Find the rate of change of f(x) = x² - 2x + 3 on [-1,2].

Answers

Answer 1

Answer:

-1.

Step-by-step explanation:

Rate of change = [ f(2) - f(-1)] / [2 - (-1)]

                          = [(2)^2 - 2(2) + 3)  - ((-1)^2  - 2(-1) + 3] / 3

                           = ( 3 - 6)/3

                            = -1.


Related Questions

Please help
(100 Points)

Answers

This might help ……..

Answer:

Equation: (14.71-4.48) [divided by] 3 =x

"Answer x": 3.41

Explanation:

14.71-4.48=10.23

10.23/3 = 3.41

3.41

A square rug has an area of 35 square ft. What is the exact side length of the rug?

Answers

The exact side length of the rug is √35.

What is the area of parallelogram

Let take the area of length as =a

As per the given question

A square rug has an area=35 sq ft

Area is the quantity that measures the number of unit square

As we know

area of square= a^2

Square area formula: A = a²

As already given a^2=35

So a=√35

The exact side length of the rug is √35.

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Hello! I'd really appreciate it if someone helped me solve this logarithm! It was my first class but the professor only showed the more simple versions :)​

Answers

Answer:

  (1/3)log(5) +(4/3)log(x) +log(y)

Step-by-step explanation:

You want the expanded form of the expression log(∛5·x^4·y^3).

Rules of logarithms

The applicable rules of logarithms are ...

  log(ab) = log(a) + log(b)

  log(a^b) = b·log(a)

In addition to these, you need to know that a root is a fractional power: the cube root is the 1/3 power. Of course, the rules of powers tell you ...

  (a^b)^c = a^(bc)

Application

You can express the root as a fractional power before or after taking logs. Either way, you get the same result.

Before

  [tex]\log\left(\sqrt[3]{5\cdot x^4y^3}\right)=\log\left(5^{\frac{1}{3}}\cdot x^{\frac{4}{3}}y^{\frac{3}{3}}\right)=\boxed{\dfrac{1}{3}\log(5)+\dfrac{4}{3}\log(x)+\log(y)}[/tex]

After

  [tex]\log\left(\sqrt[3]{5\cdot x^4y^3}\right)=\dfrac{1}{3}\log\left(5}\cdot x^{4}y^{3}}\right)=\dfrac{1}{3}\left(\log(5)+4\log(x)+3\log(y)\right)\\\\=\boxed{\dfrac{1}{3}\log(5)+\dfrac{4}{3}\log(x)+\log(y)}[/tex]

__

Additional comment

Working a more complex problem is like working a simple problem, except it has more parts and may require the use of the rules more times. It may be tedious to keep track of all the parts, but it is not difficult.

​"The unemployment rate has risen more than a percentage point to 8.9​% in February from 7.1% last​ November." What is the relative change in the unemployment rate expressed as a​ percentage?

Answers

If the  unemployment rate has risen more than a percentage point to 8.9​% in February from 7.1% last​ November, then the relative change in the unemployment rate expressed as a  percentage is 25.35%

Given,

The unemployment rate in February = 8.9%

The unemployment rate in November = 7.1%

The relative change in unemployment rate = [(unemployment rate in February - unemployment rate in November )÷ unemployment rate in November ] ×100

The relative change in unemployment rate= [tex](\frac{8.9-7.1}{7.1} )100[/tex]

=25.35%

Hence, If the  unemployment rate has risen more than a percentage point to 8.9​% in February from 7.1% last​ November, then the relative change in the unemployment rate expressed as a  percentage is 25.35%

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what is the vertex of f(x)=x^2+10x+1

Answers

The vertex of f(x)=x²+10x+1 is found to be  (-5,-24).

The Vertex of the quadratic equation f(x)=ax²+bx+c is (h,k) where

h=-b/2a  and k=f(h).

In the given question

f(x)=x²+10x+1

On comparing with ax²+bx+c

we get a=1 , b=10 , c=1

So , h=-b/2a

h=-10/2(1)

h=-5     ...(i)

k=f(h)

Substituting the value of x=h in f(x) we get

k=(-5)²+10(-5)+1

k=25-50+1

k=-25+1

k=-24

Therefore , the vertex of f(x)=x²+10x+1 is (-5,-24).

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Determine if the conclusion follows logically from the premises. Is this a valid or invalid argument? Premise: No loving persons are thoughtless persons. Premise: No loving persons are aggressive people. Conclusion: No aggressive people are thoughtless persons.

