Show your work for x+3=12

Answer:

infinity

Step-by-step explanation:

they are the same line on a graph so they have infinty solutions

Answer:

Step-by-step explanation:

In this section, we will focus on graphing hyperbolas that open left and right or ... To easily sketch the asymptotes we make use of two special line segments ... From the center (5,4), mark points 3 units left and right as well as 2 units up and down. ... standard form for the equation of a hyperbola given the following information.

Answer:

the measure of angle A to the nearest degree is 36°

The measure of angle A to the nearest degree is 21°.

There are three commonly used trigonometric identities.

Sin x = Perpendicular / Hypotenuse

Cosec = Hypotenuse / Perpendicular

Cos x = Base / Hypotenuse

Sec x = Hypotenuse / Base

Tan x = Perpendicular / Base

Cot x = Base / Perpendicular

We have,

We can use the inverse sine function (denoted as sin⁻¹ or arcsin) to find the measure of angle A:

sin A = 0.3642

Taking the inverse sine of both sides, we get:

A = sin⁻¹(0.3642)

Using a calculator, we get:

A ≈ 21.3°

Rounding to the nearest degree, we get:

A ≈ 21°

Therefore,

The measure of angle A to the nearest degree is 21°.

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The pair of equations whose lines are perpendicular is (d) y = 1/6x + 3; y = -6x - 3

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

The pair of equations

By definition;

The slopes of perpendicular lines are opposite reciporcals

So, we have

(a) -1/3 and -3 false

(b) -3 and -6 false

(c) 3 and 3 false

(d) 1/6 and -6 true

Hence, the equations are (d) y = 1/6x + 3; y = -6x - 3

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Answer:

6inches^2

Step-by-step explanation:

Answer:

A ≈ 62.8 cm²

Step-by-step explanation:

the area (A) of the triangle is calculated as

A = \(\frac{1}{2}\) ab sinC

where a = 10, b = 13 and C = 105° , then

A = \(\frac{1}{2}\) × 10 × 13 × sin105° = 65 × sin105° ≈ 62.8 cm² ( to 1 dec. place )

Answer:

\(\displaystyle \frac{\tan\theta}{\sec\theta - \cos\theta} = \frac{1}{\sin\theta} = \csc\theta\)

Step-by-step explanation:

We have the expression:

\(\displaystyle \frac{\tan\theta}{\sec\theta - \cos\theta}\)

And we want to write the expression in terms of sine and cosine and simplify.

Thus, let tanθ = sinθ / cosθ and secθ = 1 / cosθ. Substitute:

\(=\displaystyle \frac{\dfrac{\sin\theta}{\cos\theta}}{\dfrac{1}{\cos\theta}-\cos\theta}\)

Multiply both layers by cosθ:

\(=\displaystyle \frac{\left(\dfrac{\sin\theta}{\cos\theta}\right)\cdot \cos\theta}{\left(\dfrac{1}{\cos\theta}-\cos\theta\right)\cdot \cos\theta}\)

Distribute:

\(\displaystyle =\frac{\sin\theta}{1-\cos^2\theta}\)

Recall from the Pythagorean Theorem that sin²θ + cos²θ = 1. Hence, 1 - cos²θ = sin²θ. Substitute and simplify:

\(\displaystyle =\frac{\sin\theta}{\sin^2\theta} \\ \\ =\frac{1}{\sin\theta}\)

We can convert this to cosecant if we wish.

Answer:

it should be C. and A. because it is a straight line and not curved and it has a positive slope

Step-by-step explanation:

Mr. clean

Answer: 1.785

Step-by-step explanation:

Answer:

Step-by-step explanation:

To determine the radius of a circle given its area, we can use the formula:

Area = π * radius^2

Given that the area is 10, we can set up the equation as follows:

10 = π * radius^2

To solve for the radius, we need to isolate it on one side of the equation. Dividing both sides by π, we get:

10 / π = radius^2

To find the radius, we can take the square root of both sides of the equation:

radius = √(10 / π)

