Given the tunction
f(x)= - x^2 + 4x - 3 ,find the rate of chango over the interval [-2,7] (you can take the negative leading coefficlent off for reg ed if you want) *

Answers

Answer 1

Answer:

-1

Step-by-step explanation:

Given function:  [tex]f(x)=-x^2+4x-3[/tex]

[tex]\implies f(-2)=-(-2)^2+4(-2)-3=-15[/tex]

[tex]\implies f(7)=-(7)^2+4(7)-3=-24[/tex]

[tex]\textsf{Average rate of change}=\dfrac{f(b)-f(a)}{b-a}\quad\textsf{for}\:a\leq x\leq b[/tex]

Therefore, average rate of change over the interval -2 ≤ x ≤ 7

[tex]\implies \textsf{Average rate of change}=\dfrac{f(7)-f(-2)}{7-(-2)}=\dfrac{-24-(-15)}{9}=-1[/tex]


Related Questions

On their vacation, the Lupines stay at a hotel that
has a rectangular swamp for a swimming pool. The
swamp has a perimeter of 124 feet. The length is
10 feet less than 5 times its width. What are the
length and width of the swamp?

Answers

Step-by-step explanation:

Given :-

Let width be x and length be 5x - 10 according to the question

To find:-

Measurement of length and width

Solution :-

Formula for perimeter of rectangular swamp = 2(L+W)

Putting the known values ,

124 ft. = 2( 5x -10 + x )

124 ft. = 2(6x - 10)

124 ft. = 12x - 20

124+20 = 12x

144/12 = x

12 = x

putting the values of x

Length = 5x-10

5×12 - 10 = 50 feet

width = X

12 feet

perimeter =2L+2W or 2(L+W)

124= 2(5W-10+W)

perimeter =2( 6W-10)

124 = 12W-20

124+20=(12W+20-20

144=12W

144÷12=12W÷12

12=W

I WILL GIVE BRAINLYEST AND 60 POINTS. Please help me ASAP.
Rectangle PQRS is plotted on a coordinate plane. The coordinates of P are (– 1, 4) and the
coordinates of Q are (– 1, – 4). Each unit on the coordinate plane represents 1 centimeter, and
the area of Rectangle PQRS is 64 square centimeters. Find the coordinates of Points R and S
given these conditions:.aPoints R and S are to the left of Points P and Q.bPoints R and S are to the right of Points P and Q

Answers

Answer:

This may or may not help be it might get you close.  

What is the classification of the pair of angles shown?

F. complementary
G. supplementary
H. vertical
I. no relationship

Answers

Answer:

Vertical

Step-by-step explanation:

Since both the angles are located directly opposite of each other, this is a vertical angle pair.

Drag each equation to its equivalent fact. DUE TODAY

Answers

Answer:

left left right

Step-by-step explanation:

rearange the formula as normal

I need this done right now please i need help​

Answers

Step-by-step explanation:

AB = x + 5 ...................

If made $90.00 how much was paid hourly?​

Answers

Answer:

Made in how long of a workshift?

Step-by-step explanation:

Determine the net change between the given values of the variable.
f(x) = 7x − 9; x = 2, x = 3

Answers

Answer:

the net change is 7

if u substitute x with

2 u get 5

3u get 12

4 u get 19

What is the y-intercept of the quadratic function
f(x) = (x – 6)(x – 2)?

(0,–6)
(0,12)
(–8,0)
(2,0)

Answers

Answer:

(0,12)

Step-by-step explanation:

B.(0,12)

The two figures are similar. Write the similarity statement. Justify your answer using factor and showing all work. Describe (in general since it isn't on a graph) the transformations from ABC to the new figure. Please don't troll this is for a unit test!!!!
First Triangle
A to B: 40
B to C: 60
C to A: 50

Second Triangle
X to Y: 31.25
Y to Z: 25
Z to X: 37.5 ​

Answers

Answer:

B to C;60

Step-by-step explanation:

