What is the equation of a circle with center (-3,-5) and radius 4?
O A. (x+3)2 + (y + 5)2 = 4
O B. (x-3)2 + (y- 5)2 = 16
O C. (x-3)2 + (y- 5)2 = 4
O D. (x + 3)2 + (y + 5)2 = 16

The results of the expression are given by;

\[tex]\mathbf{log_3(27) = 3}\\\\\mathbf{log_{11}(121) = 2}\\\\mathbf{log_{5}(125) = 3}\\\mathbf{log_{2}(128) = 7}\\\mathbf{(a) log_3(27)}\\[/tex]

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Expressions can be expressed using logarithms;

Express 27 as 3³

[tex]\mathbf{log_3(27) = log_3(3^3)}[/tex]

Apply law of logarithm;

[tex]\mathbf{log_3(27) = 3log_3(3)}[/tex]

So,

[tex]\mathbf{log_3(27) = 3\times 1}\\\mathbf{log_3(27) = 3}\\\mathbf{(b)\ log_{11}(121)}[/tex]

Express 121 as 11³

[tex]\mathbf{log_{11}(121) = log_{11}(11^2)}[/tex]

So, we have:

[tex]\mathbf{log_{11}(121) = 2\times 1}\\\mathbf{log_{11}(121) = 2}\\\mathbf{(c)\ log_{5}(125)}[/tex]

Express 125 as 5³

[tex]\mathbf{log_{5}(125) = log_5(5^3)}[/tex]

Apply law of logarithm;

[tex]\mathbf{log_{5}(125) = 3log_5(5)}[/tex]

So, we have;

[tex]\mathbf{log_{5}(125) = 3\times 1}\\\mathbf{log_{5}(125) = 3}\\\mathbf{dc)\ log_{2}(128)}[/tex]

Express 128 as 2^7;

[tex]\mathbf{log_{2}(128) = log_2{2^7}}[/tex]

Apply law of logarithm;

[tex]\mathbf{log_{2}(128) = 7log_2{2}}[/tex]

So, we have;

[tex]\mathbf{log_{2}(128) = 7\times 1}\\\mathbf{log_{2}(128) = 7}[/tex]

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Answer:

104

Step-by-step explanation:

Answer:

104

Step-by-step explanation:

For this equation you go left to right because all you have is addition and subtraction, and they are equal in PEMDAS (Parenthesis, exponents, multiplication, division, addition and subtraction)

Since we go left to right we start wtih 200-100

200-100=100

Now we do the last step

100+4=104

61.23 square inches of metal is needed to create a cylindrical can.

Solution:

Diameter of the base = 3 in

Radius of the base = 3 ÷ 2 = 1.5 in

Height of the cylinder = 5 in

The value of π = 3.14

To find the surface area of the cylinder:

Surface area of the cylinder = [tex]2 \pi r^{2}+2 \pi r h[/tex]

                                               = 2 × 3.14 × (1.5)² + 2 × 3.14 × 1.5 × 5

                                               = 14.13 + 47.1

Surface area of the cylinder = 61.23 sq. in

Hence 61.23 square inches of metal is needed to create a cylindrical can.

Answer:

1/4=0.25

Step-by-step explanation:

The required answer is 0.25.

Given that, 1.6 ÷ 6.4.

To divide a decimal by another decimal:

Now, 1.6/6.4=0.25

Therefore, the required answer is 0.25.

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Answer:

scatter-plots

Step-by-step explanation:

Scatter plots are similar to line graphs in that they use horizontal and vertical axes to plot data points. However, they have a very specific purpose. Scatter plots show how much one variable is affected by another. The relationship between two variables is called their correlation .

[tex]\bf \textit{volume of a cone}\\\\ V=\cfrac{\pi r^2 h }{3}~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r = 11\\ h = 15 \end{cases}\implies V=\cfrac{\pi (11)^2(15)}{3} \\\\\\ V=605\pi \implies V \approx 1900.664\implies \stackrel{\textit{rounded up}}{V = 1901}[/tex]

The average of 15, 12, 14, 11, and 13 is 13, calculated using the mean averaging method.


Step-by-Step Solution to Find the Average

1. Identify the averaging method:

In this case, you asked for the "average," which generally refers to the mean. The other options provided, "median" and "mode," represent different averaging methods.

2. Calculate the mean:

To find the mean, we add all the numbers and then divide by the total number of numbers:

(15 + 12 + 14 + 11 + 13) / 5 = 65 / 5 = 13

3. Conclusion:

Therefore, the average of 15, 12, 14, 11, and 13 is 13, calculated using the mean averaging method.

4. (Optional) Explain other mentioned methods:

Median: The median is the middle number when the numbers are arranged in order. In this case, 12, 13, 14, 15, and 11. So, the median is 13.

Mode: The mode is the most frequent number. In this case, all numbers appear only once, so there is no mode.

The average of the given numbers is 13.

The average of the given numbers: 15, 12, 14, 11, 13 is calculated by adding all the numbers together and then dividing by the count of numbers. This method is known as the arithmetic mean.

First, we add all the numbers:

15 + 12 + 14 + 11 + 13 = 65.

 Next, we count the number of values, which is 5.

Now, we divide the sum by the count:

Average = 65 / 5 = 13.

Therefore, the average of the given numbers is 13.

The method used to find this answer is the arithmetic mean, which is also known as the Average or Mean method. In the given options, the correct term for the method used is Mean. The other options, Drop Zone 1, Drop Zone 2, Median, and Mode, refer to different statistical measures and are not applicable in this context for finding the average.

Step-by-step explanation:

Let the measure of required angle be x degree

[tex] \therefore \tan \: x = \frac{45}{28} \\ \\ \therefore \tan \: x = 1.60714286 \\ \\ \therefore \: x = {\tan}^{ - 1} (1.60714286) \\ \\ \therefore \: x = {\tan}^{ - 1} ( \tan \: 58.109 \degree) \\ \\ \huge \red{ \boxed{\therefore \: x = 58\degree}}[/tex]

Thus, first option is the correct answer.

Answer:

47

Step-by-step explanation:

32+[4×(15÷3)]−5

At first we have to apply "BODMAS" rule. According to the rule, we will work 1st bracket.

Hence,

32+[4×5]−5

Then, we will take 3rd bracket into consideration,

32+20−5

Then, we will use addition from the BODMAS rule-

52 - 5

Finally, subtracting 5 from 52, we can get

= 47

The value of the expression is 47.

Final answer:

The value of the expression 32+[4×(15÷3)]−5 is calculated using the order of operations to be 47.

Explanation:

The value of the expression 32+[4×(15÷3)]−5 can be calculated by following the order of operations, also known as PEMDAS (Parentheses, Exponents, Multiplication and Division from left to right, Addition and Subtraction from left to right). Let's solve it step by step:

Solve the expression inside the parentheses: (15÷3) = 5.

Multiply this result by 4: 4×5 = 20.

Add this result to 32: 32 + 20 = 52.

Finally, subtract 5 from this sum: 52 − 5 = 47.

Therefore, the value of the expression is 47.

Answer:

1)

A. m arc QRS = 100°

B. m arc QRT = 255°

C. m arc UTS = 180°

D. m arc UTR = 205°

2)

1] The major arc CA = 255°

2] The minor arc AB = 90°

Step-by-step explanation:

In a circle:

1)

In circle O

A.

∵ m∠QOR = 75°

∵ ∠QOR subtended by arc QR

- By using the 1st note above

∴ m of arc QR = m∠QOR

∴ m of arc QR = 75°

∵ m∠ROS = 25°

∵ ∠ROS subtended by arc RS

∴ m of arc RS = m∠ROS

∴ m of arc RS = 25°

The measure of arc QRS is the sum of the measures of arcs QR and RS

∴ m arc QRS = 75° + 25° = 100°

B.

∵ m∠SOT = 155°

∵ ∠SOT subtended by arc ST

∴ m of arc ST = m∠SOT

∴ m of arc ST = 155°

The measure of arc QRT is the sum of the measures of arcs QR, RS and ST

∴ m arc QRT = 75° + 25° + 155 °= 255°

C.

∵ m∠UOT = 25°

∵ ∠UOT subtended by arc UT

∴ m of arc UT = m∠UOT

∴ m of arc RUT = 25°

The measure of arc UTS is the sum of the measures of arcs UT and TS

∴ m arc UTS = 25° + 155° = 180°

D.

The measure of arc UTR is the sum of the measures of arcs UT, TS and SR

∴ m arc UTR = 25° + 155° + 25 = 205°

2)

1]

∵ The sum of the measures of the minor and major arcs is 360°

∵ m of minor arc AC = 105°

- Subtract 105 from 360° to find the measure of the major arc CA

∴ m of major arc CA = 360° - 105°

∴ m of major arc CA = 255°

2]

∵ m of major arc AB = 270°

- Subtract 270° from 360° to find the measure of the minor arc AB

∴ m of minor arc AB = 360° - 270°

∴ m of minor arc AB = 90°

Answer:

dam it been here that long and still unanswer

Step-by-step explanation:

Answer:

A) Table:

Value of the sofa in dollars:

Year       Value

   0         $1,500

   1         $1,050

   2        $735

   3        $514.50

   4        $360.15

B) Multiply successively by 0.70

C)    [tex]1,500(0.7)^t[/tex]: see the tests below

Explanation:

A) Find the missing values for the table shown

Although the table was not provided with the question, you can create a complete table from the supplied information.

Table: value of the sofa

Year     Value

   0        $1,500

   1             A

   2            B

   3            C

   4            D

Then, determine the missing values, i.e. A, B, C, and D

Notice that 30% is 0.30 and a reduction in the value is determined by mutiplying the starting value by 1 - 0.3 = 0.7.

Thus, once completed the table would be:

Year       Value

   0         $1,500

   1         $1,050

   2        $735

   3        $514.50

   4        $360.15

B. Explain how you found each of the missing values in the table.

I multiplied successively by 0.70 which is the constant decaying rate of the function.

C. Write an expression in the form [tex]a(b)^t[/tex] that represents the value of the sofa in dollars t years after Carlos purchased it. Then test your expression for t = 0, 1, 2, 3, and 4.

Thus, the expression is:

Test it for t = 0, 1, 2, 3, and 4:

Answer:

B. reflection, then translation

Step-by-step explanation:

Hope this helps :)

Triangle ABC can be mapped onto triangle FED through reflection, then translation

Transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, reflection, translation and dilation.

Triangle ABC can be mapped onto triangle FED through reflection, then translation

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Answer: no solution

Step-by-step explanation:

In a system of equations, if the final equation simplifies to a statement that is always true, like 5=5, this indicates the system has in fact an infinity of solutions, not no solutions.

The question given pertains to the solution of a system of equations. In a system of equations, if you simplify to a point where you end up with a statement that is always true, such as 5=5, this indicates that the system has an infinite number of solutions, not no solutions as suggested.

Let's imagine we have a system of two linear equations representing two lines on a graph. If the lines overlap perfectly (one is exactly the same as the other), every point on the line is a point of intersection, meaning it is a solution to the system. When we simplify such a system algebraically, we get an identity like 5=5 which is true no matter what values the variables may take, directly indicating that there are an infinite number of solutions.

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Answer:

11

Step-by-step explanation:

3 + 38 - 63 + 33 = 11

Answer:

11

Step-by-step explanation:

I found the answer simply by doing trial-and-error, but here are the steps:

11 - 33 = -22

-22 +  63 = 41

41 + (-38) = 3

Option A:

∠TSU and ∠QPS are corresponding angles.

Solution:

Given OQ and RT are parallel lines.

To find which angles are corresponding angles.

Option A: ∠TSU and ∠QPS

They are on the same side of the parallel lines.

These are corresponding angles.

Option B: ∠OPS and ∠OPN

These are adjacent angles in a straight line.

It is not corresponding angles.

Option C: ∠RSP and ∠QPS

These are alternate interior angles.

It is not corresponding angles.

Option D: ∠OPN and ∠TSP

These are alternate angles.

It is not corresponding angles.

Hence ∠TSU and ∠QPS are corresponding angles.

Option A is the correct answer.

Answer:

h = a/4

Step-by-step explanation:

h = a/4 has already been solved for h; there is nothing left to do here.

Answer:

$38.4

Step-by-step explanation:

20% discount means he has to pay:

100 - 20 = 80% of the marked price.

80/100 × 48 = 38.4

Answer:

$38.4

Step-by-step explanation:

To find the discounted price of a item, you need to apply the regular price and its sale percentage.

To find the "20% off sale" do this:

100% - 20% = 80%

Then multiply the regular price to the "80%".

Regular price of the watch: $48

Discounted price: $48 x 80% = $38.4

Answer:

6π,0.3636

Step-by-step explanation:

An irrational number is a number that cannot be expressed as a fraction for any integers.

So 6π and 0.3636 are irrational numbers

Answer:

8y - 56

Step-by-step explanation:

8(y - 7)

Distribute

8*y - 8*7

8y - 56

Answer:

32f+72

Step-by-step explanation:

Distribute the -8

Answer:

32f + 72

Step-by-step explanation:

-8(-4f-9)

Distribute

(-8)(-4f) + (-8)(-9)

Multiply

32f + 72

Hope this helps :)

Final answer:

The range for the cost of the plumber's services, represented by the function f(x) = 50x + 25, starts at $25 and extends to infinity, as the number of hours worked can vary.

Explanation:

The question pertains to finding a possible range for the cost of a plumber's services, where the plumber charges a $25 service fee and $50 per hour. The total cost is represented by the linear function f(x) = 50x + 25, with x representing the number of hours worked. The range of this function would be all possible values that the total cost f(x) can take.

Since the number of hours x cannot be negative, the smallest value of x is 0, which would result in the minimum cost, the service fee of $25. Therefore, the range of f(x) starts at 25 and extends to infinity because there is no upper limit on the number of hours a plumber might work, theoretically. The range can be written as {f(x) | f(x) ≥ 25}, which means the set of all f(x) such that f(x) is greater than or equal to 25.

To find out how many tiles they would need for the border of a 3 x 3 swimming pool, you would need to add 3 tiles on the top, 3 tiles on the bottom, and 2 tiles on the left and right sides, resulting in a total of 10 tiles.

The student wants to find out how many orange tiles they will need for the border of the Nguyens' 3 x 3 swimming pool. To do this, we can visualize the 3 x 3 square and count the tiles around the border, but we want to find a way to do it without counting them one-by-one.

The pool is 3 tiles by 3 tiles, which is a total of 9 tiles. However, the border tiles are only the tiles around the edges. Moreover, corners are shared by two sides. So, for a 3 x 3 square, there are 3 tiles on the top, 3 tiles on the bottom, 2 tiles on the left, and 2 tiles on the right. So, in total, we would need 3 + 3 + 2 + 2 = 10 tiles for the border of the pool.

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Final answer:

To find the number of orange tiles needed for the border of the Nguyens' 3 x 3 swimming pool, we need to calculate the perimeter of the pool and divide by the length covered by each tile.

Explanation:

To find the number of orange tiles needed for the border of the Nguyens' 3 x 3 swimming pool, we need to calculate the perimeter of the pool. The perimeter is the sum of all the sides of the pool.

In a 3 x 3 pool, each side has a length of 3 units. Since there are 4 sides, the total perimeter is 4 x 3 = 12 units.

Each tile covers a length of 1 unit, so to find the number of tiles needed, we divide the perimeter by the length covered by each tile: 12 ÷ 1 = 12 tiles.

The answer is B.)

1. Find the area of the rectangle = L x W

- 5 x 6 = 30

2. Find the area of the triangle = bh/2

- 4*3/2 = 6

3. Add the areas of the figures.

- 30 + 6 = 36 cm^2

Answer:

The easiest way of calculating discount is, in this case, to multiply the normal price $3200 by 12 then divide it by one hundred. So, the discount is equal to $384. To calculate the sales price, simply deduct the discount of $384 from the original price $3200 then get $2816 as the sales price.

Answer:

165

Step-by-step explanation:

525-360=165

Answer:

600 meters

Step-by-step explanation:

1 kilometer= 1000 meters

0.6/1=x/100

Which makes x=600

Answer:

A - y - 5= 4(x - 2)

Step-by-step explanation:

First find slope with the two points given

( -1 , -7) and ( 2 , 5)

Using

m = y_2 - y_1 / x_2 - x_1

m - slope

x_1 = -1

y_1 = -7

x_2 = 2

ÿ_2 = 5

Inserting the values

m = 5 - (-7) / 2 - (-1)

= 5 + 7 / 2 + 1

= 12 / 3

= 4

Slope is 4

Then let's proceed

y - y_1 = m ( x - x_1)

using ( 2 , 5) as x_1 and y_1 respectively

x_1 = 2

y_1 = 5

m = 4

y - 5 = m ( x - 2)

m = 4

y - 5 = 4 ( x - 2)

We are asked to give the answer in point slope form

Answer:

3

Step-by-step explanation:

51 divided by 17 equals 3