Using a calculator to approximate the value of π as 3.14159, we can calculate:

radius ≈ √(10 / 3.14159)

radius ≈ √(3.1831)

radius ≈ 1.7849

Therefore, the radius of the circle is approximately 1.7849 when the area is 10.

hope it helps!!

def longest_palindromic_substring(s):
   def is_palindrome(sub):
       return sub == sub[::-1]
   
   n = len(s)
   if n == 0:
       return ""
   
   ans = s[0]
   

To solve this problem, we can use the following approach:

1. Create a function to check whether a given substring is a palindrome or not. We can do this by comparing the first and last characters of the substring and then moving towards the center until we have checked all the characters.

2. Start with a substring of length one and check if it is a palindrome. If it is, we update our answer to be this substring.

3. Then we expand our substring by adding one character to the left and one to the right. We check if this new substring is a palindrome, and if it is, we update our answer to be this substring.

4. We keep expanding our substring until we reach the end of the string. At each step, we check if the substring is a palindrome and update our answer accordingly.

5. Finally, we return the longest palindrome substring we found.

Here's the Python code for this approach:

```
def longest_palindromic_substring(s):
   def is_palindrome(sub):
       return sub == sub[::-1]
   
   n = len(s)
   if n == 0:
       return ""
   
   ans = s[0]
   
   for i in range(n):
       for j in range(i+1, n+1):
           sub = s[i:j]
           if is_palindrome(sub) and len(sub) > len(ans):
               ans = sub
               
   return ans
```

This solution has a time complexity of O(n^3) because we are checking all possible substrings of the input string. However, we can optimize this solution by using dynamic programming or Manacher's algorithm to reduce the time complexity to O(n^2) or O(n), respectively.

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Answer:

The First answer

Step-by-step explanation:

56 divided by 2 is the radius which is 28 and that squared times pi is 2464

The vertical asymptotes for the function f(x) = (x^2)(x-6)(x+3)^-1 are x=6 and x=-3.

The vertical asymptotes for the function f(x) = (x^2)(x-6)(x+3)^-1 are x=6 and x=-3. This is because the denominator can be factored into two linear expressions: x-6 and x+3. When either of these expressions equals 0, the fraction becomes undefined and a vertical asymptote is created. To find the asymptotes, set each linear expression in the denominator equal to 0 and solve for x. For x-6, x=6; for x+3, x=-3. Therefore, the vertical asymptotes of the function are x=6 and x=-3. When x is close to either of these values, the fraction will become very large, making the graph approach the vertical asymptotes without ever touching them.

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Answer:

Step-by-step explanation:

3y = -x + 2

y = -x/3 + 2/3

y - 0 = -1/3(x - 1)

y = -1/3x + 1/3

The integral in polar coordinates to find the volume of the given solid is V = ∫[0 to 2π] ∫[0 to 3] (r²) r dr dθ, and upon evaluation, the volume is V = 81π.

To find the volume of the given solid using polar coordinates, we can set up the integral as follows,

V = ∫∫R (z) r dr dθ

Where R represents the region in the xy-plane that satisfies the conditions of the solid.

In this case, the region R is defined by the disk x² + y² ≤ 9. In polar coordinates, this disk can be represented as 0 ≤ r ≤ 3. The height (z) of the solid is given by the paraboloid z = x² + y². Converting to polar coordinates, this becomes z = r². Therefore, the integral for finding the volume becomes,

V = ∫∫R (r²) r dr dθ

Substituting the limits of integration for r and θ,

V = ∫[0 to 2π] ∫[0 to 3] (r²) r dr dθ

Now we can evaluate this integral to find the volume V of the given solid.

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Complete question - Consider the following solid. under the paraboloid z=x²+y² and above the disk x²+y²≤9. Using polar coordinates, write an integral that can be used to find the volume V of the given solid. Find the volume of the given solid.

Answer:

I hope this helps you:)

Step-by-step explanation:

Answer:

C Figure C has no bases.

D Figure D is a triangular prism.

A Figure A is a cylinder.

