if x+2 is a factor of x^3-6x-11x+k, then k=

The vertex οf the parabοla is at the pοint (-3/2, -21/4) and the range οf the functiοn wοuld be (-21/4, infinity).

A quadratic functiοn is a functiοn οf the fοrm  where a, b, and c are cοnstants, and a is nοt equal tο 0. It is a type οf pοlynοmial functiοn that can be graphed as a parabοla, which is a symmetric curve that οpens either upwards οr dοwnwards.

Given the table οf pοints fοr the cοntinuοus quadratic functiοn h(x), we can find the vertex and range οf the functiοn. Since the functiοn is quadratic and cοntinuοus, it can be represented in the standard fοrm [tex]$f(x)=a(x-h)^{2}+k,$[/tex], where (h, k) is the vertex οf the parabοla.

Tο find the vertex, we can use the fact that the x-cοοrdinate οf the vertex is given by -b/2a, where a and b are the cοefficients οf the quadratic term and the linear term, respectively. In this case, a = 1 (since the functiοn is cοntinuοus and quadratic), and b can be fοund using any twο pοints οn the parabοla:

[tex]\rm b=(h(x_2)-h(x_1))/(x_2-x1)=(4-7)/(-2+1)=3$[/tex]

Therefοre, the x-cοοrdinate οf the vertex is x = -b/2a = -3/2. Tο find the y-cοοrdinate οf the vertex, we can evaluate the functiοn at this value οf x:

[tex]$\rm h(-3/2)=(1)(-3/2-h)^{2}+k$[/tex]

Tο sοlve fοr k, we can use οne οf the pοints οn the parabοla, say (-6, 12):

[tex]$12=(1)(-6-h)^{2}+k\,$[/tex]

Expanding and simplifying, we get:

[tex]$12=(h-6)^{2}+k$[/tex]

Substituting -3/2 fοr h, we get:

[tex]$\begin{array}{l}{{12=(-(3/2)-6)^{2}+k}}\\\\ {{12=81/4+k}}\\\\ {{k=-21/4}}\end{array}$[/tex]

Therefοre, the vertex οf the parabοla is at the pοint (-3/2, -21/4).

Tο find the range οf the functiοn, we can lοοk at the shape οf the parabοla. Since the cοefficient οf the quadratic term is pοsitive, the parabοla οpens upwards, and the vertex is the lοwest pοint οn the graph. Therefοre, the range οf the functiοn is all real numbers greater than οr equal tο the y-cοοrdinate οf the vertex, which is -21/4. In interval nοtatiοn, we can write the range as (-21/4, infinity).

Hence, the vertex οf the parabοla is at the pοint (-3/2, -21/4) and the range οf the functiοn wοuld be (-21/4, infinity).

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Answer:f(2)=27
             g(-4)=3
             h(3)=28/9

Step-by-step explanation:
f(x)=-3I x- 11 I, when f(2)

f(2)= -3 I 2-11 I
f(2)= -3 I -9 I
f(2)= -3*-9
f(2)=27

g(x)=1 + the square root of x+8, when g(-4)

g(-4)=1+the square root of -4+8
g(-4)=1 + the sqaure root of 4( 2= the sqaure root of 4 )
g(-4)=1+ 2
g(-4)=3



h(x)=3x^2 +1/ x^2, when h(3)
h(3)=3(3)^2 +1/ 3^2
h(3)=3(9)+1/9
h(3)=28/9


HOPE IT HELPS :)

By analyzing the segmented income statement, Millard Corporation can identify which sales regions are contributing to the overall losses and focus on improving their performance.

We analyze the segmented income statement for Millard Corporation.

Based on the given information, the company distributes office products to three sales regions:

West, Central, and East. Each region has its own manager and sales staff.
To prepare a segmented income statement for May, the company should follow these steps:
Identify the revenue generated by each sales region.

This can be found by tracking the sales from each region and recording them separately.
Allocate direct costs to each sales region.

