Find the derivative of f(x) = 8x + 4 at x = 9

There are two complex roots of the polynomial equation.

They are mathematical expressions involving variables raised with nonnegative integers and coefficients and constants with only operations of addition, subtraction, multiplication, and nonnegative exponentiation of variables involved.

We have been given a polynomial expression as;

[tex]-3x^ 4-7x+17=0[/tex]

Since the Degree of a polynomial is the highest power that its terms (for multi-variables, the power of the term is the addition of the power of variables in that term).

Therefore, the highest power of the given polynomial is 4.

Thus, the Maximum possible roots are 4 but; only 2 are real and 2 are complex.  

Hence, There are two complex roots of the polynomial equation.

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The expression 36 + 4 can be written as a product using the greatest common factor and the distributive law is 4(9 + 1).

There are three basic math properties they are commutative property which states a + b = b + a, associative property which states

a + (b + c) = (a + b) + c and distributive property which states a(b+c) = ab + ac.

We know distributive property states a(b + c) = ab + ac.

Given 36 + 4, the here greatest common factor of 36 and 4 is 4.

∴ The expression 36 + 4 can be written as,

4(9 + 1).

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The answer is (x+5)(x-8)

The statement is true. If two angles are supplementary meaning their sum is 180 degrees, they form a linear pair because in a linear pair too, the sum of the two angles is 180 degrees.

The question is related to the concept of angles in geometry. When angles are supplementary, it means that the sum of the two angles is 180 degrees. In a linear pair, two adjacent angles form a straight line, which also sums up to 180 degrees.

So, if angles ABC and DEF are supplementary, meaning ABC + DEF = 180 degrees, they indeed form a linear pair. Because in a linear pair too, the sum of the two angles is 180 degrees. Therefore, the statement 'If ABC and DEF are supplementary, then ABC and DEF form a linear pair' is true.

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The correct question is given below:

If ABC and DEF are supplementary, then ABC and DEF form a linear pair. True or False?

Answer:

X=4

Step-by-step explanation:

3 * 4 = 12 + 2 = 14.That means your answer is C) 4.

Hope this helps!  :')

The length of each side of the square room with an area 225 ft² is 15 ft.

The area of a square is a product of it's any two sides or a product of diagonals divided by two. If side has a length a then diagonal is a√2.

The perimeter of a square is the sum of the lengths of all the sides.

Given, The area of a square room is 225 ft².

Assuming the length of each side is 'a' feet.

∴ The area of the square room is,

a×a =  225 ft².

a² = 225 ft².

a = ± 15 ft.

As length can not be negative +15 ft is the admissible value.

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The properties needed to prove n + n + n + 2n = 5n are: Distributive Property of Multiplication, Associative Property of Addition, and Commutative Property of Addition.

The commutative property of addition states that when two or more numbers are added, the order in which they are added does not affect the sum. In other words, for any two numbers a and b, a + b = b + a.

The properties required to prove n + n + n + 2n = 5n are as follows:

Thus, these properties can be used.

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Final answer:

To prove n + n + n + 2n = 5n, we use the commutative and associative properties of addition to group and combine like terms, then apply the distributive property to show that the sum equals 5n.

Explanation:

To prove the equation n + n + n + 2n = 5n, we need to use properties of equality and algebraic manipulation. First, we apply the commutative property of addition, which allows us to rearrange the terms in any order without changing the sum.

This property isn't strictly necessary here, as all terms involve 'n', but it's a useful property in general for manipulating equations.

Next, we utilize the associative property of addition, which allows us to group numbers in any combination when adding. In this specific case, we group all the 'n' terms together:

(n + n + n) + 2n

Using the associative property, we can simplify the equation further by combining like terms:

3n + 2n = 5n

Lastly, we apply the distributive property, which in this case shows that multiplying the coefficient (being 1 for n in this example) by the number of times 'n' appears (3 for the first set and 2 for the second set), gives the same result as adding 'n' that many times.

The critical numbers of [tex]\( f(x) = x^6 (x-1)^5 \)[/tex] are [tex]\( x = 0, 1, \frac{5}{6} \)[/tex]. The first derivative test determines maxima/minima by sign change, while the second derivative test confirms concavity but not explicit categorization.

1. Calculate the first derivative [tex]\( f'(x) \)[/tex]:

  Use the product rule and simplify:

[tex]\[ f(x) = x^6 (x-1)^5 \] \[ f'(x) = 6x^5 (x-1)^5 + x^6 \cdot 5(x-1)^4 \] \[ f'(x) = 6x^5 (x-1)^4 [x + 5(x-1)] \] \[ f'(x) = 6x^5 (x-1)^4 (6x - 5) \][/tex]

2. Find critical points:

  Critical points occur where [tex]\( f'(x) = 0 \)[/tex] or is undefined.

  Set [tex]\( f'(x) = 0 \)[/tex]:

 [tex]\[ 6x^5 (x-1)^4 (6x - 5) = 0 \][/tex]

  This equation is zero when:

[tex]\( 6x^5 = 0 \) -- \( x = 0 \)\\ \( (x-1)^4 = 0 \) -- \( x = 1 \)\\ \( 6x - 5 = 0 \) -- \( x = \frac{5}{6} \)[/tex]

  So, the critical numbers are [tex]\( x = 0, 1, \frac{5}{6} \)[/tex].

3. First Derivative Test vs. Second Derivative Test:

  - First Derivative Test: This test uses the sign of the derivative ( f'(x) ) to determine the nature of critical points:

    - If [tex]\( f'(x) > 0 \) to \( f'(x) < 0 \)[/tex] at x, then ( f(x) ) has a local maximum at x.

    - If [tex]\( f'(x) < 0 \) to \( f'(x) > 0 \)[/tex] at x, then ( f(x) ) has a local minimum at x.

