Find the average rate of change of f(x)=x^2-4x+1 from x=2 to x=6

Answers

Answer 1

Answer:

The answer is 4

Related Questions

the equation of the regression line for the data in the table is y = 4.9 - 198 where x represents the height and y is the predicted walking speed

Answers

The numerical value of 4.9 in the equation of the regression line

[y = (4.9x - 198)] determines "for every unit change in height, walking speed increases by 4.9 m/min" since, "x" represents the height and "y" is the predicted walking speed.

As per the question statement, the equation of the regression line goes as [y = (4.9x - 198)], where "x" represents the height and "y" is the predicted walking speed.

We are required to determine, what the numerical value of 4.9 expresses in the regression line.

To solve this question, first we need to know about the formula to express the point-slope form of a line, which goes as, [(y - y₁) = m(x - x₁)], where (x₁, y₁) is a point through which the line passes, and "m" is the slope of the line, and compare this standard form to our question mentioned equation, to establish the numerical significance of 4.9.

Now, [y = (4.9x - 198)] can be written as [(y - 0) = 4.9(x - 40.41)], and comparing it to the standard point-slope form of a line, we get (m = 4.9), i.e., the slope of our concerned line of regression is 4.9.

Hence, 4.9 in 4.9x signifies "for every unit change in height, walking speed increases by 4.9 m/min" since, "x" represents the height and "y" is the predicted walking speed.

Equation: In mathematics, an equation is a statement that expresses the relation of equality between two or more separate expressions, by connecting them with the "equal to" sign.

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Answer:

For every 1 inch increase in height, walking speed increases by 4.9 m/min.

Step-by-step explanation:

Just took it, hope this helps.

Find the value of x:

Answers

Answer:

because 3 divided by one is 3 so then you would have to divide with nine which we know is 3

Step-by-step explanation:

Have a great day!

Answer the following.

Answers

To convert 2.21 x 10⁻⁶, place 6 zeros before 2.21 and move the decimal point to the left:

= 0.000021210

To convert 28,000 to scientific notation, write the non-zero digits, placing a decimal after the first non-zero digit: 2.8, then, multiply by 10 elevated to 4 (number of digits after 2):

28,000 = 2.8 x 10

nswer:

For a test whose scores are normally distributed, with mean 470 and standard deviation 52, what is the cutoff score separating the bottom 11% of the test scores from the rest (that is, the score so that 11% of all scores are below this score)?

Answers

We will employ the z score table in this problem.

The shaded part is our area of interest.We will be required to seek the value of the z score at 0.11.

when we ahave a probability of 0.11 or 11%

This corresponds with a z-score of -1.225.

We then substitute into our z-score equation:

[tex]z=\frac{x-\mu}{\sigma}[/tex]

where

[tex]\begin{gathered} z=z\text{ score} \\ x=\text{cut off point} \\ \mu=\operatorname{mean} \\ \sigma=\text{standard deviation} \end{gathered}[/tex]

Therefore, we have

[tex]\begin{gathered} x=\sigma z+\mu \\ x=52(-1.225)+470 \\ x=406.3 \end{gathered}[/tex]

Over the last three evenings, Amy received a total of 112 phone calls at the call center. The first evening, she received 7 more calls than the second evening. The third evening, she received 3 times as many calls as the second evening. How many phone calls did she receive each evening?

Answers

Based on the relationship between the number of phone calls that Amy received for the three evenings, the number of phone calls received on each evening was:

First evening - 28 calls Second evening - 21 calls Third evening - 63 calls

How to find the number of phone calls received?

The first evening saw Amy receiving 7 more calls than the second evening while the third evening saw Amy receiving 3 times as many calls as the second evening.

Assuming the second evening is x, the relationship can be represented by the equation:

First evening calls + Second evening calls + Third evening calls = Total number of calls

(7 + x) + x + 3x = 112

Solving for the number of phone calls on the second evening gives:

(7 + x) + x + 3x = 112

7 + x + x + 3x = 112

7 + 5x = 112

5x = 112 - 7

x = 105 /5

= 21 calls

Number of calls on first evening:

= 21 + 7

= 28 calls

Number of calls on third evening:

= 21 x 3

= 63 calls

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Find the domain and range of the function represented by the graph.

The graph is a filled-in point at ordered pair negative 4 comma negative 1, a line segment from ordered pair negative 4 comma negative 1 to ordered pair 0 comma 3, a line segment from ordered pair 0 comma 3 to ordered pair 2 comma 3, a line segment from ordered pair 2 comma 3 to ordered pair 3 comma 4, and a filled-in point at ordered pair 3 comma 4.
The domain is
$\le x\le$
.

