Theo started to solve the quadratic equation

[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]

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:

a=4, b=5/2

Step-by-step explanation:

Assuming the given equation is

[tex]a(x + b) = 4x + 10[/tex]

We expand the left hand side to get:

[tex]ax + ab = 4x + 10[/tex]

If this equation must have infinitely many solutions, then

[tex]ax = 4x \\ \implies \: a = 4[/tex]

Also we must have

[tex]ab = 10[/tex]

Put a=4 to get:

[tex]4b = 10[/tex]

[tex]b = \frac{10}{4} = \frac{5}{2} [/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.

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:

x=2

Step-by-step explanation:

Since they are both equal to y set them equal to each other: 2x-3=-8x+17

Subtract 17 from both sides: 2x-20=-8x

Subtract 2x from both sides: -20=-10x

Divide both sides by -10: 2=x

Answer: x = 2 and y = 1

Step-by-step explanation: What we have here is a pair of simultaneous equations and we have been instructed to solve by using the substitution method.

The equations are

y = 2x - 3 ------(1)

y = -8x + 17 ----(2)

The y variable has a coefficient of 1 in both equations so we can start with either of equation (1) or (2).

From equation (1) y = 2x - 3. Substitute for the value of y into equation (2)

2x - 3 = -8x + 17

By collecting like terms we now have

2x + 8x = 17 + 3

(Remember that when a negative value crosses to the other side of the equation it becomes positive and vice versa)

10x = 20

Divide both sides of the equation by 10

x = 2

Having calculated the value of x, we can now substitute for the value of x into equation (1)

y = 2x - 3

y = 2(2) - 3

y = 4 - 3

y = 1

Therefore, x = 2 and y = 1.

Jessica's rate could be any rate greater than 0.1765 tiles per minute.

To determine Jessica's rate, we first find Meg's rate by dividing the number of tiles laid by the time taken: [tex]\(Rate_{\text{Meg}} = \frac{15 \, \text{tiles}}{50 \, \text{minutes}} = 0.3 \, \text{tiles per minute}\).[/tex] Since Jessica works at a faster rate per tile than Meg, her rate is greater than 0.3 tiles per minute. To calculate the minimum rate Jessica could have, we consider the case where she completes one tile in 85 minutes: [tex]\(Rate_{\text{Jessica}} = \frac{1 \, \text{tile}}{85 \, \text{minutes}} \approx 0.0118 \, \text{tiles per minute}\)[/tex]. Therefore, Jessica's rate could be any value greater than 0.0118tiles per minute.

The rate Jessica could have falls within the range of 0.0118 to 0.3 tiles per minute, as she is working at a faster rate than Meg. The provided answer, 0.1765 tiles per minute, is within this range. Jessica's rate per tile is not limited to any specific value, but it must be greater than Meg's rate of 0.3 tiles per minute. In summary, Jessica could work at any rate greater than 0.0118 tiles per minute, making 0.1765 tiles per minute a valid option.

Answer:

x+2y=3;3x-2y=5  

Solution :

{x,y} = {2,1/2}  

System of Linear Equations entered :

  [1]    x + 2y = 3

  [2]    3x - 2y = 5

Graphic Representation of the Equations :

   2y + x = 3        -2y + 3x = 5  

Solve by Substitution :

// Solve equation [1] for the variable  x  

 [1]    x = -2y + 3

// Plug this in for variable  x  in equation [2]

  [2]    3•(-2y+3) - 2y = 5

  [2]     - 8y = -4

// Solve equation [2] for the variable  y  

  [2]    8y = 4  

  [2]    y = 1/2  

// By now we know this much :

   x = -2y+3

   y = 1/2

// Use the  y  value to solve for  x  

   x = -2(1/2)+3 = 2  

Solution :

{x,y} = {2,1/2}  

  Processing ends successfully  

Step-by-step explanation:

Answer:

x=2, y=1/2

Step-by-step explanation:

Answer:

dam it been here that long and still unanswer

Step-by-step explanation:

Answer:

4 mph

Step-by-step explanation:

Givens

Current = c = 2 mph

Alberta = r = ?

d = 2 mph upstream

d1 = 6 mph downstream

Formula

d = r * t

The time is the same so the formula becomes d/r = t

2/(r  - 2) = 6/(r + 2)    

Solution

Cross Multiply

2*(r + 2) = 6*(r - 2)

2r + 4 = 6r - 12                      Subtract 2r from both sides

4 = 6r - 2r - 12                       Combine the right.

4 = 4r - 12                             Add 12 to both sides.

4 + 12 = 4r

16 = 4r                                  Divide by 4

16/4 = 4r/4

r = 4

Step-by-step explanation:

Nicole starts with the budget:

$395

Now, she only expects to pay half the deposit;

$72 ÷ 2 = $36

Subtract this from the budget:

$395 - $36 = $359

Divide by cost per hour:

$359 ÷ $60 = 5.983333... (3 repeating)

This means, Nicole can rent a maximum of 5 hours with her budget. The inequality would be

[tex]x \leqslant 5[/tex]

a) Number of days the bag will last = 12.5 days

b) The answer lies between 12 and 13.

Step-by-step explanation:

Step 1 :

Total quantity of the dog food = 25 pounds

Total quantity of food the dog eats per day = 2 pounds

We need to find number of days the bag will last

Step 2 :

The number of days the food will last can be obtained by dividing the total quantity of food by the quantity consumed per day.

Hence

Number of days = [tex]\frac{25}{2}[/tex]  = 12.5 days

The answer lies between 12 and 13.

Step 3:

Answer :

a) Number of days the bag will last = 12.5 days

b) The answer lies between 12 and 13.

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 :)

Answer:

8y - 56

Step-by-step explanation:

8(y - 7)

Distribute

8*y - 8*7

8y - 56

The Slope is 3/5, because of the rise over run method

The Y-Intercept is -1, because the point that touches the y-axis is the y-intercept

Answer:

15cm

Step-by-step explanation:

So first its 3:5 so take 25 and divide it by 5. This equals 5. Multiply it by 3 and you get 15cm. 15 is 3:5 of 25.

Answer:15cm

Step-by-step explanation: take 25 and divide it by 5 then Multiply the sum by 3 and you get 15cm

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:

$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

"Then I will need an average quality score of 3.28  to meet 85.28 goal."

Step-by-step explanation:

⇒ (4/100)[tex]\times[/tex]82

⇒ 82/25

⇒ 3.28

The improved average quality score = 82+3.28 = 85.28

The employee needs an average quality score of 3.28 to meet the goal of 85.28

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.

Answer:

Option B

Step-by-step explanation:

As shown at the graph:

The circle C ⇒ has a center at (0,0) and radius = 2

The circle C' ⇒ has a center at (0,0) and radius = 7

Circle C shown below was dilated with the origin as the center of dilation to create Circle C'

As the radius of Circle C' is greater than the radius of Circle C ⇒ so, this represents enlargement dilation.

So, the factor of dilation = 7/2

So, the rule will be [tex](x,y) \rightarrow (\frac{7}{2}x,\frac{7}{2} y)[/tex]

The answer is option B

Answer: The answer has to be B.) its facts!

Have a great Day/Night!

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.

Check the picture below.

let's recall that once we move an angle in the opposite direction of the 0-line or x-axis, we end up with a negative counterpart angle.

since we know that θ is on the IV Quadrant, then its negative counterpart must be across the line, and tangent is negative on the IV Quadrant, and positive on the I Quadrant.

If 270°<θ<360°, and tan⁡ θ= - 1/2, then the value of tan(-θ) is 1/2.

Let's start by understanding the given information. We are given that the angle θ lies between 270° and 360°, which means it is in the fourth quadrant of the unit circle. In this quadrant, both the sine and tangent functions are negative, while the cosine function is positive.

We are also given that tan(θ) = -1/2. To find the value of tan(-θ), we can use the identity for the tangent of a negative angle:

tan(-θ) = -tan(θ).

Now, let's find the value of tan(θ) using the given information. We know that tan(θ) = -1/2, and since θ is in the fourth quadrant, we can construct a right-angled triangle in which the opposite side is -1 and the adjacent side is 2. By applying the Pythagorean theorem (a² + b² = c²), we can find the length of the hypotenuse, which is

√(1² + 2²) = √5.

Now, we have all the information to find the value of tan(-θ) using the tangent identity for a negative angle:

tan(-θ) = -tan(θ).

Substituting tan(θ) = -1/2, we get:

tan(-θ) = -(-1/2) = 1/2.

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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:

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

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 .

Answer: Graph C

Step-by-step explanation:

Answer:

y = ㏒₃ x

Step-by-step explanation:

Given: the points (0.33, -1), (1, 0), and (3, 1)

We will check which function goes through the previous points

we will use the point (3,1)

1) y = ㏒₀.₄ x

㏒₀.₄ x = ㏒₀.₄ 3 = -1.199 ≠ 1

2) y = ㏒₁ x

㏒₁ x = ㏒₁ 3 ⇒ unlogic  condition

3) y = ㏒₃ x

㏒₃ x = ㏒₃ 3 = 1

4) y = ㏒₁₀ x

㏒₁₀ x = ㏒₁₀ 3 = 0.477 ≠ 1

So, from the previous explanation:

The function is y = ㏒₃ x

Another solution;

by drawing the four function we will find which function goes through the points (0.33, -1), (1, 0), and (3, 1)

See the attached figure.

So, the answer is y = ㏒₃ x

Answer:

The answer is C on ed.

Step-by-step explanation:

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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