  - Second Derivative Test: This test uses the sign of the second derivative [tex]\( f''(x) \)[/tex]:

    - If [tex]\( f''(x) > 0 \), \( f(x) \)[/tex] has a local minimum at x.

    - If [tex]\( f''(x) < 0 \), \( f(x) \)[/tex] has a local maximum at x.

4. Difference between the tests:

  - The first derivative test provides information about the nature (whether maximum or minimum) of critical points based on the sign change of the derivative.

  - The second derivative test provides more precise information by confirming the concavity of the function around the critical point, but it does not give explicit information about whether the critical point is a maximum or minimum (it only confirms the direction of concavity).

To solve this we use the z statistic. The formula for z score is:

z = (x – u) / s

where x is the sample value = less than 16, u is the sample mean = 16.1, s is standard dev = 0.1

z = (16 – 16.1) / 0.1

z = - 1

From the standard distribution tables at z = - 1,

P (z = -1) = 0.1587

So about 15.87% is underweight.

To find the percentage of bags that will likely be underweight (less than 16 ounces), we need to find the area under the normal distribution curve to the left of 16 ounces. The probability is approximately 15.87%.

To find the percentage of bags that will likely be underweight (less than 16 ounces), we need to find the area under the normal distribution curve to the left of 16 ounces. We can use a Z-table or a calculator to find this probability. First, we need to standardize the value of 16 ounces using the formula Z = (X - μ) / σ, where X is the given value, μ is the mean, and σ is the standard deviation. Plugging in the values, we get Z = (16 - 16.1) / 0.1 = -1. This means that 16 ounces is 1 standard deviation below the mean.

Next, we can use the Z-table or a calculator to find the probability associated with a Z-score of -1. From the table or calculator, we find that the probability is approximately 0.1587 or 15.87%. Therefore, approximately 15.87% of the bags will likely be underweight (less than 16 ounces).

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The lines are parallel if and only if the values of their slopes are equal. In a standard form of the equation of the line, the slope is the numerical coefficient of x. Given this condition, we determine the value of a by equation a + 12 and 4a.

    Slope = a + 12 = 4a

 The value of a from the equation is 4.

Answer: 4

Answer:

The correct answer is 5

Step-by-step explanation:

Compound interest formula is :

[tex]A=p(1+\frac{r}{n} )^{nt}[/tex]

1.

A = 3634.51

p = 2564.65

r = ?

n = 2

t = 13

Putting the values in formula, we get

[tex]3634.51=2564.65(1+\frac{r}{2} )^{2*13}[/tex]

=> [tex]3634.51=2564.65(1+\frac{r}{2} )^{26}[/tex]

=> [tex]\frac{3634.51}{2564.65}=(\frac{2+r}{2} )^{26}[/tex]

=> [tex]1.417=(\frac{2+r}{2} )^{26}[/tex]

We get [tex]\sqrt[26]{1.417}=\frac{2+r}{2}[/tex]

We get r = 0.02699 and r = -4.02699 (neglecting the negative value)

We get r = 0.027 (rounded)

And in percentage, it is 2.7%.

So, option C is the answer.

2.

p = 2651.43

r = 2.8% or 0.028

n = 2

t = 18

Putting the values in formula we get;

[tex]A=2651.43(1+\frac{0.028}{2} )^{2*18}[/tex]

=> [tex]A=2651.43(1.014)^{36}[/tex]

A = $4373.67

So, interest earned = [tex]4373.67-2651.43=1722.24[/tex] dollars

Hence, option D. $1,722.25 is the answer.

Answer:To simplify the following expression, we first simplify the terms inside the parenthesis from inner going outer. The first one is [p - (m + n - p)] equal to p - m- n + p = 2p - m - n. Then, n +2p - m - n equal to 2p -m. Then, m -  2p + m equal to 2m -2p. Answer is B

Step-by-step explanation:

add all the numbers and then divide by how many there are in the set to find the mean so

-11+22+-2+-3=6

6÷4=1.5

so 1.5 would be the mean

Hope this helps!

The area of the square is the square of the side thus the approximate length of the square will be 21 ft so option (B) will be correct.

A square is a geometrical figure in which we have four sides each side must be equal and the angle between two adjacent sides must be 90 degrees.

Area of square = Side²

As per the given question,

The area of a square boxing ring is 436 square feet.

It is known that,  

Area = Side²

Side² = 436

Take square root on both sides,

Side = √436 = 20.88 ≈ 21 ft

Hence "The area of the square is the square of the side thus the approximate length of the square will be 21 ft so option (B) will be correct".

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Answer:

The equation of the line would be y = 6x + 2

Step-by-step explanation:

Since we have a slope (6) and a point (0,2) we can use them in point slope form. The slope goes in for m and the point goes in for (x1, y1).

y - y1 = m(x - x1)

y - 2 = 6(x - 0)

y - 2 = 6x

y = 6x + 2

Since the problem is requiring us to use the loan repayment calculator and here is what the calculator gave:

Loan Balance: $25,506.00

Adjusted Loan Balance: $25,506.00

Loan Interest Rate: 6.80%

Loan Fees: 0.00%

Loan Term: 10 years

Minimum Payment: $0.00

Monthly Loan Payment: $293.52

Number of Payments: 120 months

Cumulative Payments: $35,223.07

Total Interest Paid: $9,717.07

It is projected that you will need an annual salary of a minimum $35,222.40 to be capable to have enough money to repay this loan. This approximation assumes that 10% of your gross monthly income will be keen to repaying your student loans. This resembles to a debt-to-income ratio of 0.7. If you use 15% of your gross monthly income to repay the loan, you will need an annual salary of only $23,481.60, but you may experience some financial difficulty. This corresponds to a debt-to-income ratio of 1.1.