Z to X;37.5      CORRECT ME IF IM WRONG   #Carryonstudents

Compound Shapes
Find the area of each figure, round your answer to one decimal place if necessary
12 ya
30
1)
3)
2)
3
12 yd
18
12 ya
3
20 yd
24
Area
Area
Area
4)
5)
6)
17 cm
4 cm
7.5 m
8 orn
12 cm
10 m
5 m
Area:
Area:
Area:
9)
7)
8)
35 m
3.5 m
20 in
TO in
18 in
21 m
21 in
18 in
20 in
3.5 m
21 m
Area:
Area:
Area:

Answers

Applying the formula for areas of rectangle, triangle, & circle, area of each figure is:

1. 27

2. 537.9

3. 384

4. 168.5

5. 96.3

6. 73.1

7. 357.1

8. 1,029

9. 744

What is the Area of a Circle?

Area of a circle = πr², where r is its radius.

What is the Area of a Rectangle?

Area of a rectangle = length × width

What is the Area of a Triangle?

Where b is the height and b is the base length, area of triangle = 1/2bh.

What is the Area of a Square?

Area = s², where s is the side length.

1. Area of the figure = area of square + area of rectangle = s² + length × width

Area of the figure = 3² + 6 × 3 = 27 ft²

2. Area of the figure = area of circle + area of rectangle = πr² + length × width

Area of the figure = π(7²) + 24 × 16 = 537.9 ft²

3. Area of the figure = area of smaller rectangle + area of bigger rectangle

Area = 12 × 12 + 20 × 12 = 384 yd²

4. Area of the figure = area of 1/2circle + area of triangle = 1/2πr² + 1/2bh

Area of the figure = 1/2π(8²) + 1/2(8)(17) = 168.5 cm²

5. Area of the figure = area of rectangle + area of triangle = (l)(b) + 1/2bh

Area of the figure = (10)(7.5) + 1/2(7.5)(5) = 96.3 m²

6. Area of the figure = area of 1/2circle + area of triangle = 1/2πr² + 1/2bh

Area of the figure = 1/2π(4²) + 1/2(8)(12) = 73.1 cm²

7. Area of the figure = area of 1/2circle + area of rectangle = 1/2πr² + 1/2bh

Area of the figure = 1/2π(10²) + (20)(10) = 357.1 in.²

8. Area of the figure = area of rectangle + area of triangle = (l)(b) + 1/2bh

Area of the figure = (35)(21) + 1/2(28)(21) = 1,029 m²

9. Area of the figure = area of square + area of rectangle = s² + length × width

Area of the figure = 18² + 21 × 20 = 744 in.²

Learn more about the area of rectangle, triangle and circle on:

https://brainly.com/question/14487364

Porter drove due east 20 miles on Interstate 23, then due south 23 miles on Interstate 77. To the nearest hundredth of a mile, how far was he from his starting point?

A. 30.48 mi
B. 26 mi
C. 11.36 mi
D. 43 mi

Answers

Answer: D. 30.48 miles

Step-by-step explanation:

You basically use Pythagorean Theorem!

a2 + b2 = c2

Square root 20^2 +23^2

=√20^2 + 23^2

=20 x 2 + 23 x 2

= 929

And round it=

30.48 miles.

What is the equation of the line that passes through the point (3,7) and has a slope of 2/3

Answers

Answer:

[tex]Y=\frac{2}{3} x +5[/tex]

Hope This Helped! :) Please Mark Brainliest!

Define then compare and contrast diverges and converges.​

Answers

Answer:

Convergence is defined as the movement of two forces together while divergence implies the movement of two forces apart. In the world of economics, finance, and trading, divergence and convergence describe the directional relationship between two trends, prices, or indicators.

i need help fast i will mark brainliest

Answers

Answer:

50.24

Step-by-step explanation:

Area=R^2*PI

OR
Area-R*R*PI

So, Area=4*4*3.41

=50.24

Answer:

1,661.1

Step-by-step explanation:

A= 3.14 x (23 x 23)

3.14 x 529= 1,661.06

1,661.1

hellllllllllllllp please

Answers

Answer:

The hieght should be 3 cm

Step-by-step explanation:

We can put it into an equation form:

6⋅2⋅x=36

Then solve from there!

