r=−5sinθ+4θ
Which of the following types of symmetry is demonstrated in the equation above based on the three symmetry tests for polar equations?
θ=π/2
polar axis
pole
none

Answer:

To find the greatest common factor (GCF) of 8a^3b^2 and 12ab^4, we need to factor each term into its prime factors and then find the common factors.

8a^3b^2 can be written as:

8a^3b^2 = 2^3 * 2 * a * a * a * b * b

12ab^4 can be written as:

12ab^4 = 2^2 * 3 * a * b * b * b * b

The common factors are 2, a, and b^2.

Therefore, the GCF of 8a^3b^2 and 12ab^4 is:

2 * a * b^2 = 2ab^2

The calculated measure of the arc XYZ is 83 degrees

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

The circle

The angles created by secants and tangents that intersect outside a circle, which states that

The size of the angle formed by these two lines is equivalent to half the numerical difference between the measures of the arcs that they cut out from the circle.

So, we have

XYY = 1/2 * (166 - 0)

Evaluate

XYY = 83

Hence, the measure of the angle is 83 degrees

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Answer:

7

Let's call the width = x

width : x

so (x + 2x-4)2 = 34 (perime formula of a rectangle) x+2x-4 = 7

3x = 21

x = 7

so x is 7

Answer: The California state sales tax rate is 7.25%. This rate is made up of a base rate of 6%, plus California adds a mandatory local rate of 1.25% that goes directly to city and county tax officials.

Step-by-step explanation:

Hope this helped! :)

Answer:

7(-6) + 4(8) = -42 + 32 = -10, so (-6, 8) is the solution to this system of equations.

The answer is Yes.

Answer:

a)

[tex]y = 7( {1.03}^{t} )[/tex]

[tex]y = 7( {1.03}^{5} ) = 8.11[/tex]

There were about 8.11 billion subscribers in 2019.

b)

[tex]7( {1.03}^{t}) = 7.5[/tex]

[tex]t = 2.33 \: years \: after \: 2014[/tex]

sometime in 2016

The sales tax rate for the item is 3%.

To find the sales tax rate, we can divide the sales tax amount by the original cost of the item, and then multiply by 100 to express the result as a percentage.

Given:

Sales tax amount = $11.70

Original cost of item = $390

Sales tax rate = (Sales tax amount / Original cost of item) x 100

Plugging in the given values:

Sales tax rate = (11.70 / 390) x 100

Calculating:

Sales tax rate = 0.03 x 100

Final result:

Sales tax rate = 3%

So, the sales tax rate for the item is 3%.

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The rewritten expression of y = x + 8/3x using the distributive property is y = x(1 + 8/3)

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

Y can represent the distance Frog B hopped as y=x+ 8/3 x.

This means that

y = x + 8/3x

Factor out x from the equation

So, we have

y = x(1 + 8/3)

The above equation has been rewritten using the distributive property.

Hence, the rewritten expression using the distributive property is y = x(1 + 8/3)

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The attendance at the movie theatre is;

Children = 142

Students = 44

Adults = 71

What is arithmetic?

Arithmetic is an elementary part of mathematics that consists of the study of the properties of the traditional operations on numbers—addition, subtraction, multiplication, division, exponentiation, and extraction of roots.

Here, we have

Given:

Seating capacity = 257

Charges: Children = $5.00; Students = $7.00; Adults = $12.00

Total sales of ticket = $1870

A number of children, students, and adults were present in the theatre.

Let A, C, and S represent adults, children, and students respectively.

There are half as many adults as there are children; this means that

A = ½C

If the total seat capacity is 257, then

A + C + S = 257

Also, if the total sales of tickets are $1870, then

12A + 7S + 5C = 1870

So, we have two equations to be solved simultaneously.

A + C + S = 257 --- (1)

12A + 7S + 5C = 1860 --- (2)

Substitute ½C for A in (1) and (2)

½C + C + S = 257

Multiply both sides by 2

2(½C + C + S) = 2 * 257

C + 2C + 2S = 514

3C + 2S = 514 ----- (3)

12(½C) + 7S + 5C = 1870

6C + 7S + 5C ,= 1870

6C + 5C + 7S = 1870

11C + 7S = 1870 --- (4)

Make S the subject of the formula in (3)

2S = 514 - 3C

S = ½(514 - 3C)

S = 257 - 1.5C

Substituton 257 - 1.5C for S in (4)

11C + 7(257- 1.5C) = 1870

11C + 1799 - 10.5C = 1870

Collect like terms

11C - 10.5C = 1870 - 1799

0.5C = 71

Multiply both sides by 2

2 * 0.5C = 2 * 71

C = 142

Recall that

S = 257 - 1.5C

S = 257 - 1.5(142)

S = 257 - 213

S = 44

Also, recall that

A = ½C

A = ½ * 142

A = 71

Hence, the attendance at the movie theatre is;

Children = 142

Students = 44

Adults = 71

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Therefore, P(z > 0.97) = 0.166 using standard normal distribution table.

