what is is the domain of 16 - x^2

Answer: x = -3, 1/2

Step-by-step explanation:

cscθ is the same as 1/sinθ

Explanation:

csc stands for cosec which is equivalent to   1/sinθ

The expression is thus equal to 1/[sin⁡(4π/3)]

Since we know by consulting the unit circle that  sin⁡(4π/3) = - [(√3)/2]

we get the expression  1/[sin⁡(4π/3)] = 1/(-√3/2)  

which can be simplified to 1/(-√3/2) = 2/(-√3) = (-2√3)/3

The Probability of rolling a prime number and then rolling a multiple of 2 is 1/4 or 0.25.

A number cube is rolled, there are six possible outcomes: 1, 2, 3, 4, 5, and 6. To determine the probability of rolling a prime number and then rolling a multiple of 2, we need to first identify the prime numbers and the multiples of 2.

The prime numbers are 2, 3, and 5. There are three prime numbers out of a total of six possible outcomes, so the probability of rolling a prime number on the first roll is 3/6 or 1/2.

The multiples of 2 are 2, 4, and 6. There are three multiples of 2 out of a total of six possible outcomes, so the probability of rolling a multiple of 2 on the second roll is also 3/6 or 1/2.

To find the probability of both events occurring, we can multiply the probabilities of each event. Therefore, the probability of rolling a prime number and then rolling a multiple of 2 when a number cube is rolled twice is:

(1/2) × (1/2) = 1/4

So the probability of rolling a prime number and then rolling a multiple of 2 is 1/4 or 0.25.

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Answer:

Look at the image below.

Step-by-step explanation:

Points that may Help: (0,8), (-2,4), (2,4), (4,-8), and (-4,-8)

Answer:

354 feet below sea level

Step-by-step explanation:

Subtract 23 from  215, then add 119

Answer:

Step-by-step explanation:

x = what?

To find dw/dt using the chain rule, we need to differentiate w = x + y with respect to t. We are given that x = e^t, y = 2 + sin(2t), and z = 2 + cos(5t).

Using the chain rule, the derivative of w with respect to t, dw/dt, can be found as follows:

dw/dt = dx/dt + dy/dt

Now, let's find the derivatives of x and y with respect to t:

dx/dt = d/dt(e^t) = e^t

dy/dt = d/dt(2 + sin(2t)) = 2cos(2t)

Substituting these derivatives into the expression for dw/dt, we have:

dw/dt = dx/dt + dy/dt

     = e^t + 2cos(2t)

Therefore, dw/dt = e^t + 2cos(2t).

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Answer:

4z + 6z²

Step-by-step explanation:

\(\frac{1}{3}\) (12z + 18z² ) ← multiply each term in the parenthesis by \(\frac{1}{3}\)

= 4z + 6z²

The equation of the function in standard form is -5.83x² + 816.2x - 25895 (option c).

To find the equation of the function in standard form, we can use the given values of f(x) and x to form a system of equations. Since we know that the function is quadratic, we need at least three values of f(x) to solve for the constants a, b, and c.

Using the given values from the table, we can form the following system of equations:

1,272 = a(50)² + b(50) + c

1,884.5 = a(55)² + b(55) + c

2,322 = a(60)² + b(60) + c

2,584.5 = a(65)² + b(65) + c

2,672 = a(70)² + b(70) + c

2,584.5 = a(75)² + b(75) + c

2,322 = a(80)² + b(80) + c

To find the vertex of the parabola, we can use the formula h = -b/2a and k = f(h). Once we have the vertex, we can substitute its values into the vertex form of the equation to get the standard form of the quadratic function.

Using the given values from the table, we can find the vertex of the parabola:

h = -b/2a b = (f(60) - f(70))/(60-70)

b = -49 h = -b/2a 60 = -(-49)/(2a)

a = -5.83

k = f(h) k = f(60) k =25,895

Now, we have the values of a, h, and k, which we can substitute into the vertex form of the equation:

y = a(x-h)² + k y = -5.83x² + 816.2x - 25895

Expanding this equation, we get:

y = -5.83x² + 816.2x - 25895

This is the equation of the function in standard form.