Direct costs are those that can be directly traced to each region, such as the salaries of the regional manager and sales staff.
Allocate indirect costs to each sales region.
Calculate the contribution margin for each sales region by subtracting the direct costs from the revenue.

This will show the profitability of each region before accounting for the indirect costs.
Subtract the allocated indirect costs from the contribution margin to determine the operating income (or loss) for each sales region.

This information will also help management make informed decisions on resource allocation, budgeting, and strategic planning for the future.

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Answer: 24 problems done before dinner

Step-by-step explanation:

Take the 32 total math problems and divide it by 3/4 (the amount of problems done before dinner) getting you 24 problems done before dinner

According to the given information, the equation that represents the proportional relationship is y = (1/4)x

What is proportion?

Proportion is a mathematical concept that describes the equality of two ratios. In other words, it is a statement that two ratios or fractions are equal.

For example, if we have two fractions, a/b, and c/d, we can say that they are in proportion if:

a/b = c/d

We can see that the ratio between X and Y is always 4:1, which means that Y is one-fourth of X. We can write this as:

Y = (1/4)X

Therefore, the equation that represents the proportional relationship is:

y = (1/4)x

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Answer:

Step-by-step explanation:

Fill in the blanks using the available answer choices. The vertices of a quadrilateral are A(–3, 1) , B(4, 2) , C(9, –3) and D(2, –4) . Complete the statement to best classify what type of quadrilateral ABCD is. In quadrilateral ABCD , have equal length and there are right angles, so ABCD is best classified as a .

The trees in Aspen Grove Park are under 15 feet tall are 60%

the total number of trees in Aspen Grove Park, but we can find out that number by using the given percentage of trees that are over 15 feet tall.
To do this, we can use a proportion:
[tex]40/100 = 32/x [/tex]
Simplifying this, we can cross-multiply:
[tex]40x = 32 * 100 [/tex]
[tex]40x = 3200 [/tex]
[tex]x = 80[/tex]
So, there are a total of 80 trees in Aspen Grove Park.
Now, we can calculate the percentage of trees that are not over 15 feet tall by subtracting the percentage of trees that are over 15 feet tall from 100%:
[tex]100% - 40% = 60% [/tex]

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If you were to buy one of each bond today, you would have to spend b. ABC $1104.75 and XYZ $1100.50.

The following algorithm must be used to determine a bond's price:

[tex]Bond\ price=(\frac{coupon\ payment}{(1+yield)^{time}} )+(\frac{coupon\ payment}{(1+yield)^{time+1}} )+...+(\frac{coupon\ payment+face\ value}{(1+yield)^{Time+n}} )[/tex]

Where:

dividend Payment: The bond's yearly dividend payment (in dollars)

Yield: The bond's yield to expiration (as a decimal)

Time: the interval between the issuance of each coupon and the receipt of its monetary value. (in years)

Face worth: The bond's face worth (in dollars)

The price of each bond can be determined as follows using the data in the table:

a. For bond ABC:

Coupon Payment = $7.50 (7.5% of $1000 face value)

Yield = 3.04% (convert 3.04 to a decimal)

Time = 0.5 years (since the bond's maturity date is July 15 and today marks the midway point between those dates)

Face Value = $1000

[tex]Bond\ price=(\frac{7.5}{(1+0.0304)^{0.5}} )+(\frac{7.5}{(1+0.0304)^{1.5}} )+(\frac{1000}{(1+0.0304)^{2}} )[/tex]

= 7.356 + 7.235 + 925.984

= $940.575

Since we are purchasing one bond and the face value is $1,000, we split this amount by 10 to get the price for one bond:

Price for one bond ABC = $940.575 / 10 = $94.058

b. For bond XYZ:

Coupon Payment = $84 (8.4% of $1000 face value)

Yield = 1.7% (convert 1.7 to a decimal)

Time = 0.5 years

Face Value = $1000

[tex]Bond\ Price = (84 / (1 + 0.017)^{0.5}) + (84 / (1 + 0.017)^{1.5}) + (1000 / (1 + 0.017)^2)[/tex]

= 83.379 + 81.838 + 968.661

= $1133.878

Since the face value of a bond is $1,000 and we are only purchasing one, we split this amount by 10 to get the price for one bond:

Price for one bond XYZ = $1133.878 / 10 = $113.388

Therefore, the correct answer is:b. ABC: $1104.75 XYZ: $1100.50

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An expression that equals 24 + 3B in standard form is: 36 + 9m

What is standard form ?