Hope this helps!!

Answer:

Yo I was going to answer this question but I assume there is a mistake I think your teacher meant the length of the box is 6cm if not the answer is 6 cm high if so and there's a mistake then the answer is 3 cm high.

Step-by-step explanation:

A locker combination has three nonzero digits, and digits cannot be repeated. If the first digit is odd, what is the probability that the second digit is even? A. 1/2
B. 4/9
C. 1/8
D. 1/9

Answers

Answer:

A.  1/2.

Step-by-step explanation:

After the odd digit is taken out there are 8 digits left,

and of these 4 are even so

the answer is 4/8 = 1/2.

A water storage tank is in the shape of a cone with the pointed end down. If the radius is 21 feet and the depth of the tank is 14 feet, find the volume of the tank in cubic feet. Use 22/7 for π.

Answers

The volume of the water storage tank is the amount of space in it

The volume of the water storage tank is 6468 cubic feet

How to determine the volume?

The given parameters are:

Radius (r) = 21 feet

Height (h) = 14 feet

The shape of the water storage tank is a cone.

And the volume of a cone is:

V = 1/3πr^2h

So, we have:

V = 1/3 * 22/7 * 21^2 * 14

This gives

V = 6468

Hence, the volume of the water storage tank is 6468 cubic feet

Read more about volumes at:

https://brainly.com/question/1972490

Ved drew the shape below by combining exactly 3 triangles of the same size and shape

Answers

The area of each triangle is (1/3) of the area of the whole shape.

What is an area?

Area is the amount of space occupied by a two dimensional shape or object.

Ved drew the shape below by combining exactly 3 triangles of the same size and shape.

Hence:

Combined area = sum of each area = 3 * area of each triangle

The area of each triangle is (1/3) of the area of the whole shape.

Find out more on area at: https://brainly.com/question/25292087

1)
Which of these are equations of lines that are parallel to the x-axis?
Select all that apply.
A. y=-3
3
4
B. y =5.3
5
C. X=
6
x 6
D. X=-7
k
E. y = 20
F. X = 8.2

Answers

Any equation with y=# will be parallel to x-axis since it has a slope of zero and will make a horizontal line.

Which statement is true about every exterior angle of any quadrilateral inscribed in a circle?


The measure of an exterior angle is equal to the measure of the nonadjacent interior angle.


The measure of an exterior angle is equal to the measure of an adjacent interior angle.


The measure of an exterior angle is equal to the average of the measures of the two adjacent interior angles.


The measure of an exterior angle is equal to the difference of the measures of the two adjacent interior angles.

Answers

Answer:

A

Step-by-step explanation:

In an inscribed quadrilateral, opposite angles are supplementary.

An exterior angle of a quadrilateral is supplementary to the adjacent interior angle.

Since the exterior angle is supplementary to both the adjacent interior angle and to the opposite interior angle, the exterior angle and the opposite interior angle are congruent.

Answer: A

Stacy is making a scale model of the Eiffel Tower for French class. Her model is 500 times smaller than the actual tower, which is 300 meters tall. How many millimeters tall is Stacy's model?

Answers

Answer: 600 mm

Step-by-step explanation:

Let height of her model be x meters

So,

500x = 300

[tex]\begin{aligned}&\rightarrow x=\frac{300}{500} \\&\rightarrow x=\frac{3}{5}=0.6 \text { meters } \\&\rightarrow x=0.6 \times 1000 \text { millimeters } \\&\rightarrow x=600 \text { millimeters }\end{aligned}[/tex]

Therefore, Stacy's model is 600 millimeters tall

The entire graph of the function f is shown in the figure below.

Write the domain and range of f using interval notation.

Answers

Answer:

no idea

is the answer

if you like my answer please like comment and mark me as brilliant

Joseph wants to line his garden with a fence that cost $2.25 per foot. The length of the garden is 6 yards and the width is 2.5 yards. what is the total cost?

