when the base and leg side of right triangle are the same what is the angel measure fo the hypotenuse?

For the polynomial function,

The leading terms of the polynomial is 4

The degree of f(x) is 23

And the leading coefficient is 4x²³

Polynomial function:

Polynomial function means a function that involves only non-negative integer powers or only positive integer exponents of a variable in an equation like the quadratic equation, cubic equation, etc.

Given,

Here we have the polynomial function

f(x) = -4(x-2)¹²(6-x)¹¹

Now, we need to find the leading term, degree and the leading coefficient of the polynomial function.

The degree of a polynomial is the highest of the degrees of the polynomial's individual terms. In our case, the degree is 23.

The leading term is the term with the highest degree. In our case, the leading term is 4x²³

The leading coefficient is the coefficient of the leading term. In our case, the leading coefficient is 4.

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Answer:

Refer to the step-by-step explanation, please follow along very carefully. Answers are encased in two boxes.

Step-by-step explanation:

Given the following function, find it's derivative using the definition of derivatives. Evaluate the function when θ=1, 11, and 3/11

\(p(\theta)=\sqrt{11\theta}\)

\(\hrulefill\)

The definition of derivatives states that the derivative of a function at a specific point measures the rate of change of the function at that point. It is defined as the limit of the difference quotient as the change in the input variable approaches zero.

\(f'(x) = \lim_{{h \to 0}} \dfrac{{f(x+h) - f(x)}}{{h}}\)\(\hrulefill\)

To apply the definition of derivatives to this problem, follow these step-by-step instructions:

Step 1: Identify the function: Determine the function for which you want to find the derivative. In out case the function is denoted as p(θ).

\(p(\theta)=\sqrt{11\theta}\)

Step 2: Write the difference quotient: Using the definition of derivatives, write down the difference quotient. The general form of the difference quotient is (f(x+h) - f(x))/h, where "x" is the point at which you want to find the derivative, and "h" represents a small change in the input variable. In our case:

\(p'(\theta) = \lim_{{h \to 0}} \dfrac{{p(\theta+h) - p(\theta)}}{{h}}\\\\\\\Longrightarrow p'(\theta)= \lim_{h \to 0} \dfrac{\sqrt{11(\theta + h)} - \sqrt{11\theta} }{h}\)

Step 3: Take the limit:

We need to rationalize the numerator. Rewriting using radical rules.

\(p'(\theta)= \lim_{h \to 0} \dfrac{\sqrt{11(\theta + h)} - \sqrt{11\theta} }{h} \\\\\\\Longrightarrow p'(\theta)= \lim_{h \to 0} \dfrac{\sqrt{11\theta + 11h} - \sqrt{11\theta} }{h}\\\\\\\Longrightarrow p'(\theta)= \lim_{h \to 0} \dfrac{\sqrt{11}\sqrt{\theta+h} - \sqrt{11}\sqrt{\theta} }{h}\)

Now multiply by the conjugate.

\(p'(\theta)= \lim_{h \to 0} \dfrac{\sqrt{11}\sqrt{\theta+h} - \sqrt{11}\sqrt{\theta} }{h} \cdot \dfrac{\sqrt{11}\sqrt{\theta+h} + \sqrt{11}\sqrt{\theta} }{\sqrt{11}\sqrt{\theta+h} + \sqrt{11}\sqrt{\theta} } \\\\\\\Longrightarrow p'(\theta)= \lim_{h \to 0} \dfrac{(\sqrt{11}\sqrt{\theta+h} - \sqrt{11}\sqrt{\theta} )(\sqrt{11}\sqrt{\theta+h} + \sqrt{11}\sqrt{\theta} )}{h(\sqrt{11}\sqrt{\theta+h} + \sqrt{11}\sqrt{\theta} )} \\\\\\\)

\(\Longrightarrow p'(\theta)= \lim_{h \to 0} \dfrac{11h}{h(\sqrt{11}\sqrt{\theta+h} + \sqrt{11}\sqrt{\theta} )}\\\\\\\Longrightarrow p'(\theta)= \lim_{h \to 0} \dfrac{11}{\sqrt{11}\sqrt{\theta+h} + \sqrt{11}\sqrt{\theta} }\)

Step 4: Simplify the expression: Evaluate the limit by substituting the value of h=0 into the difference quotient. Simplify the expression as much as possible.