To find an expression that equals 24 + 3B in standard form, we first need to find the value of B and then substitute it into the expression.

Given that B = 3m + 4, we can substitute it into 24 + 3B to get:

24 + 3B = 24 + 3(3m + 4)

Simplifying the expression inside the parentheses, we get:

24 + 9m + 12

Combining like terms, we get:

36 + 9m

Therefore, an expression that equals 24 + 3B in standard form is:

36 + 9m

What is an expression?

In mathematics, an expression is a combination of numbers, symbols, and operators (such as +, -, ×, ÷, etc.) that represents a value or a relationship between values. Expressions can be simple, such as a single number or variable, or complex, such as a combination of several terms with different operators.

For example, 2x + 3y - 5 is an expression that consists of three terms (2x, 3y, and -5) with two operators (+ and -). This expression can be evaluated for different values of x and y to obtain different numerical results.

Expressions can be used to represent mathematical formulas, describe geometric shapes and patterns, and solve real-world problems in a wide range of fields, including science, engineering, finance, and statistics.

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Complete question is: An expression that equals 24 + 3B in standard form is: 36 + 9m,

An expression to represent the shaded region shown in the Venn diagram is AuB.

A Venn diagram is a visual tool used to show the similarities and differences between two or more sets of items or concepts. It consists of one or more overlapping circles, with each circle representing a set and the area where the circles overlap representing the intersection of the sets.

In this context, the symbol u represents the union between two or more of the circles. Based on this, the correct expression to represent the Venn diagram is AuB.

Note: This question is incomplete, below I attach the missing image:

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The inverse function of f, what is the value of (ƒ-¹)' (-4) -1/16 ∓ i/(8√3)

We know that the point (1,-4) is on the graph of f, so we can use this information to find the value of x for which f(x) = -4:

-4 = -x³ + 3x² + (6x)

-x³ + 3x² + 6x + 4 = 0

We can solve this equation using various methods, such as graphing, factoring, or using the cubic formula. One possible method is to use synthetic division to test factors of the constant term (4) and find one that gives a remainder of zero. By testing -1 as a factor, we get:

-1 | 1 -3 6 4

-1 4 -10

1 -4 10 -6

Therefore, the equation can be factored as:

-(x + 1)(x² - 4x + 6) = 0

Using the quadratic formula or completing the square, we can find the roots of the quadratic factor:

x = 2 ± √2i

Since the function f is not one-to-one, we must restrict its domain to make it invertible. One possible domain is x ≤ 2, so the inverse function f⁻¹(x) is:

f⁻¹(x) = 1 ± √(1 - 2x)/x

Note that there are two possible values for f⁻¹(-4), one for each branch of the inverse function. To find the value of (f⁻¹)'(-4), we need to take the derivative of the inverse function at x = -4:

(f⁻¹)'(x) = -1/x² ∓ √(1 - 2x)/2x³

(f⁻¹)'(-4) = -1/16 ∓ i/(8√3)

Therefore, the value of (f⁻¹)'(-4) is either -1/16 - i/(8√3) or -1/16 + i/(8√3), depending on which branch of the inverse function we choose.

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The probability of selecting a vowel first and then not a vowel second is 2/6 x 5/5 = 10/30 = 1/3.

Probability is a branch of mathematics that deals with the likelihood of something happening. It is used to quantify the chance of a certain event occurring and can help to predict the outcome of a given situation. Probability is based on the concept of randomness, which is the idea that an event's outcome is determined by chance and cannot be controlled or predicted.

The word "replacement" contains 2 vowels (e,a) and 4 consonants (r,p,l,c). Therefore, the probability of selecting a vowel first is 2/6 (2 out of 6 cards are vowels). Since there are 5 cards left after the first selection, the probability of selecting a non-vowel second is 5/5 (5 out of 5 cards are non-vowels).