Answers

Answer:

$38.25

Step-by-step explanation:

Perimeter of a rectangle = 2W + 2L

(where W is the width and L is the length)

Given:

width = 2.5 ydlength = 6 yd

⇒ perimeter = (2 x 2.5) + (2 x 6)

                     = 5 + 12

                     = 17 yd

Given:

cost of fence = $2.25 per foot

⇒ total cost = 17 x 2.25

                    = $38.25

Length=L=6ydsWidth=B=2.5yds

Perimeter:-

2(L+B)2(6+2.5)2(8.5)17yd

Toatl cost::

17(2.25)34+4.2538.25$


PLEASE HELP ME ANSWER THIS !! I HAVE 7 MINUTES TO TURN IT IN HELP PLEASE

Answers

Step-by-step explanation:

You know that the three lines are parallel.

There weren't really any specific instructions so I'd assume that we're trying to find the lines. They are all in the same thing, as shown, one is 21 and the other is 12. That means the parallel line is cutting of 9.

We can then assume 2x+2-9=x+3

Then, to solve, you can get 2x-7=x+3

X=10

Hope this helped!

I'm a bit confused, but hope this helped again!

! PLS HELP ! In a raffle, one thousand tickets are sold. There
is a grand prize of $4000, a second prize of
$500, and a third prize of $100. What ticket
price would make this game fair?

Answers

Answer:

$4.60

Step-by-step explanation:

The universal set is U = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}. If A = {2, 3, 4, 5, 6} and B = {5, 6, 7, 8, 9}, find the following. (Enter your answers as a comma-separated list. Enter EMPTY for the empty set.) (a) A ∩ B (b) A ∪ B (c) A' (d) B'

Answers

Answer:

  a)  {5, 6}

  b)  {2, 3, 4, 5, 6, 7, 8, 9}

  c)  {0, 1, 7, 8, 9}

  d)  {0, 1, 2, 3, 4}

Step-by-step explanation:

The intersection of sets is the set of elements common to both. The union of sets is the set of all elements that are part of either set. The complement of a set is the set of elements in the universal set that are not in the set of interest.

__

A∩B

  {2,3,4,5,6} ∩ {5,6,7,8,9} = {5, 6}

__

A ∪ B

  {2,3,4,5,6} ∪ {5,6,7,8,9} = {2,3,4,5,6,7,8,9}

__

A'

  U -A = {0,1,2,3,4,5,6,7,8,9} -{2,3,4,5,6} = {0,1,7,8,9}

__

B'

  U -B = {0,1,2,3,4,5,6,7,8,9} -{5,6,7,8,9} = {0,1,2,3,4}

if right triangle RST, ST = 5, RT = 12, and RS = 13. Find tan (S).

Answers

Answer:

  tan(S) = 12/5

Step-by-step explanation:

The mnemonic SOH CAH TOA reminds you the tangent ratio is ...

  Tan = Opposite/Adjacent

In the given triangle, the side opposite angle S is RT, which has length 12. The side adjacent to angle S is ST, which has length 5. Then the tangent of angle S is ...

  tan(S) = RT/ST

  tan(S) = 12/5

_____

Additional comment

The rest of the trig functions in this triangle are ...

  sin(S) = 12/13

  cos(S) = 5/13

  tan(R) = 5/12

  sin(R) = 5/13

  cos(R) = 12/13

Answer:

tan(S) = [tex]\frac{12}{5}[/tex]

Step-by-step explanation:

Hi there!

We are given ΔRST, where ST=5, RT=12, and RS=13

We want to find the tangent of angle S (the notation tan(S) means "tangent of angle S")

In trigonometry, tangent refers to the ratio of the opposite side/adjacent side.

The opposite side is the side that is opposite to the angle that we are referencing (in this case, angle S); in this case, that side is RT, which is 12

The adjacent side is the leg that is adjacent to the opposite side; in this case, that side is ST, which we were given as 5

Therefore, tan(S) will be [tex]\frac{RT}{ST}[/tex], or [tex]\frac{12}{5}[/tex].

Hope this helps!

can you please help me solve this logarithm function

Answers

Answer:

I think the solution is x=84 if this is correct can u mark me brainliest

Answer:

[tex]\boxed{\sf{x=84}}[/tex]

Step-by-step explanation:

This problem can be solved by using the logarithm function.