\(p'(\theta)= \lim_{h \to 0} \dfrac{11}{\sqrt{11}\sqrt{\theta+h} + \sqrt{11}\sqrt{\theta} }\\\\\\\Longrightarrow p'(\theta)= \dfrac{11}{\sqrt{11}\sqrt{\theta+(0)} + \sqrt{11}\sqrt{\theta} }\\\\\\\Longrightarrow p'(\theta)= \dfrac{11}{\sqrt{11}\sqrt{\theta} + \sqrt{11}\sqrt{\theta} }\\\\\\\Longrightarrow p'(\theta)= \dfrac{11}{2\sqrt{11}\sqrt{\theta} }\\\\\\\Longrightarrow p'(\theta)= \dfrac{11}{2\sqrt{11\theta} }\\\\\\\Longrightarrow p'(\theta)= \dfrac{11}{2\sqrt{11\theta} }\)

\(\therefore \boxed{\boxed{p'(\theta)= \dfrac{\sqrt{11} }{2\sqrt{\theta} }}}\)

Thus, we have found the derivative on the function using the definition.

It's important to note that in practice, finding derivatives using the definition can be a tedious process, especially for more complex functions. However, the definition lays the foundation for understanding the concept of derivatives and its applications. In practice, there are various rules and techniques, such as the power rule, product rule, and chain rule, that can be applied to find derivatives more efficiently.\(\hrulefill\)

Now evaluating the function at the given points.  

\(p'(\theta)= \dfrac{\sqrt{11} }{2\sqrt{\theta}}; \ p'(1)=??, \ p'(11)=??, \ p'(\frac{3}{11} )=??\)

When θ=1:

\(p'(\theta)= \dfrac{\sqrt{11} }{2\sqrt{\theta}}\\\\\\\Longrightarrow p'(1)= \dfrac{\sqrt{11} }{2\sqrt{1}}\\\\\\\therefore \boxed{\boxed{p'(1)= \dfrac{\sqrt{11} }{2}}}\)

When θ=11:

\(p'(\theta)= \dfrac{\sqrt{11} }{2\sqrt{\theta}}\\\\\\\Longrightarrow p'(11)= \dfrac{\sqrt{11} }{2\sqrt{11}}\\\\\\\therefore \boxed{\boxed{p'(11)= \dfrac{1}{2}}}\)

When θ=3/11:

\(p'(\theta)= \dfrac{\sqrt{11} }{2\sqrt{\theta}}\\\\\\\Longrightarrow p'(\frac{3}{11} )= \dfrac{\sqrt{11} }{2\sqrt{\frac{3}{11} }}\\\\\\\therefore \boxed{\boxed{p'(\frac{3}{11} )= \dfrac{11\sqrt{3} }{6}}}\)

Thus, all parts are solved.

The given area of the \(52\frac{1}{2}\) ft. by 33 ft. wall less the areas of the Windows and the Door give the area of the painted part of the wall as  \(\underline{1642\frac{9}{16}}\) ft.²

The area of the painted part of the wall is \(\underline{1642\frac{9}{16}}\) ft.²

The given dimensions of the wall are;

The width of the wall = \(52\frac{1}{2}\) ft.

The height of the wall = 33 ft.

The painted area = Area of the wall - (Area of the widows + The door)

Which gives;

\(52\frac{1}{2} \times 33 - \left(6\frac{1}{4} \times 5\frac{3}{4} + 3\frac{1}{8} \times 4 + 9\frac{1}{2} + 4 \times 8 \right) = \mathbf{ 1642 \frac{9}{16}}\)

The area of the painted part of the wall is \(\underline{1642\frac{9}{16}}\) ft.²

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Answer:

 The probability is  \(P( | \^ p - p| > 0.03) =0.9945\)

Step-by-step explanation:

From the question we are told that

   The population proportion is  \(p = 0.05\)

    The sample size is  n =  408

Generally the standard deviation of the sampling distribution is mathematically represented as