The range is
$\le y\le$
.

Answers

The diminution is this by that and that by this so this is with that and that is with this

Select the correct answer.
How many solutions for x does the following equation have?
2(x+4) -1 = 2x + 7
O A. 1
О в. о
OC. 7
OD. infinite

Answers

Answer:

D. infinite

Step-by-step explanation:

2(x+4) -1 = 2x + 7

To solve for x

Distribute

2x+8 -1 = 2x+7

Combine like terms

2x +7 = 2x + 7

Subtract 2x from each side

2x+7-2x = 2x+7-2x

7 = 7

This is always true, so there are infinite solutions

A person invests 1000 dollars in a bank. The bank pays 6% interest compounded annually. To the nearest tenth of a year, how long must the person leave the money in the bank until it reaches 2100 dollars?

Answers

Solution

For this case we have the following information given:

A= 1000

r= 0.06

n = 1

A= 2100

So we can set up the following formula:

[tex]2100=1000(1+\frac{0.06}{1})^t[/tex]

We can solve for t on this way:

[tex]\ln (\frac{2100}{1000})=t\cdot\ln (1.06)[/tex]

Solving for t we got:

[tex]t=\frac{\ln (2.1)}{\ln (1.06)}=12.73[/tex]

Rounded to the nesrest tenth we got:

12.7 years

1/4(n-6)=1/4n-3/2

Hint: undo the fraction

Answers

The solution to 1/4(n - 6) = 1/4n - 3/2 is infinite many solutions

How to solve the equation?

The equation is given as

1/4(n - 6) = 1/4n - 3/2

Multiply through the fraction equation by 4

So, we have the following equation

4 x 1/4(n - 6) = 4 x 1/4n - 4 x 3/2

Evaluate the products in the equation

So, we have the following equation

n - 6 = n - 6

Evaluate the like terms

0 = 0

The equation cannot be solved further

If the solution to an equation is 0 = 0, then the equation has infinite many solutions

Answers

To check if an ordered pair is a solution to an equation, substitute the value for each coordinate into the equation.

Since the substitution has to be performed in alphabetical order, then the coordinates are given in the form:

[tex](r,s)[/tex]

Substitute r=-6 and s=-2 into the given equation to check if (-6,-2) is a solution:

[tex]\begin{gathered} r-s=4 \\ \Rightarrow(-6)-(-2)=4 \\ \Rightarrow-6+2=4 \\ \Rightarrow-4=4 \end{gathered}[/tex]

Since -4 is NOT equal to 4, then the point (-6,-2) is not a solution to the equation r-s=4.

The point (-2, 1) is on the graph of which of these functions?
A. y = -x² -1

B. y = -3x -5

C. y = x² + 3

D. Y = 1/2x

Answers

Answer: B

-3(-2)-5=Y
6-5=1

Use synthetic division to divide 2x^4 − 12x^3 + 18x^2 − 13x +20 ; x−4.

Answers

The result of the synthetic division of 2x^4 - 12x³ + 18x² - 13x + 20 by x - 4 is given by:

2x³ - 4x² + 2x - 5.

How does synthetic division works?

In synthetic division, the coefficients of a polynomial are each divided by a value.This value is the zero of the divided polynomial, which goes into the far left box.

For this problem, the polynomial is given by:

2x^4 - 12x³ + 18x² - 13x + 20.

Hence the coefficients are:

2, -12, 18, -13, 20.

The divisor is:

x - 4.

Hence the left coefficient is:

From the image at the end of the answer, the resulting coefficients are given as follows:

2, -4, 2, -5, with a remainder of 0.

Hence the result is:

2x³ - 4x² + 2x - 5.

For the procedure, we consider that the coefficient 2, the first of the polynomial, is moved down, then multiplied with 4 and added with the next coefficient(-12), and this procedure happens until the last coefficient.

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Use the definition of the derivative to find the derivative of the function with respect to the given variable.
Show steps

Answers

The derivative of the given function [g(r) = -2r + 2] is d/dr (rⁿ) = nrⁿ⁻¹.

What is derivative?The derivative of a function of a real variable in mathematics assesses how sensitively the function's value changes in response to changes in its argument. Calculus's fundamental tool is the derivative. In conclusion, the tangent line's slope, or instantaneous rate of change, at any point on the curve is essentially what the derivative is. When you take a function's derivative, you're left with a different function that gives you the slope of the original function.