Therefore, the probability of selecting a vowel first and then not a vowel second is 2/6 x 5/5 = 10/30 = 1/3.

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Complete questions as follows-
You select a card at random from the cards that make up the word “replacement”. Without replacing the card, you choose a second card.
Find the probability of choosing a vowel and then not a vowel.  There is 1 letter for each card.explain how you got the answer please?

Toy Cost Percentage

Aditya Kashyap

ohn spent 20% of his money on food. He spent 2/5 of the remainder on a toy. The toy cost $12.

(a) What percentage of his money did he spend on the toy?

b) How much money did he have at first?

(a) To find the percentage of his money that John spent on the toy, we need to first find the total amount of money he had left after spending 20% on food.

Let's say John had x amount of money initially.

Then, he spent 20% of x on food, which is 0.2x.

So, he had (x - 0.2x) = 0.8x amount of money left.

Next, he spent 2/5 of this remaining amount on a toy, which cost $12.

Therefore, 2/5 of 0.8x = $12

Simplifying this, we get:

0.32x = $12

x = $37.50

So, John had $37.50 initially.

Now, to find the percentage of his money that he spent on the toy, we can use the formula:

Percentage = (Amount spent on toy / Total initial amount) x 100

Amount spent on toy = $12

Total initial amount = $37.50

Plugging these values into the formula, we get:

Percentage = (12 / 37.50) x 100

Percentage = 32%

Therefore, John spent 32% of his money on the toy.

(b) John had $37.50 at first.

Answer:

Step-by-step explanation:

Bold = $8 or more per week,    Underlined = less than 8 per week

$5 = 1 person

$0 = 3 people

$10 = 2 people

$1 = 1 person

$8 = 2 people

The total amount of people = 1+3+2+1+2 = 9

The total amount of people who earn less than $8/week = 1+3+1 = 5 people

The total amount of people who earn $8 or more/week = 2+2 = 4 people

Conclusion, 5/9 total people earned less than $8/week

4/9 people earn $8 or more/week

Mistake there were less than half people who earned $8 or more per week unlike Pete stated

Correction; more than half of Pete's friends earn less than 8 dollars per week

Answer: Starting with the expression:

tan(x)(cot(x) - cos(x))

Recall that cot(x) is the reciprocal of tan(x), so we can substitute cot(x) = 1/tan(x):

tan(x)(1/tan(x) - cos(x))

Simplifying:

1 - cos(x)tan(x)

Next, we can use the identity cos(x) = 1/sec(x) to eliminate the cotangent term:

1 - (1/sec(x))tan(x)

Now, we can use the identity tan(x) = sin(x)/cos(x) and sec(x) = 1/cos(x) to express the expression in terms of sine and cosine:

1 - (1/cos(x))(sin(x)/cos(x))

Simplifying:

cos(x)/cos(x) - sin(x)/cos(x)

= (cos(x) - sin(x))/cos(x)

Therefore, the simplified expression in terms of sine and cosine is:

(cos(x) - sin(x))/cos(x)

Step-by-step explanation:

The numbers "1⁄2, 3⁄4, 60%, .56, 85% " are represented on number line such as given below in figure.

A number line is a pictorial representation of numbers on a straight line. It’s a reference for comparing and ordering numbers. It can be used to represent any real number that includes every whole number and natural number. Just to recollect, the whole number is a set of numbers that include all counting numbers (1, 2, 3,4,5,6 …….) and zero (0), whereas the natural number is the set of all counting numbers i.e. 1, 2, 3, 4, 5, 6……..

Writing numbers on a number line make it easier to compare the numbers. From the above figure, we can see that the integers on the left side are smaller than the integers on the right side. For example, 0 is less than 1, -1 is less than 0, -2 is less than -1, and so on.

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1. The solutions of the equation 6/(x+1)= x/(x-1) are x = 2 and x = 3.