A standard normal distribution table, also called a z-score table or a standard normal table, is a table that provides the area under the curve to the left of a specific z-score value in a standard normal distribution. A standard normal distribution is a normal distribution with a mean of zero and a standard deviation of one.

The table usually includes positive z-score values in the right-hand column and the second decimal place in the top row. The intersection of a specific z-score value and decimal place provides the area under the curve to the left of that z-score value.

For example, if we want to find the area under the curve to the left of a z-score value of 1.32, we would locate the row with 1.3 in the top row and the column with 0.02 in the right-hand column. The intersection of this row and column gives the area under the curve to the left of 1.32, which is 0.9066.

Using a standard normal distribution table or calculator, we can find the probability of z being greater than 0.97 is approximately 0.166. Therefore, P(z > 0.97) = 0.166.

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Answer:

y= -1/5x-5

Step-by-step explanation:

You can use the slope formula and the slope intercept form which is y=mx+b.

Answer:

  11

Step-by-step explanation:

You want the degree of the monomial -3q⁴rs⁶.

The degree of a variable expression is its exponent. The degrees of the variables in the given expression are ...

  q: 4

  r: 1

  s: 6

The degree of their product is the sum of the exponents:

  monomial degree = 4 + 1 + 6 = 11

The degree is 11.

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Answer:

30°

Step-by-step explanation:

Answer:

9

Step-by-step explanation:

In a 30°-60°-90° right triangle, the sides are always in the ratio of 1: √3:2, where 1 is the length of the short leg opposite the 30° angle, √3 is the length of the long leg opposite the 60° angle, and 2 is the length of the hypotenuse opposite the 90° angle1234.

In this case, we are given that the long leg is 9√3, so we can use this value to find the other sides by setting up a proportion:

short leglong leg​=13​​

short leg93​​=13​​

Cross-multiplying and solving for the short leg, we get:

short leg=3​93​×1​=9

Similarly, we can use another proportion to find the hypotenuse:

long leghypotenuse​=3​2​

93​hypotenuse​=3​2​

Cross-multiplying and solving for the hypotenuse, we get:

hypotenuse=3​2×93​​=18

Therefore, the measure of the hypotenuse n is 18 and the measure of the short leg m is 9.

Answer:

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

y = mx + b

where m is the slope and b is the y-intercept.

We are given that the y-intercept is (0,2), which means that the value of b is 2.

We are also given that the slope is -2, which means that the value of m is -2.

Substituting these values into the slope-intercept form, we get:

y = -2x + 2

Therefore, the slope-intercept form of the equation of the line is y = -2x + 2.

Step-by-step explanation:

Answer:

that is correct just to give you feedback on that

Answer:

Step-by-step explanation:

The equation for the height h of the object after t seconds is given by:

h = -16t^2 + 145t + 2

To find when the height will be 230 feet, we can set h = 230 and solve for t:

230 = -16t^2 + 145t + 2

We can simplify this equation by moving all the terms to one side:

16t^2 - 145t + 228 = 0

To solve for t, we can use the quadratic formula:

t = (-b ± sqrt(b^2 - 4ac)) / 2a

where a = 16, b = -145, and c = 228. Plugging in these values, we get:

t = (-(-145) ± sqrt((-145)^2 - 4(16)(228))) / 2(16)

t = (145 ± sqrt(21025 - 14592)) / 32

t = (145 ± sqrt(6433)) / 32

t ≈ 0.56 seconds or t ≈ 9.17 seconds

Therefore, the height of the object will be 230 feet at approximately 0.56 seconds or 9.17 seconds after it is thrown.

To find when the object will reach the ground, we can set h = 0 and solve for t:

0 = -16t^2 + 145t + 2

Again, we can simplify this equation by moving all the terms to one side:

16t^2 - 145t - 2 = 0

Using the quadratic formula again, we get:

t = (-(-145) ± sqrt((-145)^2 - 4(16)(-2))) / 2(16)

t = (145 ± sqrt(21249)) / 32

t ≈ 9.51 seconds or t ≈ 0.15 seconds

Therefore, the object will reach the ground at approximately 0.15 seconds or 9.51 seconds after it is thrown. However, since the negative solution does not make physical sense in this context, the object will reach the ground after approximately 9.51 seconds.

~~~Harsha~~~

The maximum FUTA deductions for the first quarter is $1092.Because none of the given options correspond to this result, the correct answer is not listed.

The Federal Unemployment Tax Act (FUTA) tax rate is 6% on the first $7,000 paid to each employee in a calendar year. Therefore, the maximum FUTA deduction for each employee is $420 ($7,000 x 0.06).

Person 1 earned $4700, so the FUTA deduction for Person 1 is $282 ($4700 x 0.06).

Person 2 earned $19,800, but only the first $7,000 is subject to FUTA. Therefore, the FUTA deduction for Person 2 is $420.

Person 3 earned $6500, so the FUTA deduction for Person 3 is $390 ($6500 x 0.06).

The total FUTA deduction for the first quarter is the sum of the FUTA deductions for each employee:

$282 + $420 + $390 = $1092

Therefore, the maximum FUTA deductions for the first quarter is $1092.Because none of the given options correspond to this result, the correct answer is not listed.

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