So, g(r) = -2r + 2:

Differentiate with respect to r as follows:

g(r) = -2r + 2

Using Power rule:

d/dr (rⁿ) = nrⁿ⁻¹

Therefore, the derivative of the given function is d/dr (rⁿ) = nrⁿ⁻¹.

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Does the table show a proportional relationship? If so, what is the value of y when x is 11?
x 4 5 6 10
y 64 125 216 1,000

Answers

Yes. As each number in x is cubed to give y

A particle moves along the r-axis so that its velocity vat any given time t, for 0 St $ 16, is given byW(0) =e»-1. At time r=0, the particle is at the origin. At what time does the particle's accelerationequal zero for the first time?Round to the nearest thousandth or write as a fraction

Answers

Given: The velocity function of a moving particle as

[tex]V(t)=e^{2sint}-1[/tex]

To Determine: The time at which the acceleration equals to zero

Solution

Note that at time t=0, the particle is at origin, so

[tex]\begin{gathered} V(0)=e^{2sin0}-1 \\ V(0)=e^{2\times0}-1 \\ V(0)=e^0-1 \\ V(0)=1-1 \\ V(0)=0 \end{gathered}[/tex]

Determine the acceleration function

The acceleration of a particle is the rate of change of velocity or the derivative of the velocity function. Therefore,

[tex]A(t)=\frac{dV(t)}{dt},or,A(t)=V^{\prime}(t)[/tex][tex]\begin{gathered} V(t)=e^{2sint}-1 \\ let:u=2sint:\frac{du}{dt}=2cost \\ V(t)=e^u \\ \frac{dV(t)}{du}=e^u=e^{2sint} \\ A(t)=\frac{dV(t)}{dt}=\frac{dV}{du}\times\frac{du}{dt} \\ A(t)=e^{2sint}\times2cost \\ A(t)=2e^{2sint}cost \end{gathered}[/tex]

When the acceleration is equal to zero, then we have

[tex]\begin{gathered} A(t)=0 \\ 2e^{2sint}cost=0 \end{gathered}[/tex]

Let us plot the graph of the acceleration function

The time for given interval for which the acceleration is zero are

[tex]t=\frac{\pi}{2},\frac{3\pi}{2},\frac{5\pi}{2},\frac{7\pi}{2},\frac{9\pi}{2}[/tex]

ence, thre first time the acceleration is zero is π/2 or 1.571

1.
find a
a =
21°
explain why using one of these
words: adjacent,
complementary, supplementary,
vertical
explanation goes here
add a pic of your work
(or just type it here)
to show HOW you got your
answer
pic (or typing) goes Hereford

Answers

[tex]21+a=90 \implies a=69^{\circ} [/tex]

This is because the angles are complementary.

Can I get help please ?

Answers

SOLUTION:

Case: Pythagoras Triple

Method:

The Pythagorean triple:

(8, 15, 17) can be formed with factor integers

8----> 4

15---->3.

Final answer:

x=4, y= 3

#6 and #7 Axioms of Equality

Answers

It is proved that ∠2 and ∠3 are supplementary angles.

What are angles?An angle is a figure in Euclidean geometry made up of two rays that share a common endpoint and are referred to as the angle's sides and vertex, respectively. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles. We refer to these as dihedral angles.

So, according to the given image below:

(A) m∠1 = m∠3 ⇒ Alternate angles.

(B) m∠1 + m∠2 = 180°

Reason:

R is a straight line through which line m asses making two angles m∠1 and m∠2.As we know a straight line has an angle of 180°.And since, line m divides the angle of 180° into two parts ∠1 and ∠2.So w ecam conclude that: m1 + m∠2 = 180°.

(D) m∠2 and m∠3 are supplementary because: Since a linear pair of angles always results in a straight line, their sum is always 180°.

Therefore, it is proved that ∠2 and ∠3 are supplementary angles.

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Determine if the sequence below is arithmetic or geometric and determine
the common difference / ratio in simplest form.
64, 16, 4, ...

Answers

The sequence 64, 16, 4,. is geometric

What is an arithmetic sequence?

Arithmetic Sequence can simply be defined as a sequence in which the difference between successive or consecutive terms is known as a constant.

The sequence is in the form a, a + d, a + 2d, a + 3d, a + 4d

Where;

a is the first termd is the common difference of the sequence

The formula for the nth term of an arithmetic sequence is expressed as;

Tn = a + (n – 1)d

What is a geometric sequence?

Geometric sequence can simply be defined as a sequence where the ratio of every two consecutive or successive terms is a known constant.

Given the sequence;

64, 16, 4, ...