Therefore, the answer is (C) -5.83x² + 816.2x - 25895

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Answer:2 7/8              Simplified version=23/8

Step-by-step explanation:3 1/8-1/4=2 7/8

Answer:

2 7/8

Step-by-step explanation:

Ok first lets make them have the same denominator...

so it would be 3 1/8 for Tony and for his brother would be 2/8

now you would subtract 2/8 from 3 1/8 which would be 2 7/8

Hope this helps

Answer:

x = 36˚

Step-by-step explanation:

Answer:

Step-by-step explanation:

In isosceles triangle, the base angles (the angles opposite to equal sides) are equal.

∠A = ∠B = 72

72+ 72 + x = 180  {Angle sum property of triangle}

   144 + x = 180

            x = 180 - 144

           x = 36°

Answer:

the answer is b

Step-by-step explanation:

radius is half the number of diameter

Answer:

Quadrant ll

Step-by-step explanation:

Answer:

the answer is ll

Step-by-step explanation. \

its where it is on the graph

Answer:  9/10

=======================================================

Explanation:

Imagine a pizza split into 5 equal slices. Then imagine that you split each slice in half. This means we now have 5*2 = 10 slices.

Eating 3 out of the original 5 is equivalent to eating 6 smaller slices out of the now 10 total.

In other words:  The fraction 3/5 is the same as 6/10

Put another way: Multiply top and bottom of 3/5 by 2 to get 6/10.

---------------

Gary painted 3/10 of the fence in the morning, and then 3/5 of it in the afternoon. We can replace the "3/5" with "6/10".

3/10 + 6/10 = (3+6)/10 = 9/10 total

Going back to the pizza scenario, we can imagine 3/10 as eating 3 slices out of 10 total. Then 6/10 adds 6 more slices to get 3+6 = 9 slices total. That's how we end up with 9/10 as the answer.

Answer:

34, and if 55 was replaced with 33, the new median would be 33.

Step-by-step explanation:

The median is the number that is in the middle of a data set, once the numbers are organized from least to greatest. If we put the numbers in order (18, 22, 24, 32, 34, 39, 55, 57, 59), the number in the middle is 34. If we do the same, but replace 55 with 33, (18, 22, 24, 32, 33, 34, 39, 57, 59), we get 33 as the median.

Answer:

Since it is Quadratic Function(also Polynomial Function), All Real Numbers are Domain for this function

Answer:

a)3240°

what is the sum of the internal angles of an icosagon?

The given expression, \(d(n)d(n)d(n)\), represents the duration in seconds for Hailey to run her \(n^{th}\) lap. The specific values provided, 333, 777, 999, correspond to the durations of the 3rd, 7th, and 9th laps, respectively. The values 858585, 999999, and 110110110 are unrelated and do not provide any additional information about lap durations.

The expression \(d(n)d(n)d(n)\) suggests that each lap duration is represented by the function \(d(n)\), where \(n\) denotes the lap number. The specific values given (333, 777, 999) correspond to the 3rd, 7th, and 9th laps, respectively. However, the remaining values (858585, 999999, 110110110) do not appear to have a direct connection to the lap durations or the function \(d(n)\).

Without further information or a specific pattern, it is difficult to interpret the significance of the remaining values. It's important to note that more context or information about the pattern or relationship between the values would be necessary to provide a more detailed explanation or analysis.

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Answer:

The cubic function f(x) = x3 is symmetric about the origin (it is an odd function). Here are some types of functions that are odd: Lines Through The Origin – any line with a zero y intercept (b = 0) and a nonzero slope (m not zero) will have equation f(x) = mx.

Step-by-step explanation:

Answer: No

f(x) = x³ + 2x − 5

Step-by-step explanation:

No

f(x) = x³ + 2x − 5

The value of a(t) is -1 and b(t) is 55 + \(e^t\)

No, the given equation y' - y = 55 + \(e^t\) is not in the standard form of a first-order linear differential equation.

In the method for solving a first-order linear differential equation, an integrating factor is a function used to transform the equation into a form that can be easily solved.

For an equation in the standard form y' + a(t)y = b(t), the integrating factor is defined as:

μ(t) = e^∫a(t)dt

To solve the equation, you multiply both sides of the equation by the integrating factor μ(t) and then simplify. This multiplication helps to make the left side of the equation integrable and simplifies the process of finding the solution.

To put it in standard form, we need to rewrite it as y' + a(t)y = b(t).