2. The solutions of the equation x+ 4/x= -5 are x = -1 and x = -4.

What are the solutions ?

1. 6/(x+1) = x/(x-1)

To solve this equation, we first need to get rid of the fractions by multiplying both sides of the equation by the least common multiple of the denominators, which is (x+1)(x-1):

6(x-1) = x(x+1)

Expanding the left side, we get:

6x - 6 = x² + x

Moving all the terms to one side, we get:

x² - 5x + 6 = 0

This is a quadratic equation that can be factored as:

(x - 2)(x - 3) = 0

So, the solutions are x = 2 and x = 3. However, we need to check if these solutions are valid, because we cannot divide by zero.

Checking x = 2:

6/(2+1) = 2/(2-1)

2 = 2, which is true

Checking x = 3:

6/(3+1) = 3/(3-1)

3/2 = 3/2, which is true

Therefore, the solutions are x = 2 and x = 3.

2. x + 4/x = -5

To solve this equation, we first need to get rid of the fraction by multiplying both sides of the equation by x:

x² + 4 = -5x

Moving all the terms to one side, we get:

x² + 5x + 4 = 0

This is a quadratic equation that can be factored as:

(x + 1)(x + 4) = 0

So, the solutions are x = -1 and x = -4. However, we need to check if these solutions are valid, because we cannot divide by zero.

Checking x = -1:

-1 + 4/(-1) = -5

-1 - 4 = -5, which is true

Checking x = -4:

-4 + 4/(-4) = -5

-4 - 1 = -5, which is true

Therefore, the solutions are x = -1 and x = -4.

What is common multiple?

A common multiple is a number that is a multiple of two or more given numbers. For example, the common multiples of 2 and 3 are 6, 12, 18, 24, etc. These are all numbers that can be divided by both 2 and 3 without a remainder. A common multiple is "common" to the given numbers because it is a multiple of all of them.

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Complete question is:

1. The solutions of the equation 6/(x+1)= x/(x-1) are x = 2 and x = 3.

2. The solutions of the equation x+ 4/x= -5 are x = -1 and x = -4.

Answer: 40

Step-by-step explanation: out of 600 members, 360 (600*0.6) of them were males. When 200 new members joined the club, the total number of members would be 800. If 50% of 800 members were males, then 400 are males. 40 new male members joined.

Answer:

A 30 degree angle is an acute angle cause its less than 90 degrees

Answer:

A thirty degree angle is an acute angle.

A thirty degree angle is formed when two lines meet or intercept at a point .

A thirty degree angle is one in which the measure is less than 90 degrees

Answer:

To find the area and perimeter of a rhombus, you can follow these steps:

1. Find the length of one side of the rhombus.

2. Use the length of one side to find the length of the diagonals. The diagonals of a rhombus are perpendicular bisectors of each other, which means that they intersect at a 90-degree angle, and each diagonal cuts the rhombus into two congruent right triangles. The length of each diagonal can be found using the Pythagorean theorem: diagonal^2 = (side/2)^2 + (side/2)^2.

3. Once you have found the length of the diagonals, you can use them to calculate the area of the rhombus. The area of a rhombus is equal to half the product of the length of the diagonals: area = (diagonal1 x diagonal2) / 2.

4. To find the perimeter of the rhombus, you simply add up the lengths of all four sides: perimeter = 4 x side.

In summary, the steps to find the area and perimeter of a rhombus are:

1. Find the length of one side of the rhombus.

2. Use the length of one side to find the length of the diagonals.

3. Use the diagonals to calculate the area of the rhombus: area = (diagonal1 x diagonal2) / 2.

4. Add up the lengths of all four sides to find the perimeter: perimeter = 4 x side.

To find the area and perimeter of a rhombus, you can use the following formulas:

Area = (diagonal 1 × diagonal 2) / 2

Perimeter = 4 × side length

A rhombus is a quadrilateral that has four equal sides.

Some of the properties we need to know are:

- The opposite sides are parallel to each other.

- The opposite angles are equal.

- The adjacent angles add upto 180 degrees.

We have,

To find the area and perimeter of a rhombus, you can use the following formulas:

Area of a Rhombus:

The area of a rhombus can be found by multiplying the length of the two diagonals and dividing by 2. That is,

Area = (diagonal 1 × diagonal 2) / 2

The perimeter of a Rhombus:

The perimeter of a rhombus can be found by multiplying the length of one side by 4. That is,

Perimeter = 4 × side length

Thus,

To find the area and perimeter of a rhombus, you can use the following formulas:

Area = (diagonal 1 × diagonal 2) / 2

Perimeter = 4 × side length

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Answer:

There are no two numbers whose product is 52 and whose sum is 11.

Step-by-step explanation:

give the 1st number is x and the 2nd number is y, then

x + y = 11 and xy = 52

x + y = 11 => y = 11 - x

x(11 - x) = 52

11x - x^2 = 52

=> x^2 - 11x + 52 = 0

Using quadratic formula: ax^2 + bx + c = 0

with a = 1, b = -11, c = 52

=> x = [-b ± √(b^2 - 4ac)]/2a

=> x = [-(-11) ± √((-11)^2 - 4x1x52)]/2x1

=> x = [11 ± √(121 - 208)]/2

=> x = [11 ± √(-87)]/2

Since the square root of a negative number is not a real number, there are no real solutions to this equation. Therefore, there are no two numbers whose product is 52 and whose sum is 11.

Tara invests $555 into a savings account that has an interest rate of 12.6% and is compounded quarterly. It will take 18.6 years for the account to reach a balance of $5,600.

The amount that the lender charges the client above and beyond the initial amount is referred to as the interest rate. Given the time worth of money, a person who deposits money in a bank or other financial organisation also gets extra revenue known as interest received by the depositor.

Using the quarter compound formula given below-

[tex]$ \rm A = P (1 + \frac{r}{4})^{4 \times t}[/tex]

Where,

Interest in a year (r)= 12.6% = 12.6/100= 0.126

Actual amount (P)= $555

Final amount (A)= $5,600

Lets solve:

[tex]5,600 = 555(1+0.126/4)^{4t[/tex]

Or, [tex](4.126/4)^{4t}= 5600/555[/tex]

Or, 4t ln(4.126/4)= ln 5600/555

Or, 4t =74.532

Or, t ≈ 18.6

Hence the correct answer is 18.6 years

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Answer: 6 + 18j

Step-by-step explanation: you distribute the 3

Answer:

Step-by-step explanation:

(a) We can use the standard normal distribution to solve this problem. We first need to standardize the distribution by using the formula:

Z = (X - μ) / σ

where X is the transaction time, μ is the mean, σ is the standard deviation, and Z is the standard normal variable.

For 5 customers to finish the transaction within 20 seconds, we need to find the probability that 5 out of 6 customers have a transaction time less than or equal to 20 seconds. We can use the binomial distribution to find this probability:

P(X = 5) = 6C5 * (0.5)^5 * (0.5)^1 = 0.2344

where 6C5 is the number of ways to choose 5 customers out of 6.

(b) After the network upgrade, the transaction time will be reduced by 15%, so the new mean and standard deviation are:

μ' = 0.85 * μ = 17 seconds

σ' = 0.85 * σ = 4.25 seconds

(c) To find the 97th percentile of Y, we need to find the value of t such that P(Y ≤ t) = 0.97. Since Y is a normally distributed variable, we can standardize it using the formula:

Z = (Y - μ') / σ'

Then we can find the value of t using a standard normal distribution table or calculator:

Z = 1.88

t = μ' + Z * σ' = 17 + 1.88 * 4.25 = 25.99 seconds

(d) After the upgrade, a higher proportion of customers can finish the transaction within 20 seconds. This is because the mean transaction time has decreased from 20 seconds to 17 seconds, which means that more customers will have a transaction time less than or equal to 20 seconds.

Step-by-step explanation:

The quantity of a drug, Q mg, present in the body t hours after an injection of the drug is given is Q =f 140te 0.6t Find f (1) , f' (1) , f (6) ,and f' (6) .