We can see that the common ratio between the terms is 4 and hence a geometric sequence

Hence, it is a geometric sequence

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Help Me Pleaseeeeeee.

Answers

Based on the dimensions of the right triangle, the equation to be used to find the missing lengths is hypotenuse² = Known leg² + Unknown leg².

How to find a missing length on a right angled triangle?

To find the missing length of a right-angled triangle, you should use Pythagoras theorem.

This theorem allows you to find the dimensions of missing leg as:

hypotenuse² = Known leg² + Unknown leg²

When you solve for the missing length, the length is:

9² = 6² + Unknown leg²

81 = 36 + Unknown leg²

Unknown leg² = 81 - 36

Unknown leg = √(81 - 36)

Unknown leg = 6.7

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Suppose that the mean cranial capacity for men is 1160 cc (cubic centimeters) and that the standard deviation is 200 cc. Assuming that men's cranial capacities are normally distributed, complete the following statements.

Answers

Solution:

Given;

[tex]\mu=1160,\sigma=200[/tex]

The z-score is calculated using;

[tex]\begin{gathered} z=\frac{x-\mu}{\sigma} \\ \\ z=\frac{760-1160}{200}\text{ at }x=760 \\ \\ z=-2 \\ \\ z=\frac{1560-1160}{200}\text{ at }x=1560 \\ \\ z=2 \end{gathered}[/tex]

Thus;

[tex]P(-2ANSWER: 95%

(b) The z-score of 99.7 probability is between -3 and 3. Thus;

[tex]\begin{gathered} -3=\frac{x_1-1160}{200} \\ \\ x_1=560 \\ \\ 3=\frac{x_2-1,160}{200} \\ \\ x_2=1760 \end{gathered}[/tex]

ANSWER: Approximately 99.7% of men have cranial capacities between 560 cc and 1760 cc

Consider the lines that contain the segments in the figure and the planes that contain the faces of the figure. All angles are right angles. Which plane(s) contain point B and appear to be parallel to plane CDH?

Answers

The plane containing point B and parallel to the plane CDH is plane ABF.

What is defined as the parallel plane?Parallel planes are spatial planes that never intersect. The length about any line segment perpendicular both to planes connecting two parallel planes is indeed the distance between them. There are an infinite number of perpendicular line segments between two parallel planes. Two of the perpendicular segments the above are line segments AB and CD. Any line segment that is perpendicular to both planes also has the shortest distance between them.

As, from the diagram we can see that there are two plane passing from point B; plane ABF and ABC.

But plane ABC is intersecting the given plane CDH, while plane ABF is not.

Thus, plane ABF is parallel to the plane CDH.

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The rooftop of a 5-story building is 50 feet above the ground.
How long does it take the water balloon dropped from the
rooftop to pass by a third-story window at 24 feet?
Using the model h(t) = h, 16², solve the equation
h(t) = 24. (When you reach the step at which you divide
both sides by -16, leave 16 in the denominator rather than
simplifying the fraction because you'll get a rational
denominator when you later use the quotient property.)

Answers

With the help of the quotient, we know that the time the water balloon dropped from the rooftop is 1.3sec.

What do we mean by Quotient?In this example, the number divided by (15) is known as the dividend, and the number divided by (3 in this instance) is known as the divisor. The quotient is the outcome of the division.The quotient is the result of dividing two numbers by each other. As in the case of 8 ÷ 4 = 2, when the division produced the number 2, the outcome is the quotient. The dividend is 8 and the divisor is 4. The quotient and divisor are always less than their dividend, as you can see.

So, h(t) = 24:

= 50

Then, calculate as follows:

h(t) = - 1624 = 50 - 1616 = 50 - 2416 = 26 = 26/16t = √26/16t = 1.3sec

Therefore, with the help of the quotient, we know that the time the water balloon dropped from the rooftop is 1.3sec.

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Determine the rate of this problem -> A 18-kg bag of cherries for $2.65 =_____per kg

Answers

Answer:

$0.14 per kg

Step-by-step explanation:

A 18-kg bag of cherries for $2.65

for 1 kg

[tex] \frac{2.65}{18} = 0.14 \\ [/tex]

so, the answer is $0.14

HURRY!!!!!!!1Solve the equation −112 = 8x for x. −14 14 −104 120

Answers

The solution to the equation, −112 = 8x, is: x = -14.

How to Solve an Equation?

To find the value of the variable in an equation, means to solve the equation.

To solve any given equation, we are to apply all necessary properties of equality in other to isolate, as much as possible, the variable of the equation to one side of the equation. Th value of the variable is the solution to the equation.