Isolate the term of x from one side of the equation.

First, you divide by -6 from both sides.

[tex]\Longrightarrow: \sf{\dfrac{-6\log _3(x-3)}{-6}=\dfrac{-24}{-6}}[/tex]

Solve.

Divide the numbers from left to right.

-24/-6=4

Rewrite the problem down.

[tex]\Longrightarrow: \sf{\log _3(x-3)=4}[/tex]

x-3=81

Add by 3 from both sides.

[tex]\Longrightarrow:\sf{x-3+3=81+3}[/tex]

Solve.

Add the numbers from left to right.

81+3=84

[tex]\Longrightarrow: \boxed{\sf{x=84}}[/tex]

Therefore, the solution is x=84, which is our answer.

I hope this helps you! Let me know if my answer is wrong or not.

HELP The recursive rule for a sequence is shown An=An-1 +4 a1=14 write the explicit rule in simplified form for the sequence An=

Answers

Answer:

aₙ = 4n + 10

Step-by-step explanation:

Given is the AP with

The first term of 14The common difference of 4

Explicit rule for the sequence is

[tex]a_n=a_1+(n-1)d=14+(n-1)(4)=14+4n-4=4n+10[/tex]

Answer:

[tex]\sf a_n=4n+10[/tex]

Step-by-step explanation:

A recursive formula for an arithmetic sequence allows you to find the nth term of the sequence provided you know the value of the previous term in the sequence.

An explicit formula for an arithmetic sequence allows you to find the nth term of the sequence.

Given recursive rule:

[tex]\begin{cases} \sf a_n=a_{n-1}+4\\ \sf a_1=14\end{cases}[/tex]

Therefore, the next two values in the sequence are:

[tex]\begin{aligned} \implies \sf a_2 & = \sf a_{2-1}+4\\& = \sf a_1+4\\& = \sf 14+4\\& = \sf 18\end{aligned}[/tex]

[tex]\begin{aligned} \implies \sf a_3 & =\sf a_{3-1}+4\\& = \sf a_2+4\\& = \sf 18+4\\& = \sf 22\end{aligned}[/tex]

Explicit formula

  [tex]\sf a_n=a+(n-1)d[/tex]

where:

[tex]\sf a_n[/tex] is the nth terma is the first termn is the number of the termd is the common difference between terms

Given:

[tex]\sf a = a_1=14[/tex][tex]\sf d = 22-18=4[/tex]

Substituting the given values into the formula:

[tex]\sf \implies a_n=14+(n-1)4[/tex]

[tex]\sf \implies a_n=14+4n-4[/tex]

[tex]\sf \implies a_n=4n+10[/tex]

Therefore, the explicit rule in simplified form for the sequence is:

[tex]\sf a_n=4n+10[/tex]

Learn more about arithmetic sequences here:

https://brainly.com/question/27806372

https://brainly.com/question/27783089

A research study compares three treatments with n=5 in each treatment. If the Ex values for the three treatments are 5, 10, and 15, then the between treatments' degrees of freedom would be equal to_
a) 12
b) 3
c) 2
d) 14

Answers

The between treatments' degrees of freedom would be equal to 10

What is degrees of freedom?

Degrees of freedom is a combination of how much data you have and how many parameters you need to estimate.

Given the data in the question;

A research study comparing three treatments with n = 5 in each treatment produce;

that is: n₁ = 5, n₂ = 5, n₃ = 5

T₁ = 5, T₂ = 10, T₃ = 15,

SS₁ = 6, SS₂ = 9, SS₃ = 9

∑x² = 94

First, we obtain the grand total;

G = T₁ + T₂ + T₃ = 5 + 10 + 15 = 30

N = n₁ + n₂ + n₃ = 5 + 5 + 5 = 15

Total SS =  ∑x² - ( G²/N )

we substitute

Total SS =  94 - ( (30)²/ 15 )

Total SS =  94 - ( 900 / 15 )

Total SS =  94 - 60

Total SS =  34

To get the SSbetween or Between SS;

Between SS = ∑( T²/n ) - ( G²/N )

Between SS = ∑( (5)²/5 + (10)²/5 + (15)²/5 ) - ( (30)²/ 15 )

Between SS = ∑( 25/5 + 100/5 + 225/5 ) - ( 900 / 15 )

Between SS = ∑( 5 + 20 + 45 ) - 60

Between SS = 70 - 60

Between SS = 10

Hence the between treatments' degrees of freedom would be equal to 10.