Answers

"Premise: No loving persons are thoughtless persons. Premise: No loving persons are aggressive people. Conclusion: No aggressive people are thoughtless persons." This is a Valid Argument

This is further explained below.

What is a Valid Argument?

Generally, In the context of deductive reasoning, an argument is considered to be sound if and only if it can be expressed in a way that makes it logically impossible for all of the premises to be true while still leading to an incorrect conclusion.

In conclusion, This is a Valid Argument

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If angle YXZ measures 90 degrees, which statement is true?

A. segment XZ is perpendicular to segment WY


B. WX =XY


C. segment XZ is a perpendicular bisector of segment WY


D. X is the midpoint of segment WY

Answers

Answer:

The 1st option is correct.

We are not clear that WX = XY.

3rd is is not correct.

4th option is also incorrect.

30 points!!! But I need a 2 step problem with variables on both side and a fraction that equal 23

Answers

The equation of the two-step problem is 2x = x + 2/3

How to determine the two-step problem?

The conditions are given as

Fraction = 2/3Variable on both sides

Let the variable in the equation be x

So, a possible equation is as follows

2x = x + 2/3

The solution to the equation is as follows

2x = x + 2/3

Subtract x from both sides

x = 2/3

Hence, the equation of the two-step problem is 2x = x + 2/3

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What is: 14 - (-20) + (-13)

Answers

Answer:

21

Step-by-step explanation:

14 - (-20) + (-13) =

= 14 + 20 - 13

= 34 - 13

= 21

What is the equation of a line through the points (0, 9) and (3, 0)?
0-9
3-0 y=-3x + 9
Obecause m=
Obecause m=
Obecause m=
O because m=
0-9
3-0 y=-3x + 3
3-0
0-9;y=-
y=-x+9
3-0
1
0-9; X=-3x+3

Answers

[tex](\stackrel{x_1}{0}~,~\stackrel{y_1}{9})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{0}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{0}-\stackrel{y1}{9}}}{\underset{run} {\underset{x_2}{3}-\underset{x_1}{0}}} \implies \cfrac{ -9 }{ 3 }\implies -3 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{9}=\stackrel{m}{-3}(x-\stackrel{x_1}{0}) \\\\\\ y-9=-3x\implies y=-3x+9[/tex]

A 14 yo client with type 1 diabetes
Heighing 110 pounds has on attack of
hypoglycemia. He has been prescribed
0.5g/kg of 50%. dextrose. The 50%
dextrose is supplied in 0.5mg/ml
Prefilled syringes. Calculate the dosage for
the client by converting the weight into Kilograms and the amount of
dextrose in syringe into grams.

Answers

Answer:

Step-by-step explanation: it will be having 10 kg each

Evaluate 13a+4b when a = 2 and b = 5

Answers

Answer:

46

Step-by-step explanation:

13a+4b

Substitute

13(2)+4(5)

Multiply

26+20

Add

46

An average middle-income family will spend $242,020 to raise a child born in 2004
from birth to age 17. The graph shows the percents spent for various categories. To
the nearest dollar, how much will be spent to provide housing for the child? Use the
graph to answer.

graph numbers-- housing 34%, food 17%, miscellaneous 11%, child care 11%, health care 7%, clothing 6%, transportation 14%

Answers

Answer:  $82,287

Work Shown:

34% of $242,020 = 0.34*242020 = 82,286.80

This rounds to 82,287 when rounding to the nearest whole number.

Decide whether the conditional statement is true or false:
It is noon when the clock strikes 12.

Answers

Answer:

True, When the clock transitions from 11:59am to 12:00pm, it is the first hour of noon.

Step-by-step explanation:

if you know how to do this problem please let me know, thank you.

Answers

As per the question statement, we are given a mathematical expression [tex]|a+5| -1[/tex] is [tex]$\left[\begin{array}{cc}\text { Solution: } & -\infty < a < \infty \\ \text { Interval Notation: } & (-\infty, \infty)\end{array}\right]$[/tex]

As this question involves a modulus function therefore let us suppose that [tex]b=|a+5|-1[/tex]

Find the absolute value vertex. In this case, the vertex for [tex]b=|a+5|-1[/tex] is [tex](-5,-1)[/tex]

Function range definition

The set of values of the dependent variable for which a function is defined

Domain of [tex]$|a-5|-1: \quad-\infty < a < \infty$[/tex]

Extreme Points of [tex]$|a-5|-1: \quad$[/tex] Minimum [tex]$(5,-1)$[/tex]

Find the range for the interval [tex]$-\infty < a < \infty: \quad-1 \leq f(x) < \infty$[/tex]

Combine the ranges of all domain intervals to obtain the function range [tex]$f(x) \geq-1$[/tex]

Axis interception points of [tex]$|a-5|-1: \quad X$[/tex]Intercepts: [tex]$(4,0),(6,0), Y$[/tex]Intercepts:[tex]$(0,4)$[/tex]

x - axis interception points of[tex]$|a-5|-1: \quad(4,0),(6,0)$[/tex]

y - axis interception point of [tex]$|a-5|-1: \quad(0,4)$[/tex]

X Intercepts: [tex]$(4,0),(6,0), Y$[/tex] Intercepts: [tex]$(0,4)$[/tex]

Asymptotes of [tex]$|a-5|-1$[/tex] : None

Vertical asymptotes of [tex]$|a-5|-1$[/tex] : None

Horizontal Asymptotes of [tex]$|a-5|-1$[/tex] : None

Extreme Points of[tex]$|a-5|-1$[/tex] : Minimum [tex]$(5,-1)$[/tex]

First Derivative Test definition

Suppose that [tex]$x=c$[/tex] is a critical point of [tex]$f(x)$[/tex] then,

If [tex]$f^{\prime}(x) > 0$[/tex] to the left of [tex]$x=c$[/tex]and [tex]$f^{\prime}(x) < 0$[/tex] to the right of [tex]$x=c$[/tex] then $x=c$ is a local maximum.

If [tex]$f^{\prime}(x) < 0$[/tex] to the left of [tex]$x=c$[/tex] and [tex]$f^{\prime}(x) > 0$[/tex] to the right of[tex]$x=c$[/tex] then $x=c$ is a local minimum.

If [tex]$f^{\prime}(x)$[/tex] is the same sign on both sides of [tex]$x=c$[/tex] then [tex]$x=c$[/tex]

is neither a local maximum nor a local minimum.

[tex]f^{\prime}(a)=\frac{a-5}{a-5}$$[/tex]

Plug [tex]$a=5$[/tex] into [tex]$|a-5|-1: \quad-1$[/tex]

Minimum [tex]$(5,-1)$[/tex]

Absolute value vertex: The difference between two numbers; a number's positive value.Interval: A collection of values spanning two endpoints.

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the midpoint of AB is M (2,0). if the coordinates of A are (-3,3), what are the coordinates of B?

Answers

Hence , the coordinate of point B is (7 , -3) .

Midpoint refers to some extent that's within the middle of the road connexion 2 points. A centre could be a purpose lying between 2 points and is within the middle of the road connexion the 2 points. If a line is drawn connexion the 2 points, then the centre could be a purpose at the center of the road and is equal from the 2 points.The centre formula is outlined for the points within the coordinate axes. Let (x₁), (y₁) and (x₂), (y₂) be the endpoints of a line section is given by  M = (x₁ + x₂ /2 , y₁ + y₂ /2 ).

We have given two coordinate A (-3,3) and M (2,0) .

Let the coordinate of B (x, y) .

Using midpoint formula , we get

[tex](2,0) = ( \frac{-3+x}{2} ,\frac{3+y}{2} )[/tex]

On comparing , we get

[tex]\frac{-3+x}{2} =2\\\ \\-3+x = 4\\x = 7[/tex]

[tex]\frac{3+y}{2} =0\\3+y=0\\y=-3[/tex]

We get coordinate (7 , -3) .

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What's the answer someone please help!

Answers

Step-by-step explanation:

Across

1.26

2.59

3.19

5.38

6.82

7.62

8.48

9.72

11.40

12.64

Down

1.24

2.59

3.18

4 42

5.32

6.88

7.65

8.42

9.70

10.34

When time equals 0, why is the temperature in the oven not equal to 0? Why does the temperature eventually oscillate around 350°F?

Answers

The ambient temperature, aka the outside air temperature, isn't 0 degrees Fahrenheit. This is the reason why the oven isn't at 0 degrees Fahrenheit when the oven is off. For example, if it is 68 degrees Fahrenheit outside, then the oven's temperature is likely around this figure when it is off.

------------------------------

The way the oven works is that it heats the air using a gas or electric source. Once reaching 350 or slightly higher, the oven burner will turn off for a set period of time. This is so the temperature doesn't go too far over 350.

After the burner is turned off, the air inside the oven is still really hot and will stay around 350 for a while. But the temperature will slowly decrease. Once dipping slightly below 350, the oven will turn back on to heat back up to 350 again. This process repeats over and over.

This explains why you see the oscillating bouncing curve like this. It also explains why ovens seem to go on or off in the middle of a baking session.

Find rules for the tables below. State your rules in two different ways: (1) as a sentence; and (2) as a rule, using x for the input and y for the output. a. X 6 0 2 -3 1 Process y -3 9 -21 3 33 Rule: (1) X and Topic 3: Foundations of Y are Linear (2) relationship Y = 6x=3​

Answers

Answer:6x+3

Step-by-step explanation:

what is the value of x?!?
please help!

Answers

Answer:

  x = 25

Step-by-step explanation:

The given angles, x° and (6x+5)° form a linear pair. You want the value of x.

Linear pair

Two angles that together form a straight line are called a linear pair. A linear pair of angles has a total measure of 180°.

  x° +(6x +5)° = 180°

  7x +5 = 180 . . . . . . . . . divide by °, collect terms

  7x = 175 . . . . . . . . . . subtract 5

  x = 25 . . . . . . . . . . divide by 7

The value of x is 25.

If the third of three consecutive integers is subtracted from 132, the result is the sum of the first and second. What are the integers?

Answers

Answer:

gg

Step-by-step explanation:

Answer:

Three consecutive integers are 43, 44, 45

Step-by-step explanation:

Let three consecutive integers be x, (x + 1), (x + 2)

According to the question, if the third of three consecutive integers is subtracted from 132, the result is the sum of the first and second.

[tex] \therefore [/tex]

[tex] \implies \rm 132 - (x + 2) = x + (x + 1) \\ \\ \implies \rm 132 - x - 2 = x + x + 1 \\ \\ \implies \rm 130 - x = 2x + 1 \\ \\ \implies \rm 130 - 1 = 2x + x \\ \\ \implies \rm 129 = 3x \\ \\ \implies \rm 3x = 129 \\ \\ \implies \rm x = \frac{129}{3} \\ \\ \implies \rm x = 43[/tex]

So,

The integers are as follows:

x = 43

x + 1 = 44

x + 2 = 45

Use equivalent ratios to answer

Answers

If out of 7 squares, 4 squares are in grey colour then if there are 15 white squares there will be 20 grey squares by solving through ratios.

Given that out of 7 squares, 4 squares are in grey colour.

We are required to find the number of grey colour squares if there are 15 white squares by using equivalent ratios.

Equivalent ratios are basically the ratios that are the same when we compare them. Two or more ratios can be compared with each other to find whether they are equivalent or not.

Ratio of white squares in 7 total squares=3:4

Total number of squares if there are 15 white squares=15*7/3=35

Number of grey squares=35-15=20

Hence if out of 7 squares, 4 squares are in grey colour then if there are 15 white squares there will be 20 grey squares by solving through ratios.

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1.
destions. Show your wor
For a recent Broadway musical, orchestra main floor seats cost $148 each, and
balcony seats cost $65 each. A theatre group purchased 30 tickets for an upcoming
show in June. If the total cost of the 30 tickets was $2,614, how many of each type
of ticket did the theatre group buy?
Number of orchestra tickets
Number of balcony tickets

Answers

Answer:

Number of orchestra tickets = 8

Number of balcony tickets = 22

Step-by-step explanation:

Let the number of orchestra tickets be x and number of balcony tickets be y.

So, cost of x orchestra tickets = $148 × x = $148x

Cost of y balcony tickets = $65 × x = $65y

Also given, total number of tickets = 30

Cost of 30 tickets = $2,614

So, the system of equations that can ne formed is :

x + y = 30     ....eq 1

148x + 65y = 2614    ....eq 2

Multiplying eq 1 by 148 and subtracting eq 2 by it,

148x + 148y - 148x - 65y = 4440 - 2614

83y = 1826

y = 1826/83 = 22

Substituting y = 22 in eq 1,

x + 22 = 30

So, x = 30 - 22 = 8

Thus,

Number of orchestra tickets = 8

Number of balcony tickets = 22

If an employee at Tacos R US gets paid $11.50 per hour. Find his net pay if the
employee works 38 hours in that one week. Employee has a 10% federal tax rate. SS
tax is 6.2% and Medicare tax is 1.45%

Answers

the net pay (weekly) is $359.87

How to find the net pay?

First, we know that the employee wins $11.50 per hour. The employee works 38 hours per week, then the weekly pay is:

38*$11.50  = $437

Now we need to discount the taxes:

There are 10% from federal tax, 6.2% from social services and 1.45% from medicare.

The total is:

10% + 6.2% + 1.45% = 17.65%

Then we need to discount a 17.65% of the weekly pay, we will get:

$437*(1 - 17.65%/100%) = $437*(1 - 0.1765) = $359.87

We conclude that the net pay (weekly) is $359.87

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need answer asap:
Shelby made a list of her test scores: 88,100,92,80,85,94,90. What is the lowest score she can get on her next test to have a mean score of 90?

ty pls answer quickk

Answers

......................

In the diagram m∠ACB=25° and CE bisects ∠DCF. explain how to find m∠DCE​

Answers

The measure of ∠ DCE is equal to 57.5° by using the property of bisectors and vertically opposite angles.

We are given a ray diagram.

In the diagram, the measure of angles are given as:

∠ ACB = 25°

∠ ACG = 90°

We need to find the measure of angle ∠ DCE​ when CE bisects ∠ DCEF.

Now, we know that:

∠ BCG = ∠ DCF ( Vertically opposite angles.)      … (1)

Now,

∠ BCG = ∠ ACB + ∠ ACG

∠ BCG = 25° + 90°

∠ BCG = 115°     … (2)

∠ DCF = ∠ DCE + ∠ CEF

∠ DCF = ∠ DCE + ∠DCE ( as ∠ DCE = ∠ CEF since CE bisects them)

∠ DCF = 2 ∠ DCE   … (3)

Now, put (2) and (3) in (1), we get that:

115° = 2 ∠ DCE

∠ DCE = 115 / 2°

∠ DCE = 57.5°

Therefore, we get that, the measure of ∠ DCE is equal to 57.5° by using the property of bisectors and vertically opposite angles.

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Find an equation for the line tangent to the circle
x2 + y2 = 100
at the point
(8, −6).


Answers

First, this circle has center at the origin with a radius of 10. Draw this picture.
Second, plot the point (-6,8) on the circle.
Third, draw a radius from the origin to this point. You should be able to determine the SLOPE of this radius. Since slope is -8/6, this reduces to -4/3.
Fourth, use the point-slope form to find the equation:
y - y1 = m ( x - x1)
y - 8 = -4/3 ( x - -6 )
y - 8 = -4/3 ( x + 6 ) This is the Point-Slope form of the equation.
Fifth, sometimes the question specifies the Slope-Intercept form of the equation. If that is the case, then you only have 2 steps left. First, distribute the -4/3 on the right side of the equation.
y - 8 = -4/3(x) + 8 Now, we isolate the "y" by adding 8 to both sides of the equation.
+8 +8
_________________
y = -4/3(x) + 16

helpnsisiisisisisiwiwiwi​

Answers

Answer:

For Ai - P = 4 , Q = 4 , R = 4

For Aii - P = 3 , Q = 4 , R = 5

For Aiii - b^13 × b^-2 / b^1 = b^10

Step-by-step explanation:

I hope this is correct answer.

the answer is - a^12

Kenny and his family went on a backpacking trip. They started hiking at 3:48 P.M. It took 2 hours and 59 minutes to reach their campsite. After they arrived, it took 1 hour and 35 minutes to set up the campsite. What time was it when Kenny and his family finished setting up their campsite?

Answers

Based on the time that it took Kenny and his family to reach the campsite and set it up, the time when they finished setting up the campsite was 8:22 pm

How to find the time taken to set up?

First, find the time that Kenny and his family reached their campsite:
= 3:48 pm + 2 hours 59 minutes

= 6:47 pm

After getting to the campsite at 6:47 pm, Kenny and his family took 1 hour 35 minutes to finish setting up their campsite:

= 6:47 pm + 1 hour 35 minutes

= 8:22 pm

In conclusion, Kenny and his family finished setting up at 8:22 pm.

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Figurative language is different from literal language because _____.
A. it means exactly what it says
B.it is unclear
C.it contains meaning other than the actual word for word meaning
D.it is hard to define

Answers

Answer:

C i think

Step-by-step explanation:

Answer:

C.

Step-by-step explanation:

Answer A is the definition of literal language, while C is the definition of figurative. So, C is correct.

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