Given the equation:

-112 = 8x

Divide both sides of the equation by 8:

-112/8 = 8x/8 [division property of equality]

-14 = x

x = -14

Check: Plug in x = -14 into the equation:

-112 = 8(-14)

-112 = -112 [true]

Thus, the solution to -112 = 8x is: x = -14.

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What is the value of 8 in 8.260

Answers

Answer:

Step-by-step explanation:

The value of 8 in 8.260 is 8 units.

Find a function f whose graph is a parabola with the given vertex and that passes through the given point.
vertex (−1, 9); point (−2, −8)

Answers

[tex]~~~~~~\textit{vertical parabola vertex form} \\\\ y=a(x- h)^2+ k\qquad \begin{cases} \stackrel{vertex}{(h,k)}\\\\ \stackrel{"a"~is~negative}{op ens~\cap}\qquad \stackrel{"a"~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} h=-1\\ k=9 \end{cases}\implies y=a(~~x(-1)~~)^2 +9\implies y=a(x+1)^2 + 9 \\\\\\ \textit{we also know that} \begin{cases} x=-2\\ y=-8 \end{cases}\implies -8=a(-2+1)^2 + 9 \\\\\\ -17=a(-1)^2\implies -17=a\hspace{9em}\boxed{y=-17(x+1)^2 + 9}[/tex]

Where is the least common denominator of two fractions to product of the denominator?

Answers

When two or more fractions are provided, the least common denominator is defined as the smallest common multiple of all the common multiples of the denominators.

What is the least common denominator?The smallest number that is a common denominator for a particular set of fractions is referred to as the least common denominator (LCD). For fraction addition and subtraction, as well as comparing two or more fractions, the given fractions must have common denominators.

Let's assume we have to add the fractions: (2/9)+(3/4)

We need to determine a common integer that is a multiple of both denominators, which are 9 and 4.

This common multiple will aid in the solution of the problem. As a result, the least frequent multiple for 9 and 4 is 36. As a result, the expression can be written as follows:

(2/9)+(3/4) = (2/9 × 4/4) + (3/4 × 9/9) = (8/36) + (27/36) = 35/36

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Drag the tiles to the boxes to form correct pairs. Not all tiles will be used.
Match the function with its inverse.

Answers

The correct pairs of the functions and their inverses are given by the image at the end of the answer.

How to find the inverse function?

To find the inverse function, we exchange x and y in the original function, then isolate y.

The first function that we want to find the inverse is:

f(x) = (2x - 1)/(x + 2).

Hence:

x = (2y - 1)/(y + 2)

(y + 2)x = 2y - 1

xy + 2x = 2y - 1

xy - 2y = -1 - 2x

y(x - 2) = -1 - 2x

y = (-1 - 2x)/(x - 2) (which is the inverse function).

The second function which we want to find the inverse is:

y = (x + 2)/(-2x + 1)

Then:

x = (y + 2)/(-2y + 1)

x(-2y + 1) = y + 2

-2yx + x = y + 2

-2yx - y = 2 - x

-y(2x + 1) = 2 - x

y = (x - 2)/(2x + 1) (which is the inverse function).

The third function which we want to find the inverse is:

y = (x - 1)/(2x + 1)

Then:

x = (y - 1)/(2y + 1)

2yx + x = y - 1

2yx - y = -1 - x

y(2x - 1) = -1 - x

y = (-x - 1)/(2x - 1) (which is the inverse function).

The fourth function which we want to find the inverse is:

y = (2x + 1)/(2x - 1)

Then:

x = (2y + 1)(2y - 1)

2yx - x = 2y + 1

2yx - 2y = 1 + x

2y(x - 1) = (1 + x)

y = (x + 1)/(2(x - 1)) (which is the inverse function).

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Tammy has 4 more then five times the amount of dimes than nickels in her pocket. She has total of $1.50 in her pocket. Write an equation that could be used to determine the number of nickels(x) she has in her pocket.

Answers

In a case whereby Tammy has 4 more then five times the amount of dimes than nickels in her pocket and have total of $1.50 in her pocket the equation that could be used to determine the number of nickels(x) she has in her pocket is (0.05)(X+3) = 1.50.

How can the number of nickels(x) she has in her pocket been determined?

The number of nickels(x) that can be found her pocket be determined by adding the the number of times the amount of dimes is than nickels, which can be expressed as :

let x will be number of dimes

let x+4 will be number of nickels

Therefore the number of nickels(x) that is required will be (0.10)X + (0.05)(X+3) = 1.50