       \(\sigma = \sqrt{\frac{p (1- p)}{n} }\)

=>    \(\sigma = \sqrt{\frac{ 0.05 (1- 0.05)}{408} }\)

=>    \(\sigma = 0.0108\)

Generally the probability that the sample proportion will differ from the population proportion by greater than 0.03 is mathematically represented as

        \(P( | \^ p - p| > 0.03) = P( \frac{|\^ p - p | }{\sigma } > \frac{0.03}{0.0108} )\)

\(\frac{|\^ p -p |}{\sigma }  =  |Z| (The  \ standardized \  value\  of  \ |\^ p -p | )\)

So    

       \(P( | \^ p - p| > 0.03) = P( |Z|> 2.778 )\)

=>   \(P( | \^ p - p| > 0.03) = P( Z < 2.778) - P(Z < -2.777)\)

From the z table  the area under the normal curve to the left corresponding to  2.778  and  -2.778  is

     \(P( Z < 2.778) = 0.99727\)

and

     \(P( Z < -2.778) = 0.0027347\)

So

     \(P( | \^ p - p| > 0.03) = 0.99727 - 0.0027347\)

=>  \(P( | \^ p - p| > 0.03) =0.9945\)

Answer:

275

Step-by-step explanation:

110 x 2.5 = 275

If 110 km is one gallon, you would multiply 110 by 2.5, and that's what i did above.

Answer: 38

Step-by-step explanation:

Step 1: use variables to replace the two numbers

the second number = x

six more than twice the second number = 2x + 6

Their sum is 120: 3x + 6 = 120

Step 2: solve the equation

3x = 114

x = 114/3 = 38

Step 3: check your answer (optional)

six more than twice 38 = 82

38 + 82 = 120

hope this helps

Answer:

the answer will be S = D/T

Answer:

Domain = (-∞, ∞) Range = (-∞, ∞)

End Behavior: As X -> -∞, Y -> -∞ | As X -> ∞, Y -> ∞

Inflection Point: (2,0)

Step-by-step explanation:

The result of the synthetic division is the final row. In this case, the result is -3, 5, -15, 18.

A polynomial is an expression consisting of variable and coefficient and are used to model real world situation it is an equation of degree greater than one where the exponents of the variables can be any non-negative integer for example the polynomial equation x 2 + 3x + 2 represent a parable of windcraft polynomial are used in name variety of field such as mathematics and physics.

The process of synthetic division is used to divide polynomials of the form ax^n + bx^n-1 + ... + c, where a is the coefficient of the highest power of the variable x.

To divide -3 into the polynomial 1 8 9 -18 0, the following steps should be taken:

Step 1: Line up the divisor, -3, to the left of the polynomial, as shown below:

-3 | 1 8 9 -18 0

Step 2: Bring down the first coefficient in the polynomial, which is 1, and place it directly below the -3.

-3 | 1 8 9 -18 0
  -3

Step 3: Multiply the -3 by the first coefficient and place the result in the next row, directly below the 8.

-3 | 1 8 9 -18 0
  -3
 -3

Step 4: Add the result to the 8, and place the new result in the next row.

-3 | 1 8 9 -18 0
  -3
 -3
  5

Step 5: Repeat steps 3 and 4 for each coefficient in the polynomial.

-3 | 1 8 9 -18 0
  -3
 -3
  5
 -15
-15
 18

Step 6: The result of the synthetic division is the final row. In this case, the result is -3, 5, -15, 18.
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Complete questions as follows-
Divide Using Synthetic Division
-3|1 8 9 -18 0

Answer:

The third one

Answer:

b

Step-by-step explanation:

i think the answers b

Answer:

32842

Step-by-step explanation:

837428942

Answer:

tgdfhfghhfrhdtjshdhhdgjggdf

Step-by-step explanation:

Answer:

The selling price is $92

Step-by-step explanation:

First you find out how much 20% is out of 115 an that is $23. Then you do 115-23 and that gives you the answer of $92.

Answer:

6.1

Step-by-step explanation:

I might be wrong, but it in decimal Form.

