are supplementary angles. Then the correct option is C.

The angle is the distance between the intersecting lines or surfaces. The angle is also expressed in degrees. The angle is 360 degrees for one complete spin.

Supplementary angle - Two angles are said to be supplementary angles if their sum is 180 degrees.

Linear angle - If the total of two angles is 180 degrees, they are said to be linear angles.

From the figure, the supplementary are given below.

The angles ∠1 and ∠2, ∠3 and ∠4, ∠5 and ∠6, ∠7 and ∠8, ∠1 and ∠3, ∠2 and ∠4, ∠5 and ∠7, and ∠6 and ∠8 are supplementary angles.

The sum of angle ∠5 and angle ∠3 is 180 degrees.

Then Angle ∠5 and angle ∠3 are supplementary angles.

Then the correct option is C.

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Answer:

$8.80

Step-by-step explanation:

In order to find the new price, you need to add 60% of the original price (5.50) to the original price. You have two options:

1) multiply $5.50*0.6 to get 60% of the original price. You would get $3.30. Then add $3.30+$5.50, which equals $8.80. This way takes longer but shows you all the steps.

2) The shorter way is to simply multiply $5.50*1.6, which also equals $8.80. This works because the "1" automatically adds the 5.50 to 60% of the original price, this way you don't have to multiply then add.

If you don't understand how the second way works or your teacher taught you #1, just do it the first way.

Final answer:

To find the new price after a 60% markup, you need to calculate 60% of the original price and then add it to the original price.

Explanation:

To find the new price after a 60% markup, you need to calculate 60% of the original price and then add it to the original price.

Step 1: Calculate 60% of $5.50. 60% is equivalent to 0.60, so multiply 0.60 by $5.50 to get $3.30.

Step 2: Add $3.30 to $5.50 to find the new price. $3.30 + $5.50 = $8.80.

Therefore, the new price of the item after the 60% markup is $8.80.

Let the number of marbles Tim has = X

Then Sue has twice as many, so she has 2X

Jim has 15.

All three of them when added together have 63:

x + 2x + 15 = 63

Combine like terms:

3x +15 = 63

Subtract 15 from both sides:

3x = 48

Divide both sides by 3:

X = 48 /3

x = 16

Tim has 16 marbles.

Answer: 5 cm

Step-by-step explanation: If you liked this answer check out my channel Saltygum and subscribe

Answer:

12-3+(2.7x2)-7

Step-by-step explanation:

you would have to divide each number in the equation by 3 which would look like this:

36 / 3 = 12

-9 / 3 = -3

8 / 3 = 2.6666 repeating, which would be rounded up to 2.7

6 / 3 = 2

-21 / 3 = -7

i hope this helps :)

Answer:

18

Step-by-step explanation:

using Pemdas

you would do the parentheses first

in the parentheses theres parentheses so 8*6 is 48

then do the rest of the parentheses so 36-9+48-21 which equals 54

then lastly divide by 3

which equals 18

Answer:

A. 72

Step-by-step explanation:

Answer:

72fl

Step-by-step

Answer:50%

Step-by-step explanation:

Whenever you are trying to find the percentage  Use this euation for exmaple based off your question it would be

22*100/44

Answer:

If the coin is fair, then the chances of you getting heads is equal to the chances of getting heads. This means the chances of always getting tails on a  fair coin is close to nothing, if not 0.

Step-by-step explanation:

Answer:

The answer is unlikely

Step-by-step explanation:

oof did u ever find out the answer...

Answer:

The scatter plot that represents the data that is shown in the table is attached below.

Step-by-step explanation:

The given table represents the balance of bank account at the beginning of the past week was and how much it increased or decreased by the end of the past week.

In the scatter plot, x-axis represents the beginning balance in thousands of dollars and the y-axis represents the change in the bank account in hundreds of dollars.

From the table, it is clear that the points of scatter plot are (4,7), (7,5), (2,3), (3,4), (1,6), (5,3), (6,1) and (4,2).

Therefore the scatter plot that represents the data that is shown in the table is attached below.

For this case we must find the inverse of the following function:

[tex]f (x) = x ^ 2-1[/tex]

For them we follow the steps:

We change f (x) to y:

[tex]y = x ^ 2-1[/tex]

We exchange variables:

[tex]x = y ^ 2-1[/tex]

We solve for "y":

[tex]y ^ 2-1 = x[/tex]

We add 1 to both sides of the equation:

[tex]y ^ 2 = x + 1[/tex]

We apply square root to eliminate the exponent:

[tex]y = \pm \sqrt {x + 1}[/tex]

We change y by [tex]f ^ {- 1} (x)[/tex]:

[tex]f ^ {- 1} (x) =\pm \sqrt {x + 1}[/tex]

Answer:

Option D

Answer:

6,000

Step-by-step explanation:

every number 5 and over, you round it one number up. if youre rounding the thousands place, look at the hundreds place. if its 5 or over you round the thousands number up one then add the zeros.

Answer:

[tex]-x^5+3x^4+16x^3+7x^2-3x+6[/tex]

Step-by-step explanation:

Given polynomials are:

[tex]x^5-4x^4+7x^3+8[/tex], [tex]9x^3+7x^2-10[/tex] and [tex]-2x^5+7x^4-3x+8[/tex]

Now we need to add the given polynomials, then place the answer in the proper location on the grid. Also we need to write answer in descending powers of x.

So let's add them by combining like terms:

[tex]x^5-4x^4+7x^3+8+9x^3+7x^2-10-2x^5+7x^4-3x+8[/tex]

[tex]-x^5+3x^4+16x^3+7x^2-3x+6[/tex]

Hence final answer in descending order is [tex]-x^5+3x^4+16x^3+7x^2-3x+6[/tex]

The answer is 2/5. (or 0.4 if you need a decimal answer.)

For this case we have that by definition, the slope of a line is given by:

[tex]m = \frac {y_ {2} -y_ {1}} {x_ {2} -x_ {1}}[/tex]

We must find two points through which the line passes:

[tex](x_ {1}, y_ {1}) :( 2,3)\\(x_ {2}, y_ {2}}: (- 3,1)[/tex]

Substituting:

[tex]m = \frac {1-3} {- 3-2} = \frac {-2} {- 5} = \frac {2} {5}[/tex]

Answer:

[tex]m = \frac {2} {5}[/tex]

Answer:

30 degrees

Step-by-step explanation:

P+Q+R=180

80+70+Q=180

Q=30

PQR = angle Q

Answer:30 degrees!!

Step-by-step explanation:

happy Friday! :) hope this helps!

Answer:

4$ for large 3$ for a small

Step-by-step explanation:

Answer:

(A) cost of one large popcorn is $4.

(B) cost of one small drink is $3.

Step-by-step explanation:

Given information:

Let the cost one of large popcorn [tex]=P[/tex]

And the cost of one small drink [tex]= D[/tex]

Now according to the given information the equations that can be formed are:

[tex]2P+4D=20\\2P+2D=14\\[/tex]

Now solving the above equation by elimination method:

[tex]4D-2D=20-14\\2D=6\\D=3[/tex]

So, the cost of one small drink is $3

Now, find the cost of one large popcorn is;

[tex]2P+4 \times 3=20\\2P=20-12\\P=4[/tex]

So, the cost of one large popcorn is $4

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the answers 11/6 which can't be reduced

45 miles in one hour. You take the total of 315 and divide that by the 7 hours and that gives you how much is in the one hours

Answer:

45 MPH

Step-by-step explanation:

To find the unit rate - divide the total miles driven by the total number of hours

315/7 = 45 miles per hour

Answer:

Pretty sure its Quadratic

Step-by-step explanation:

Linear, needs to be in a straight line.

Quadratic, involving the second and no higher power of an unknown quantity or variable.

Exponential, (of an increase) becoming more and more rapid.

Answer:

He will cover 120 miles.

Step-by-step explanation:

K so provided is a picture of my work. I drew a unit rate table thing. Then off the side i calculated how fast he would need to go in 1 hour. So i could add it correctly. I hope this makes sense, if it doesnt just ask me lol

Answer:

Step-by-step explanation:

Alright, lets get started.

Suppose the distance to the park is d.

Suppose the speed is s.

Adam takes 4 hours to drive to park.

Applying speed, time , distance formula

[tex]time=\frac{distance}{speed}[/tex]

[tex]4=\frac{d}{s}[/tex]

[tex]s=\frac{d}{4}[/tex] .......................... equation 1

If the speed is 45 faster, time is 2.5 times less, means

[tex]\frac{4}{2.5}=\frac{d}{s+45}[/tex]

[tex]1.6=\frac{d}{s+45}[/tex]

Cross multiply

[tex]1.6(s+45)=d[/tex]

Plugging the value of s from equation 1

[tex]1.6(\frac{d}{4}+45)=d[/tex]

[tex]1.6*\frac{d}{4}+1.6*45=d[/tex]

[tex]0.4d+72=d[/tex]

[tex]0.6d=72[/tex]

[tex]d=\frac{72}{0.6}[/tex]

[tex]d=120[/tex]

So the distance is 120 miles.  :   Answer

Hope it will help :)

The equation of the parabola with vertex (2, -4) and directrix y = -6 is y = 0.25(x - 2)² - 4.

The equation of a parabola in vertex form is y = a(x - h)² + k, where (h, k) is the vertex, and a is a constant that determines the shape and direction of the parabola. Given the vertex (2, -4) and the directrix y = -6, we can determine the value of a using the formula a = 1 / 4(c), where c is the distance from the vertex to the directrix. Since the vertex lies two units above the directrix, the constant c = 2; hence, a = 1 / 4(2) = 0.25 or 1/4.

Thus, the equation of the parabola is y = 0.25(x - 2)² - 4.

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Answer:

( X -2 ) ^2 = 8(y +4)

Step-by-step explanation:

Answer:

After 9 movies they will have paid the same amount

Step-by-step explanation:

We must write an equation for Duke's expenses and an equation to represent Tennessee's expenses.

For Duke expenses we have:

A fixed expense of $ 111.60 per year

A variable expense of $ 4.00 for each movie.

The equation that represents the expenses is a linear equation like the one shown below

[tex]C = 111.60 + 4.00x[/tex]

Where C represents the cost and x the number of movies.

For Tennessee expenses we have:

A variable expense of $ 16.40 for each film.

The equation that represents the expenses is a linear equation like the one shown below

[tex]C = 16.40x[/tex]

Where C represents the cost and x the number of movies.

To know after how many movies have paid the same amount, we equate both equations and solve the variable x

[tex]111.60 +4.00x=16.40x\\\\16.40x - 4x = 111.60\\\\12.40x =111.60\\\\x =\frac{111.60}{12.40}\\\\x =9[/tex]

After 9 movies they will have paid the same amount

0.329 is rational, 127.5 is rational, -89 is rational rational

The area of a square is length*width and since a square has the same side measurements, √1225 or 35 is one side. (35 * 35 = 1225)

There are 4 sides so 35*4 = 140ft² as the perimeter

I hope this helps!

Answer:

140 ft

Step-by-step explanation:

Here, A = 1225 ft² = s², where s represents the length of one side of the room.  Here, s = √( 1225 ft² ) = 35 ft.

Thus, the perimeter, P = 2L + 2W, is 4(35 ft) = 140 ft

Answer:

First option: You start with $3 and save $1 each month.

In this case, the relationship is linear. So the corresponding equation is: y=x+3. Where 'x' represents the month. For example, the amount of money that you will have after 7 months is going to be: y = 7 + 3 = 10. (Ten dollars).

Second option: You save $3 the first month, and then each month the amount triples.

In this case, the relationship is exponential. If each month the amount triples, it means that the first month you have $3, the second month $9 and the third month $27. The equation that correctly models this situation is [tex]y=3^{x}[/tex]. For example, the amount of money that you will have after 7 months is going to be [tex]y=3^{7} = 2187[/tex] (2187 dollars)

Third option: Your total savings is 3 times the number of months multiplied by itself.

In this case, the relation is quadratic. So the equation that models this situation is: [tex]y=3x^{2}[/tex]. For example, the amount of money that you will have after 7 months is going to be [tex]y=3(7)^{2} = 147[/tex] (147 dollars)

✅✅✅✅ BONUS: The best option is the SECOND ONE ✅✅✅✅

Answer:

[tex]x_1=4\\x_2=-3[/tex]

Step-by-step explanation:

Multiply both sides of the equation by -1:

[tex](-1)(-x^2+x+12)=0(-1)\\x^2-x-12=0[/tex]

Now, you can Factor the quadratic equation to solve it:

Choose two number that when you multiply them you get -12 and when you add them you get -1. These numbers are: -4 and 3

Therefore, you get:

[tex](x-4)(x+3)=0\\x_1=4\\x_2=-3[/tex]

For this case we have the following quadratic equation:

[tex]-x ^ 2 + x + 12 = 0[/tex]

We can solve it by:

[tex]x = \frac {-b \pm \sqrt {b ^ 2-4 (a) (c)}} {2 (a)}[/tex]

Where:

[tex]a = -1\\b = 1\\c = 12[/tex]

Substituting:

[tex]x = \frac {-1 \pm \sqrt {1 ^ 2-4 (-1) (12)}} {2 (-1)}\\x = \frac {-1 \pm \sqrt {1 + 48}} {- 2}\\x = \frac {-1 \pm \sqrt {49}} {- 2}\\x = \frac {-1 \pm \sqrt {49}} {- 2}\\x = \frac {-1 \pm7} {- 2}[/tex]

We have two roots:

[tex]x_ {1} = \frac {-1 + 7} {- 2} = \frac {6} {- 2} = - 3\\x_ {2} = \frac {-1-7} {- 2} = \frac {-8} {- 2} = 4[/tex]

Answer:

[tex]x_ {1} = - 3\\x_ {2} = 4[/tex]

Answer:

A = 102 cm^2

Step-by-step explanation:

This figure is a trapezoid.  The area is given by

A = 1/2 (b1+b2) *h  where b1 is the base and b2 is the top

b1 = 21   b2 = (6+7)  and h = 6

A = 1/2 (21+13) *6

A = 1/2 (34)*6

A = 102 cm^2

Answer:

C. 3:2

D. 21:14

Step-by-step explanation:

The scale factor of the larger figure to the smaller figure is the factor

that gives the dimensions of the smaller figure from the larger figure.

Correct response:

The possible dimensions given in the question as obtained from a similar question are;

Diameter of a smaller cylinder = 12 m

Diameter of a larger cylinder = 18 m

The scale factor of the larger figure to the small figure is given by ratio

of the diameter diameters is found by dividing the diameter of the larger

figure by the diameter of the smaller figure as follows;

The ratio is 3:2

Therefore;

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Answer:

D, x = 3

Step-by-step explanation:

to know if a line is parallel, we need to know what kind of line x = 6 is

we can use the mnemonic VUX/HOY to determine the slope, the type of line, and which axis it corresponds to. VUX/HOY stands for:

Vertical line

Undefined slope

X axis

Horizontal line

0 is the slope

Y axis

according to this, the equation x = 6 is a vertical line

now we can start eliminating answer choices

A. a line containing the point (6,2)

the point lies on the line x = 6, as the x-coordinate in the ordered pair is 6. this  is not parallel to the line

B. y = 6

this intersects x = 6 and is not parallel

C. y = 4

this intersects x = 6 as well and is not parallel

D. x = 3

this leaves us with x = 3, which is a vertical line as seen by the equation and therefore x = 3 is our answer

Answer:

D, x = 3

Step-by-step explanation:

to know if a line is parallel, we need to know what kind of line x = 6 is

we can use the mnemonic VUX/HOY to determine the slope, the type of line, and which axis it corresponds to. VUX/HOY stands for:

Vertical line

Undefined slope

X axis

Horizontal line

0 is the slope

Y axis

according to this, the equation x = 6 is a vertical line

now we can start eliminating answer choices

A. a line containing the point (6,2)

the point lies on the line x = 6, as the x-coordinate in the ordered pair is 6. this  is not parallel to the line

B. y = 6

this intersects x = 6 and is not parallel

C. y = 4

this intersects x = 6 as well and is not parallel

D. x = 3

this leaves us with x = 3, which is a vertical line as seen by the equation and therefore x = 3 is our answer

Step-by-step explanation:

To determine how long to leave $7500 in the bank at 6% interest compounded semi-annually to reach $16200, use the compound interest formula. Solving for t, time in years, yields approximately 11.9 years for the investment to grow to the desired amount.

To calculate how long the person must leave their money in the bank for it to grow from $7500 to $16200 with an interest rate of 6% compounded semi-annually, we'll use the formula for compound interest:

A = P(1 + \frac{r}{n})^{nt}

Where:

We are given:

Our goal is to solve for t, the time in years. Plugging the known values into the formula:

$16200 = $7500(1 + \frac{0.06}{2})^{2t}

Divide both sides by $7500:

2.16 = (1 + \frac{0.06}{2})^{2t}

Now take the natural logarithm of both sides:

ln(2.16) = ln((1 + \frac{0.06}{2})^{2t})

Use properties of logarithms to bring down the exponent:

ln(2.16) = 2t \cdot ln(1 + \frac{0.06}{2})

Divide both sides by 2ln(1 + \frac{0.06}{2}) to solve for t:

t = \frac{ln(2.16)}{2 \cdot ln(1 + \frac{0.06}{2})}

t = \frac{ln(2.16)}{2 \cdot ln(1.03)}

Using a calculator, we find t ≈ 11.9 years. Therefore, the person must leave the money in the bank for approximately 11.9 years to reach $16200.

To the nearest tenth of a year, the person must leave the money in the bank for approximately 13 years.

To find the time required for the investment to reach $16200, we can use the formula for compound interest:

[tex]\[ A = P \left(1 + \frac{r}{n}\right)^{nt} \][/tex]

Where:

- ( A ) is the amount of money accumulated after ( t ) years.

- ( P ) is the principal amount (the initial investment).

- ( r ) is the annual interest rate (in decimal form).

- ( n ) is the number of times interest is compounded per year.

- ( t ) is the time the money is invested for (in years).

Given:

- ( P = 7500 )

- ( A = 16200 )

- ( r = 0.06 ) (6% interest, converted to decimal)

- Interest is compounded semi-annually, so ( n = 2 )

We need to solve for ( t ):

[tex]\[ 16200 = 7500 \left(1 + \frac{0.06}{2}\right)^{2t} \][/tex]

[tex]\[ \frac{16200}{7500} = \left(1 + 0.03\right)^{2t} \][/tex]

[tex]\[ 2.16 = \left(1.03\right)^{2t} \][/tex]

Take the natural logarithm of both sides:

[tex]\[ \ln(2.16) = \ln\left(\left(1.03\right)^{2t}\right) \][/tex]

[tex]\[ \ln(2.16) = 2t \cdot \ln(1.03) \][/tex]

Now, solve for [tex]\( t \)[/tex]:

[tex]\[ t = \frac{\ln(2.16)}{2 \cdot \ln(1.03)} \][/tex]

[tex]\[ t \approx \frac{0.7693}{2 \cdot 0.0296} \][/tex]

[tex]\[ t \approx \frac{0.7693}{0.0592} \][/tex]

[tex]\[ t \approx 13 \][/tex]

So, to the nearest tenth of a year, the person must leave the money in the bank for approximately 13 years.

Check the picture below.

now, we know the base is a square, thus the length = width, namely L = w, so

[tex]\bf SA=2(Lw+Lh+wh)\implies \stackrel{\textit{since we know that L=w}}{380=2(ww+wh+wh)} \\\\\\ \cfrac{380}{2}=w^2+2wh\implies 190=w^2+2wh \implies 0=w^2+2wh-190 \\\\\\ 0=(w+19)(w-10)\implies w= \begin{cases} -19\\ \boxed{10} \end{cases}[/tex]

since the units must be positive, we can't use -19.

Final answer:

To find the largest width for the voting box, we need to consider its surface area. By setting up an equation and differentiating it with respect to the width, we can find the maximum width. The largest width for the box would be approximately 58.46 inches.

Explanation:

To find the largest width of the voting box, we need to consider its surface area. The surface area of a square-based box is given by 2lw + lh + wh, where l is the length, w is the width, and h is the height. We are given that the height is 4.5 inches, and we need to find the maximum width. The maximum surface area is 380 in2, so we can set up the equation as follows:

2lw + lh + wh = 380

Substituting the given height and rearranging the equation:

2lw + (4.5)(w) + (w)(w) = 380

Simplifying the equation:

2lw + 4.5w + w2 = 380

Since we are trying to find the maximum width, we can differentiate the equation with respect to w and set the derivative equal to zero:

d(2lw + 4.5w + w2)/dw = 0

2l + 4.5 + 2w = 0

Solving for w:

w = (380 - 4.5l)/2

Since the width should be the largest possible, we can substitute the maximum value of the length. Given that the box has a square base, the length and width are equal. Therefore, we substitute l = w:

w = (380 - 4.5w)/2

Simplifying the equation:

2w = 380 - 4.5w

6.5w = 380

w ~ 58.46 inches

Therefore, the largest width that the box could have is approximately 58.46 inches.