To know more about Degrees of freedom follow

https://brainly.com/question/17175673

#SPJ1

Other Questions
. Assuming that the pool is 10 ft deep, approximately how many cubic heters of water will this pool hold when filled? (3.3 feet 1 meter) How is the sun a special star? Match each definition with the appropriate measurement of economic output.a. the market value of all final goods and services produced by resources owned by citizens of a particular country in a given year b. GDP adjusted to base year prices c. GDP divided by population d. GDP adjusted for differences in the cost of living in different countries e. the market value of all final goods and services produced by resources located in a particular country in a given yearWORD BANKreal GDPGDP PPPGNPnominal GDPGDP per capita . a) Practice changing the underlined active verbs into passive. : 1. Albert read the story last night. The story was read last night by Al 2. My brother broke the window. The window by 3. They have made the chair of iron The chair 4. My sister is sweeping the room now. The room 5. Someone may pay a million for that car A million 6. Dad punishes me whenever I'm lazy. 1 whenev 7. The teacher may postpone the test. The test . 8. Ida has given the flowers to the teacher The flowers 9. Someone was searching Carla's bag Carla's bag 10. Jim will send Ida a book of poems. Ida a boot 11. They have caught the thief with then had killed the zoo keeper. The zoo keeper 14. The company will pull down the buildings. The buildings 15. Be careful! Someone is following you. Be careful! You 16. I could eat no more cake. No more cake 17. They serve rice in the restaurant. Rice in th 18. The president's speech should convince the audience. The audience 10 Describe what the term poverty line means and how it was first calculated What would be the finite rate of increase for a population that has leveled off at its carrying capacity(K)? (Hint: if we assume carrying capacity is 149 and the population is at carrying capacity from T9-T12, calculate the finite rate of increase). CAN SOMEBODY SOLVE THIS EQUATION Which statements describe how the cardiovascular system and the respiratory system work together?Select all that apply.The cardiovascular system provides gases to the respiratory system to help it function.The respiratory system provides oxygen used in the cardiovascular system.The respiratory system provides nutrients and energy to the cardiovascular system.The cardiovascular system provides the respiratory system with what it needs to function. the ratio of the sides of a certain triangle is 2:7:8 if the longest side of the triangle is 40cm how long are the other two sides HelpppFor triangle ABC below, find missing side length BC and both missing angle measures how do i simplify this: (8 2/3)^4 Evaluate the following integral or state that it diverges. *integral 0 to 1 (ln x)do 3. Use the GCF and the Distributive Property to factor, 60a + 45.a. 3(20a +15)b. 5(12a +9). 20( + 2)d. 15(4a + 3) Students will write a paragraph (3-5 sentences): 1. Make at least one text-to-text connection to the folk stories read in the 1st.semester("My Lord Bag of Rice","Dragonwings") 2. Determine one or more elements they have in common. For example : Both folk tales and fables are fictional genres. What was one of the main goals of the mission system?to teach Indigenous peoples new skills and tradesto replace cultures of Indigenous peoples with European cultureto train Indigenous peoples as potential soldierso to learn from Indigenous peoples how to use resources A fruit company guarantees that 94% of the pineapples it ships will ripen within four days of delivery. Find the probability that at least 10 pineapples in a case of 12 are ripe within four days. PLEASE HELP PLEASE HELP How does primary and secondary succession affect ecosystems? Give examples 2. Asterisk (*) symbol in criteria for query stands for:(al Any number of characters(b) One characterC zero characters From a club of 20 people, in how many ways can a group of three members be selected to attend a conference?