Answer:

6.1

Step-by-step explanation:

3.5 + 2 \(\frac{3}{5}\) = 3.5 +\(\frac{13}{5}\) = 3.5 + 2.6 = 6.1

Answer: 24km

Step-by-step explanation:

given 1cm : 8km

distance between cafe and restaurant upply store= 3cm

Real distance = 3x8 =24 km

Answer:

30 degrees

Step-by-step explanation:

It's a pateelogram so oppate angles are equal so

x = 30 degrees

Hope this helps :)

The measure of x is 30 degree.

The fundamental characteristics listed below make it simple to recognise parallel lines.

As, we know that the Property of Parallel line are:

Corresponding angle are Equal.

Alternate interior Angles are Congruent.

Vertical angles are Congruent.

As, per the figure we can see that

AB || CD

So, by Alternate Interior Angle

<DCB = <CBA

x = 30

Thus, the measure of x is 30 degree.

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Answer:

0.92 as a fraction is 23/25

Good luck, hope this helped!

Answer:

92/100

Step-by-step explanation:

Explanation

We are told to select the best option that best describes the scores

From the test score of r .Mack,'s 2nd period, w can observe from the plot below that the plot ios symmetrical

The vector whose magnitude is 3 and whose components I. the I and j direction are equal is; <3√2/2i, 3√2/2j>.

It follows that the magnitude of a vector in terms of its components in the i and j direction is;

M = √(x² + y²).

On this note, since the i and j components are equal; x = y and hence, we have;

3 = √(x² + x²).

3² = 2x²

x² = 9/2

x = 3/√2

x = 3√2/2

On this note, the required vector which is as described is; <3√2/2i, 3√2/2j>.

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Answer:

2.5

Step-by-step explanation:

(-5/6 ) / (-1/3)

multiply the numerator and denominator by the same number -3 gives:

(-5 * -3 /6 ) / (-1* -3/3)

(15/6 ) / (3/3)

(15/6 ) / 1

(15/6 )

12/6 + 3/6

2 3/6

2 1/2

2.5

The population of US is 330 million approx.

A percentage is a figure or ratio that can be stated as a fraction of 100. If we need to calculate the percentage of a number, we must divide it by its full value and then multiply it by 100. As a result, the percentage is one part in one hundred. "Per 100" is short for "per percent." The number "%" is used to symbolize it.

Given

population of new york = 2.727272% population of US

population of new york = 9 million

population of US = 1/2.727272% of new york

population of US =  36.6666 x 90,00,000

population of US = 33,00,00,087.9 = 330 million approx

Hence population of US is approx 330 million.

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Answer:

\(5 { \times 54}^{2} \)

Answer:

Height = 0.7857 m = 13/16 m

Step-by-step explanation:

Height x 7 x 2 = 11

Height = 0.7857 m = 13/16 m

The amount of the check with 6 percent of the amount invested was (2) $27.00.

So, 6% of $450:
Then,

Therefore, the amount of the check with 6 percent of the amount invested was (2) $27.00.

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Answer:

The 90% confidence interval = (83.9, 86.1)

Step-by-step explanation:

The formula for confidence interval =

Mean ± z × standard deviation/√n

From the question:

n = 38

Mean = 85 points

Standard deviation = 4 points

Z score for 90% confidence interval = 1.645

85 ± 1.645 × 4/√38

85 ± 1.067416951

Confidence Interval =

85 - 1.067416951

= 83.932583049

≈ 83.9

85 + 1.067416951

= 86.067416951

≈ 86.1

Therefore, the 90% confidence interval = (83.9, 86.1)

Answer:

Step-by-step explanation:

I can help

In interval notation, this can be written as (0, 6), which corresponds to option A.

To determine over which interval of the domain the function is negative, we need to examine the behavior of the linear function between the x-axis intercept and the y-axis intercept.

Given that the linear function intersects the y-axis at (0, 4) and the x-axis at (6, 0), we can calculate the slope of the line using the formula:Slope = (change in y) / (change in x) = (0 - 4) / (6 - 0) = -4 / 6 = -2/3

Since the slope of the line is negative, we know that the function is decreasing as x increases. Therefore, the function is negative over the interval of the domain where x is greater than 0 and less than 6, excluding the endpoints.O

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