Comparing the given equation with the standard form, we can identify:

a(t) = -1

b(t) = 55 + \(e^t\)

Therefore, The value of a(t) is -1 and b(t) is 55 + \(e^t\)

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Answer:

\(\displaystyle \theta = \left\{\frac{7\pi}{6}, \, \frac{3\pi}{2}, \frac{11\pi}{6}\right\}\)

Step-by-step explanation:

We want to solve the equation:

\(2\sin ^2 \theta + 3\sin \theta + 1 = 0\)

In the interval [0, 2π).

Notice that this is in quadratic form. Namely, by letting u = sin(θ), we acquire:

\(\displaystyle 2u^2 + 3u + 1 = 0\)

Factor:

\(\displaystyle (2u+1)(u+1) = 0\)

By the Zero Product Property:

\(\displaystyle 2u + 1 = 0\text{ or } u + 1 = 0\)

Solve for each case:

\(\displaystyle u = -\frac{1}{2} \text{ or } u = -1\)

Back-substitute:

\(\displaystyle \sin \theta = -\frac{1}{2} \text{ or } \sin \theta =-1\)

Use the Unit Circle. Hence, our three solutions in the interval [0, 2π) are:

\(\displaystyle \theta = \left\{\frac{7\pi}{6}, \, \frac{3\pi}{2}, \frac{11\pi}{6}\right\}\)

Answer:

1. Rational

2. Irrational

3. Irrational

4. Rational

5. Irrational

Step-by-step explanation:

Rational numbers are numbers you can identify as the ratio of two integers. Which means they don't go on forever. 1 and 4 are both rational numbers while 2, 3, and 5 are irrational.

In algebra, a number exists even equal to itself according to the reflexive property of equality. The equality's reflexive quality. If a is a number, then. a = a.

In algebra, a number is always equal to itself according to the reflexive property of equality. The equality's reflexive quality. If a is a number, then. a = a.

2. AD = BC due to the congruence of a rectangle's opposite sides.

3. Due to the reflexive property of congruence, DC=DC, each segment is identical to itself.

4. ADC and BCD are right angles since any rectangle's internal angles are right angles (Definition of rectangle).

5. Since they form right angles and all right angles are congruent, ADC=BCD.

6. ADC and BCD are congruent because they have two congruent sides (AD with BC and DC with DC) and a congruent angle between them: Side Angle Postulate Side Congruence Postulate (SAS Congruence Postulate).

7. AC must match BD because Congruent Parts in Congruent Triangles must match (CPCTC).

Statement                                    Reason

1. Rectangle ABCD                         Given

2. AD=BC                                        Opposite sides of a rectangle are congruent

3. DC=DC                                        Reflexive Property of Congruence

4. <ADC and <BCD are                  Definition of rectangle

  right angles

5.  <ADC=<BCD                              All right angles are congruent

6. ∆ADC=∆BCD                              SAS Congruence Postulate

7. AC=BD                                        CPCTC  

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it helps to organize and categorize large amounts of information, making it more accessible and manageable. This organizational structure helps users to locate specific codes and information efficiently. indexing system True.

The National Codes index lists entries under one main term, which is usually a broad topic or subject area. Under each main term, there may be several subentries that provide more specific details or categories related to the main term. This type of indexing system allows users to quickly and easily find information related to a specific topic, without having to search through an entire document or database. Additionally, it helps to organize and categorize large amounts of information, making it more accessible and manageable.

In the index of the National Codes, entries are listed under one main term to ensure easy navigation and understanding of the content. This organizational structure helps users to locate specific codes and information efficiently.

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Answer:

4 sqr 465 = 86.2554346114

Step-by-step explanation:

   Isolate the radical on one side of the equation.

   Raise both sides of the equation to the power of the index.

   Solve the new equation.

   Check the answer in the original  

for example

3sqr3x-5-8=4

3sqr3x-5=12

sqr3x-5=4

(sqr3x-5)^2 = (4)^2

3x - 5 = 16

3x=21

x = 7

Answer:

0

Step-by-step explanation:

The line is horizontal

Answer: 9 is incorrect the anwser is acactually D . The square root of 58

Step-by-step explanation:

Answer:

The anwser is 6.01176470588

Answer:

1 solution

Step-by-step explanation:

x = 12