Step-by-step explanation:

Answer:

B,D,C

Step-by-step explanation:

because thats the anwser

Answer:

Area = 6x² - 20x + 16

Step-by-step explanation:

The area of a rectangle is length x width.

Plug the values into that equation:

\(A = (2x-4)(3x-4)\)

Now you use the FOIL method to find the answer:

First: 2x × 3x = 6x²

Outer: 2x × (-4) = - 8x

Inner: (-4) × 3x = - 12x

Last: (-4) × (-4) = 16

Area = 6x² + (-8x) + (-12x) + 16

Area = 6x² - 20x + 16

In a cubic polynomial function f is defined by f(x) = 4x³ + ax² + bx + k, where a, b, k, are constants and has a local minimum at x = -2 and a local maximum at x = 0, then values of a and b is 12 and 0 respectively. If integrate of f(x)dx = 32 from 0 to 1, then value of k is 27.

The given cubic polynomial function is

f(x) = 4x³ + ax² + bx + k

f'(x) = 12x² + 2ax + b

f''(x) = 24x + 2a

At local maximum f' = 0

f'(0) = 12×(0)² + 2a×(0) + b = 0

b = 0

At local minimum, f' = 0

That is f'(-2) = 0 and f''(-2) > 0

f'(-2) = 12×(-2)² + 2a×(-2) + b = 0

48 - 4a + b = 0

4a - b = 48  

a = 12

Therefore, f(x) =  4x³ + 12x² + k

Integrate f(x)dx = 32 from 0 to 1, that is

∫₀¹ f(x)dx = 32

∫₀¹ (4x³ + 12x² + k) dx = 32

[ x⁴ + 4x³ + kx ]₀¹ = 32

(1⁴ - 0⁴) + 4(1³ - 0³) + k(1 - 0) = 32

1 + 4 + k = 32

k = 27

-- The question is incomplete, answering to the question below--

"A cubic polynomial function f is defined by f(x) = 4x³ + ax² + bx + k, where a, b, k, are constants. The function f has a local minimum at x = -2 and a local maximum at x = 0.

A. Find the values of a and b

B. If you integrate f(x)dx = 32 from 0 to 1, what is the value of k?"

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a) The probability space is (1, 1), (1, 2), (1, 3), (2, 1), (2, 2), (2, 3), (3, 1), (3, 2), (3, 3).

b) The probability that the sum of the numbers drawn is 4 is 2/9.

c) The probability that the sum of the numbers is at least 4 is 2/3.

a) The probability of an event is measured between 0 and 1, and the probability space is a collection of all probable results, hence the probability space is:

P= (1, 1), (1, 2), (1, 3), (2, 1), (2, 2), (2, 3), (3, 1), (3, 2), (3, 3)

Hence, the probability space can be written as a set, S = {1,2,3}.

b) If 2 balls are drawn and sum of the numbers is 4, then there could be only one probable way of drawing the balls, which is ball 1 and 3, so probability that the sum of the numbers is 4 is:

P = 2/9

c) If 2 balls are drawn and sum of the numbers is at least 4, then probable ways of drawing the balls are:

(1,3), (2,2), (2,3), (3, 1), (3, 2), and (3, 3)

Hence, the probability that the sum of the numbers is at least 4 = 6/9 = 2/3

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John travelled 22 miles.

$36 - $3 = $33

$33/$1.50 = 22 miles

B. Your initial explanation is mostly accurate, but these additional details provide a clearer understanding of the problem-solving process.

A. The process you described is commonly known as problem-solving or decision-making. Here's a breakdown of the steps involved: Identify the problem, Generate alternative solutions, Evaluate alternatives, Select the best solution, Implement the solution.

Identify the problem: The first step is to clearly identify and define the problem at hand. This involves understanding the nature of the problem, its causes, and its consequences or effects. Without a clear understanding of the problem, it would be difficult to find an appropriate solution.

Generate alternative solutions: Once the problem is identified, the next step is to brainstorm and generate multiple possible solutions or approaches to address the problem. This step encourages creativity and exploration of different options.

Evaluate alternatives: After generating alternative solutions, each option should be evaluated carefully. Factors such as feasibility, cost, time, resources required, and potential risks or benefits should be considered. This evaluation helps in narrowing down the options to those that are most viable.

Select the best solution: Based on the evaluation, one or more solutions may stand out as being the most effective or suitable for solving the problem. The best solution is selected based on its ability to address the problem efficiently and meet the desired objectives.

Implement the solution: Once the best solution is chosen, it is put into action. Implementation may involve planning, executing tasks, allocating resources, and managing the necessary steps to bring the solution to fruition.

It's important to note that the order of the steps may vary depending on the context and the complexity of the problem. While it's generally logical to evaluate and select the best solution before implementing it, sometimes it may be necessary to iterate through the steps, re-evaluate options, or make adjustments during the implementation phase.

Regarding the other options you mentioned:

A. This option suggests starting with identifying the best solution without understanding the nature of the problem or considering other possible solutions. As you correctly pointed out, this approach is flawed because it skips important steps in the problem-solving process.

C. This option implies evaluating and selecting the best solution before understanding the problem or considering other alternatives. Again, this is incorrect because a thorough understanding of the problem and exploration of multiple solutions should precede the evaluation and selection stage.

D. This option suggests implementing the solution before evaluating and selecting the best one. However, it's generally more effective to assess the potential effectiveness of different solutions before committing to their implementation.

In summary, your initial explanation is mostly accurate, but these additional details provide a clearer understanding of the problem-solving process.

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The Cartesian coordinate system is also referred to as a plane because it represents a two-dimensional space.

In mathematics, a plane is a flat surface that extends infinitely in all directions. The Cartesian coordinate system consists of two perpendicular lines, known as the x-axis and y-axis, which intersect at a point called the origin. These axes divide the plane into four quadrants.

The term "plane" in the context of the Cartesian coordinate system originates from the concept of a geometric plane, which is a fundamental concept in Euclidean geometry. In Euclidean geometry, a plane is a flat, two-dimensional surface that extends infinitely in all directions.

The Cartesian coordinate system borrows this concept and applies it to represent points, lines, curves, and shapes in a two-dimensional space.

By using the Cartesian coordinate system, we can assign coordinates (x, y) to any point in the plane, where the x-coordinate represents the horizontal position and the y-coordinate represents the vertical position.

This system allows us to precisely locate and describe objects or phenomena within the two-dimensional space, making it a valuable tool in various fields such as mathematics, physics, engineering, and computer graphics.

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129.5 dollars would be he cost for 7 adult tickets and 21 kids ticket at the rate of 8 dollars for adult and 3.5 dollars for kids.

8a + 3.5k is the total for a adult and k kids.

rate is a ratio that compares two different quantities which have different units. For example, if we say John types 50 words in a minute, then his rate of typing is 50 words per minute. The word "per" gives a clue that we are dealing with a rate.

if an adult ticket is 8 dollars then 7 adult tickets is 8 x 7 = 56 dollars

if a kid ticket is 3.5 dollars then 21 kids will be 21 x 3.5 = 73.5 dollars

Total = 56 = 73.5 which is 129.5 dollars

for a adult at the rate of 8 dollars, total is 8a

for k kids at the rate of 3.5 dollars total is 3.5k

so Total for both = 8a + 3.5k

In conclusion the total for both scenarios are 129.5 dollars and 8a + 3.5k dollars

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Answer:

Answer is in the attached photo.

Step-by-step explanation:

The solution is in the attached photo, do take note for this question, we will have to make x the subject and solve for x.

To design a cylindrical can (with a lid) to contain 1 liter (= 1000 cm3) of water, using the minimum amount of metal, we need to consider the following parameters:Height and Diameter of the canThickness of the metalMaterial used for making the canLet's assume we use Aluminium as a material. Now, let's start designing the can:Height of the can:

Volume of water = 1000 cm3Volume of cylinder = πr²hVolume of cylinder = π (d/2)² hVolume of cylinder = π (d²/4) hVolume of cylinder = 1000 cm³π (d²/4) h = 1000 cm³d²h = 4000 cm³h = (4000 cm³) / (π d²) h = (4000 cm³) / (3.14 * d²) h = (1273.24) / d²Diameter of the can:

Volume of cylinder = πr²hVolume of cylinder = π (d/2)² hVolume of cylinder = π (d²/4) hVolume of cylinder = 1000 cm³π (d²/4) h = 1000 cm³d²h = 4000 cm³d² = (4000 cm³) / h d² = (4000 cm³) / (1273.24/d²) d² = 3.1425d = 17.8 cmThickness of the metal:We can assume the thickness to be 0.5 mm.Material used for making the can:AluminiumTotal Surface Area of the can:Total Surface Area of cylinder = 2πrhTotal Surface Area of cylinder = 2π(d/2)(1273.24/d²)Total Surface Area of cylinder = 1273.24/d Total Surface Area of lid = πr²Total Surface Area of lid = π (d/2)²Total Surface Area of lid = π (17.8/2)²Total Surface Area of lid = 248.5Total Surface Area of the Can = 1273.24/d + 248.5Now, we can calculate the minimum amount of Aluminium required to make the can by minimizing the Total Surface Area of the can.Total Surface Area of the can = 1273.24/d + 248.5d (in cm)Total Surface Area of the can = 1273.24/7.09 + 248.5(7.09)Total Surface Area of the can = 584.24Therefore, the minimum amount of Aluminium required to make the can is 584.24 cm².

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The equation of the parabola is:

(y - 6)² = -12(x +2)

Parabola is the locus of a point such that its distance from a fixed point (called the focus) and a given line (called the directrix) is always the same.

The equation of a parabola is given by:

(y - k)² = 4p(x - h)

Where (h, k) is the vertex, (h + p, k) is the focus

Given the vertex of a parabola is (-2,6), and its focus is (-5,6).

Hence, k = 6, h = -2;

h + p = -5

-2 + p = -5

p = -3

Hence the equation of the parabola is:

(y - 6)² = -12(x +2)

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The scale factor is given as follows:

5/3.

The value of x is given as follows:

x = 7.

Two triangles are defined as similar triangles when they share these two features listed as follows:

Equivalent side lengths for this problem are given as follows:

YZ and BC.

Hence the scale factor is given as follows:

10/6 = 5/3.

Then the value of x can be obtained as follows:

(12x - 59)/(2x + 1) = 5/3

Applying cross multiplication, we have that:

3(12x - 59) = 5(2x + 1)

26x = 182

x = 182/26

x = 7.

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Answer:

area is 100m  bc u do 10 times 10

Step-by-step explanation:

Answer:

139.27 meters squared

Step-by-step explanation:

So what you're doing is calculating the square's area and half of the circle's area.

The square's area is 100m^2 since 10*10=100

For the circle part, you use πr^2. You know the diameter of the circle, and radius is half of the diameter, so 10/2=5.

π*5^2 = 78.54 m^2

Since you have half of a circle you divide this by 2.

39.27

Finally you add your two areas together

100+39.27=139.27 meters ^2

Answer: 6m^2 +m -40

Step-by-step explanation: Distributing binomials calls for the FOIL method.

Multiply the First times the First: 3m×2m= 6m^2. (^2 means squared when we can't use superscript for exponents.)

Then multiply and combine the Outside and Inside terms: 2m ×8=16m. and -5 ×3m= -15m

16m - 15m = m

Then multiply the Last terms: -5×8= -40

You end up with

6m^2 + m -40

Answer:

6m^2 + m - 40.

Step-by-step explanation:

(2m - 5)(3m + 8)

= (2m * 3m) + (-5 * 3m) + (2m * 8) + (-5 * 8)

= 6m^2 - 15m + 16m - 40

= 6m^2 + m - 40.

Hope this helps!

Answer:

there are only two options?

Step-by-step explanation:

id say b is the answer

Answer:

B

Step-by-step explanation: