Given the function h(x)=-x²+4x+12, determine the average rate of change of the function over the interval -1≤x≤8

So, the question can be displayed in 362880 ways.

A multiple-choice question on an online quiz has 9 answer choices, which are shown in random order to each student. The number of ways the question can be displayed is determined by the number of permutations of the 9 answer choices. In this case, the question can be displayed in 9! (9 factorial) different ways.

9! is the shorthand notation for 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1. Factorial notation is used to indicate the product of all integers from 1 to a given number. In this case, 9! means that the product of all integers from 1 to 9 is calculated.

The reason why it is 9! and not 9^9 is because, when arranging the 9 items in different ways, order matters. So, in the first slot, we have 9 options to choose from, in the second slot, we have 8 options left to choose from, in the third slot we have 7 options left and so on.

Therefore, the question can be displayed in 362880 ways.

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The abbreviation 9! stands for 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1. To represent the sum of all integers from 1 to a specified number, the factororial notation is used. 9! in this context denotes the computation of the product of all numbers from 1 to 9.

Because order counts when arranging the 9 items in various ways, the answer is 9! rather than 99. Therefore, we have nine options to choose from in the first spot, eight options are still available in the second slot, seven options are still available in the third slot, and so on.

The midsegment of a trapezoid with only the coordinates given can be determine by following steps 1,2 and 3 below

The midsegment of a trapezoid is a line segment that connects the midpoints of the two parallel sides of the trapezoid.

To solve for the midsegment of a trapezoid with only the coordinates given, you can use the following steps:

1. Find the coordinates of the midpoints of the two parallel sides of the trapezoid. To do this, you need the coordinates of the four vertices of the trapezoid. For example, if the trapezoid has vertices A(x1, y1), B(x2, y2), C(x3, y3), and D(x4, y4), the midpoints of the two parallel sides are:

Midpoint of AB: ((x1 + x2)/2, (y1 + y2)/2)

Midpoint of CD: ((x3 + x4)/2, (y3 + y4)/2)

2. Use the coordinates of the two midpoints found in step 1 to find the equation of the line that contains the midsegment. The slope of the midsegment is the average of the slopes of the two parallel sides of the trapezoid.

The equation of the line can be written in slope-intercept form (y = mx + b) or point-slope form (y - y1 = m(x - x1))

3. Once you have the equation of the line you can use it to find the y-intercept b and the slope m.

For example:

Trapezoid with coordinates A(2,3), B(4,4) , C(7,5) and D(5,6)

Midpoint of AB: (3,3.5)

Midpoint of CD: (6,5.5)

Slope of AB = (y2-y1)/(x2-x1) = (4-3)/(4-2) = 1/2

Slope of CD = (y4-y3)/(x4-x3) = (6-5)/(5-7) = -1/2

Midsegment slope = (1/2 + (-1/2))/2 = 0

The equation of the midsegment line is y = 0x+b

by using the point (3,3.5)

we can find the value of b = 3.5

Thus, the equation of midsegment is y = 0x + 3.5

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The types of sum are following :

Sum of numbers is defined as the total which is result of adding numbers. Now, we have to discuss about types of sum. It is represented by plus sign (+) and summation, sigma symbol.

Type 1 : Sum of one-digit numbers : We can get the sum of 2, single-digit numbers such as 1, 2, 3, 4, 5, 6, 7, 8, 9 with different combinations. For example: 3 + 15 = 18.

Type 2 : Sum of two-digits numbers : first add the one's place digits if result is greater than 9 then transfer carry digit. After that add the ten's place digits with carry digit. For example, 35 + 56 = 91

Sum of n natural numbers : The summation formulas are used to calculate the sum of the sequence. To write the sum of more terms, say n numbers of a sequence {aₙ}, we use the summation formula instead of writing the whole sum, i.e., a₁ + a₂ + ------+ aₙ = ∑ aᵢ ; 1≤ i ≤ n. There are various types of sequences such as arithmetic sequence, geometric sequence, etc and hence there are various types of summation formulas of different sequences.

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Answer:

[tex]\frac{16}{3}[/tex]

Step-by-step explanation:

Multiply the whole number by the denominator

5 × 12 = 60

Add the answer from Step 1 to the numerator

60 + 4 = 64

Write the answer from Step 2 over the denominator

64/12

Simplify the fraction :

Find the greatest common factor of 64 and 12

GCF of 64 and 12 = 4

64 ÷ 4   = 16

______

12 ÷ 4    = 3

The mixed number 5 4/12 converted to an improper fraction is, therefore :

16/3

Answer:

16/3

Step-by-step explanation:

=5x12

=60.

2. Add the product to the numerator

=60+4

=64.

3. Answer = 64/12.

4. Simplify the answer by using the

greatest common factor of 64 and

12, which is 4.

=64÷4

12÷4

=16

3

The improper fraction for 5 4/12 is 16/3.

The given statement " the notation "f(x)" is another way of representing y-values in a function" is true because f (x) and y are the same things.

The notation f(x), read as "f of x", indicates a function named f. It reflects that 'y is a function of x'. The letter 'x' refers to the input value or independent variable. While the letter 'y' is replaced by f(x) and it refers to the output value or dependent variable.

The notation 'f (x)' is exactly the same as that of 'y'. Even on graphs, y-axis can be labelled with 'f (x)'.

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Answer:

We are given that the mass of a cube, M, is proportional to the cube of the length of its edge, L. This means that we can write the relationship between M and L as:

M = kL^3

where k is the proportionality constant.

We are also given that when the length of the cube's edge is 35 cm, the mass of the cube is 40 kg. So we can use this information to find the value of the proportionality constant k.

35 cm = 0.35 m (converting cm to m)

Now we can substitute the given values into the equation and find k:

40 = k(0.35)^3

k = 40 / (0.35)^3

Now that we have the value of k, we can use it to find the mass of the cube when the length of its edge is 0.6 m.

M = kL^3

M = 40 / (0.35)^3 * (0.6)^3

M = 40 / (0.35)^3 * (0.216)

M = 40 / (0.003375) * (0.216)

M = 40 / 0.00726 * 0.216

M = 40 / 0.015856

M = 2511.53 kg (to 2 decimal places)

So the mass of the cube when the length of its edge is 0.6m is 2511.53kg

The answer would be M = 204.6 kg

The mass of the cube, M, is given by the equation M = kL^3, where k is the proportionality constant.

Given that M = 40 kg when L = 0.35 m, we can find k by substituting these values into the equation:

40 = k(0.35)^3

k = 40 / (0.35)^3

= 40 / 0.0421875

= 947.125

To find M when L = 0.6 m, we can substitute this value of L into the equation:

M = 947.125 * (0.6)^3

= 947.125 * 0.216

= 204.6

The given information is that M is proportional to the cube of L. This means that the mass of the cube is directly proportional to the cube of the length of its edge. The proportionality constant k is found by using the given values of M and L, and then using that constant value we can find the mass when we know the length of the edge.

We have found the mass of the cube when the length of its edge is 0.6m is 204.6 kg by using the proportionality constant and equation we have derived from the given information.

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The required (A) maximum height of the ball is 60 yards, (b) the height of the Brad cannot be justified and (C) the horizontal distance the ball traveled is 300 yards.

Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.

Here,
Draw the function of the ball on the coordinate plane, as shown.
From the figure, the maximum height of the golf ball is given as 60 yards while the maximum horizontal distance is 300 yards.

Thus, the required (A) maximum height of the ball is 60 yards, (b) the height of the Brad cannot be justified and (C) the horizontal distance the ball traveled is 300 yards.

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When drawing horizontal or vertical lines with a triangle, you need to use two triangles at the same time. You can draw lines at angles of 30, 45, 60, and 90 degrees by combining the two.

Additionally, the values of the side lengths of this triangle are always inversely proportional to one another. and x2 is the side length that is in opposition to the 90-degree angle. likewise, the side length that is in opposition to the 90-degree angle is 72. Additionally, the side length at the opposite end of the 45-degree angle is 2.

Tips for Remembering the 30-60-90 Triangle Rule Remembering the ratio 1 is all it takes to remember the 30-60-90 triangle rules: √3 : 2, and being aware that the longest side length is always in opposition to the largest angle (90 degrees) and the shortest side length is always in opposition to the shortest angle (30 degrees).

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The assertion is untrue. Regardless of whether a matrix is considered to be an augmented matrix for a linear system, the procedure can be applied to any matrix.

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Sector perimeter equals 2 radius plus arc length. The formula for calculating arc length is: arc length = l = (/360) 2 r. As a result, the sector's perimeter is equal to 2 Radius plus ((/360) 2r).

The perimeter of a form is its entire outer circumference. Using what we know about determining the length of an arc, we can get the perimeter of a sector. The intersection of two radii and an arc creates a sector. We must sum these values in order to determine the perimeter. Arc length plus two is the perimeter.

Sector area is easily calculated by multiplying the central angle by the radius squared and dividing by two: Sector Area is equal to r2 / 2.

When the sector angle = 360° , curved length of the arc = 2πR

Hence when the central angle = 80 degree, the curved length = (80/360x(2πR)

= 1.3963 R = 1.3963 * 6 = 8.3776 cm.

Hence the perimeter = R + R + 8.3776 = 20.3776 cm

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Answer:

-27

10x +8.

Step-by-step explanation:

x² - 9 ÷ x² - 4x - 5

=x²+5x+4 x² - 2x - 15

x² - 9 × x² - 2x - 15

=x² +5x +4 x² - 4x - 5

-9 × 3

=5x. 4. 2

-27.

=10x + 8 .

Roman and Sienna read equal number of the pages of the book.

Comparison or comparing is the act of evaluating two or more things by determining the relevant, comparable characteristics of each thing, and then determining which characteristics of each are similar to the other, which are different, and to what degree.

Given that, Roman and Sienna are comparing the number of pages they’ve each read over the Winter Break. Roman said he read 40% of his book, which has a total of 200 pages. Sienna’s book has a total of 400 pages, and she read 1/5 of it.

Book read by Roman = 40% of 200

= 40 / 100 x 200

= 80 pages

Book read by Sienna = 1/5 of 400

= 400 x 1/5

= 400/5

= 80 pages

Since, both of them read equal number of pages.

Hence, Roman and Sienna read equal number of the pages of the book.

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The average midterm exam grade for the entire class is 82.

The middle value in a set of numbers is the average, which is calculated by dividing the total of all the values by the number of values.

Here given that,

Math class contains 18 twelve graders.

Also contains 4 eleventh graders

Total number of students = 18 + 4 = 22

Total marks of students in the twelve grade = 18 x 83 = 1494

Total marks of students in the eleventh grade = 4 x 79 = 316

Total marks = 1494 + 316 = 1810

Therefore to find the average grade of midterm exam is :

1810 / 22 = 82.2

Therefore the average grade on the midterm exam for the entire class is 82.

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The inverse of a linear graph can be graphed by x and y coordinates.

When a function is stated in the form which is y = mx + b, where m and b are real integers and m is not equal to 0, the function is said to be linear.  The variables in this equation are x and y, while the coefficients are m and b. A linear graph is the graph of a linear function, where a linear function has a straight line as its graph; its slope is m and its y-intercept is (0,b). The inverse of a linear graph can be thus created as -

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for  x² + 2x + 16 = 0, we have to add (2/2)²  number would have to be added to "complete the square"

A quadratic equation is a second-order polynomial equation in a single variable x , ax2+bx+c=0. with a ≠ 0 .

x² + 2x + 16 = 0

Subtract 16 on both sides

x² + 2x = -16  

(Add (2/2)²  on both sides)

x²  + 2x + 1 = -16 + 1    

Factor using Perfect Square Trinomial and add -16 and 1

(x + 1)²  = -15    

Square root on both sides

x + 1 = ±√-15    

Subtract 1 on both sides and use i = √-1

x = -1 ± i√15    

Hence, for  x² + 2x + 16 = 0, we have to add (2/2)²  number would have to be added to "complete the square"

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To find the value of x in a logarithmic function, you need to use the definition of logarithms, which states that log_b x is the power to which b must be raised to produce x.

In other words, if f(x) = log_b x, then b^(f(x)) = x. To find x, you simply need to raise b to the power of f(x), using the inverse of the logarithmic function, which is the exponential function. This can be done using a calculator or by using logarithmic rules and properties to simplify the expression and solve for x. It's important to remember that logarithmic functions are only defined for positive values of x and that the base b must be positive and not equal to 1.

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Answer: the most accurate measurement of Pat's temperature in degrees Celsius is 37.3 degrees.

Step-by-step explanation:

The conversion from Fahrenheit to Celsius is C = 5/9 (F-32).

First, we substitute Pat's temperature of 99.3 degrees Fahrenheit into the equation:

C = 5/9 (99.3-32)

C = 5/9 * 67.3

C = 37.3 degrees Celsius

So the most accurate measurement of Pat's temperature in degrees Celsius is 37.3 degrees.

Answer:

37.4 degrees

Step-by-step explanation:

C = 5/9 (F-32)

F = 99.3 so plug F into the equation

C = 5/9 (99.3 - 32)

C = 5/9 (67.3)

5/9 in a calculator = .555 repeating

.555 x 67.3 = 37.35

Rounded = 37.4 degrees

The maximum number of minutes that it is possible to talk without spending more than $5.00 is <= 11.30

While many calls are included in the contract's inclusive minutes and hence are free of charge, some fall outside of bundle packages and are paid "per minute" or "per call" instead. The normal minimum and maximum rates for domestic calls inside the UK are listed below.

The prices listed on this page are simply illustrative and shouldn't be taken as a complete list of call costs. Actual costs vary depending on your communication provider, as well as a variety of elements such unique calling plans, the time of day, and the precise number contacted. Before dialing, you should double-check with your provider.

An x-minute call costs $2.40 + $0.23x. An inequality that states that an x-minute call costs at most $5.00 can be written as:

$2.40 + $0.23x <= $5.00

To solve for x, we first subtract $2.40 from both sides:

$0.23x <= $2.60

Then, we divide both sides by 0.23:

x <= 11.30

The solution is x <= 11.30, which means that it is possible to talk for at most 11.30 minutes without spending more than $5.00. However, since the number of minutes must be an integer, the maximum number of minutes that it is possible to talk without spending more than $5.00 is 11 minutes.

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The centroid is the object's focal point. The centroid of a triangle is the location where the three medians of the triangle intersect.

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Then  p + $0.36 is an equation to represent the total cost, C, of pounds, p of oranges.

The formula for average total cost is created by dividing the sum of all production costs by the sum of all payments in money. The total-cost formula is a simple and user-friendly process that works by dividing the total production cost by the quantity of goods produced.

Together, fixed and variable costs make up the overall cost. The total cost, for instance, would be $35 if a company had a fixed cost per unit of $30 and a variable cost per unit of $5 that increased as output increased.

Then  p + $0.36 is an equation to represent the total cost, C, of pounds, p of oranges.

p + $0.36

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To transform a mixed fraction into an improper fraction, first, we multiply the denominator of the proper fraction by the whole number attached to it, and then we add the numerator.

An improper fraction is a kind of fraction in which the numerator will be greater than or equal to the denominator.

Let's take an example to understand the process completely.

For example, 3(1/2) is a mixed fraction. Convert it into an improper fraction.

Step 1: Multiply the denominator with the whole number of the fraction, i.e. Multiply 2 with 3 in the given example, 3(1/2).

2 × 3 = 6

Step 2: Add the numerator of the Fraction to the answer from step 1. i.e., Add 1 + 6

= 7.

Step 3: Keep the Denominator the same, i.e. 2.

Step 4: The Improper fraction obtained is: 7/2.

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The value of the equation is x² - x - 1 = 0

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

x - ( 1/x ) = 1   be equation (1)

On simplifying the equation , we get

( x² - 1 ) / x = 1

Multiply by x on both sides of the equation , we get

x² - 1 = x

Subtracting x on both sides of the equation , we get

x² - x - 1 = 0

Now , given that ( x / ( x² + 3x - 1 ) ) = 1/4

On simplifying the equation , we get

Cross multiplying the equation , we get

4x = ( x² + 3x - 1 )

Subtracting 4x on both sides of the equation , we get

x² - x - 1 = 0

Hence , the equation is x² - x - 1 = 0

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Answer:

12.5

Step-by-step explanation:

0.06 apples does she have if,She has 3 papayas.

Calculate the item's quantity. P:Q = p/Q should be used as the format.

The total quantities for the two objects would be equal to the sum of "p" and "q."

If you can, reduce the complexity of the object ratios.

Final outcome is the ratio in its simplest form.

Much like fractions, ratios can be entirely simplified. Divide every number in a ratio by the same number until it is impossible to divide it any more. This will simplify the ratio.

Divide every number in a ratio by the same number until it is impossible to divide it any more. This will simplify the ratio.

Explanation:

6/100 = 0.06.

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0.06 apples does she have if,She has 3 papayas.

Calculate the item's quantity. P:Q = p/Q should be used as the format.

The total quantities for the two objects would be equal to the sum of "p" and "q."

If you can, reduce the complexity of the object ratios.

Final outcome is the ratio in its simplest form.

Much like fractions, ratios can be entirely simplified. Divide every number in a ratio by the same number until it is impossible to divide it any more. This will simplify the ratio.

Divide every number in a ratio by the same number until it is impossible to divide it any more. This will simplify the ratio.

6/100 = 0.06.

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A Set is a collection of well-defined entities or elements.

A capital alphabetic symbol represents a set, and the number of elements in the finite set is represented as the cardinal number of a set in a curly bracket {…}. For example, set A is a collection of all the natural numbers, such as A = {1, 2, 3, 4, 5, 6, 7, 8,…..∞}.

Sets can be represented in three forms:

Roster Form: Set of even numbers less than 8 = {2, 4, 6}

Statement Form: A = {Set of Odd numbers less than 9}

Set Builder Form: A = {x: x = 2n, n ∈ N and 1 ≤ n ≤ 4}

Examples of sets are,

(a) Set of first 8 multiples of 7

Suppose the set of first 8 multiples of 7 is A

Set A = {7, 14, 21, 28, 35, 42, 49, 56}.

As there are 8 elements in the set, cardinal number n(A) = 8

(b) Set B = {a, e, i, o, u, j, k}

Set B = {a, e, i, o, u, j, k}. This set contains 7 elements,

Thus, the cardinal number of set B, n(B) = 7.

(c) Set C = {x | x are even numbers between 10 and 20}

Set C = {12, 14, 16, 18}. These numbers create the elements of set C.

Thus, the cardinal number of set C, n(C) = 4.

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Answer:

First, there are NO 5-digit pin codes that include the digits 7, 2, 4, 6, 9, and 3. But, there are 720 pin codes that include 5 out of the 6 digits.

Step-by-step explanation:

Answer:

Question 2: 6x-21

Question 1: -9x+3

Step-by-step explanation: