Let f(x)=x2 2x 3. What is the average rate of change for the quadratic function from x=−2 to x = 5? Enter your answer in the box.

Answers

Answer 1

The average rate of change for the quadratic function x²+2x+3 from x=−2 to x = 5 is 5.

What is Slope?

A slope is also known as the gradient of a line or the average rate of change of a number that helps to know both the direction and the steepness of the line.

The rate of change of any function is the slope of the function, therefore, the slope of the function is written as,

[tex]m = \dfrac{y_2 - y_1}{x_2-x_1}[/tex]

As the value of the y is the function of the x, while the value of x is given, therefore,

[tex]x_2 = 5\\x_1=-2\\\\[/tex]

Now, the value of y,

[tex]y_2 = f(5) = x^2 +2x+3 = (5)^2+2(5)+3 = 38\\y_1 = f(-2) = x^2 +2x+3 = (-2)^2+2(-2)+3 = 3[/tex]

Substituting the value of x and y in the formula of the slope, we can write the slope as,

[tex]m = \dfrac{y_2-y_1}{x_2-x_1}\\\\m = \dfrac{f(x=5) - f(x=-2)}{5-(-2)}\\\\m = \dfrac{38-3}{7}\\\\m= 5[/tex]

Hence, the average rate of change for the quadratic function x²+2x+3 from x=−2 to x = 5 is 5.

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Related Questions

I WILL GIVE 20 POINTS TO THOSE WHO ANSWER THIS QUESTION RIGHT NOOOO SCAMS

Answers

Answer:

8 m²

Step-by-step explanation:

1/2 × d1 × d2

= 1/2 × 4m × 4m

= 8 m²

Find mZCBA.
A
B
49°
с

Answers

[tex]AB=BC=>\angle A=\angle C=49а\\\angle CBA=180а-\angle A-\angle C=180а-49а-49а=82а[/tex]

plese guys I need help.

Answers

Answer:

1. 5 child tickets

Step-by-step explanation:

So 2 adult tickets would be 24$

So we do 64-24=40. So each child tickets cost 8$

So we do 40/8=5

So for number 1 they can buy 5 child tickets.

Jacob has $50 to spend he is going to buy a game for $15 and he wants to buy a gift for seven of his friends how much can he spend on each friend?

Answers

Answer:

$5

Step-by-step explanation:

Start by finding how much money Jacob has after buying a game for himself:

$50-$15=$35

Now, we have to divide $35 by 7 since he has 7 friends...

$35/7=$5

He can spend $5 on each friend

15$ for the game and 5$ to spend for each of Jacobs friends

50-15=35 35/5=5 or I'm wrong?

In the figure below, line j is parallel to line k and line r is parallel to s. Which statement is FALSE?
d° = f°
a° + d° = 180°
a° = c°
b° + e° = 180°

Answers

a+d=180

This question is logical because based on the graph or diagram a+d are two acute angles so they cannot equal 180.

Hope this is helpful! Please like and brainiest

The false statement:

a° + d° = 180°

The correct option is B.

What are the corresponding angles?

Corresponding angles are those formed at matching or corresponding corners with the transversal when two parallel lines are crossed by another line (i.e. the transversal).

Given:

Two pairs of parallel lines j and k, and r and s traverse each other.

d° = f° {opposite angles}

a° + d° = 180°

This is an incorrect statement.

a° = c° {Corresponding angles}

b° + e° = 180° (Sum of linear pair)

Therefore, a° + d° = 180°.

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Noah bought a new car costing $25,350 He took out a 5 year loan at a simple interest rate of 6 5% How much interest did Noah pay on his car?​

Answers

Answer:

1,647.75

Step-by-step explanation:

Well 25,340 times the interest rate .065 which equals 1647.75

PLEASE HELP
I've tried putting all my working out into the box but it said wrong to..​

Answers

Answer:

£59.25

Step-by-step explanation:

It appears you can measure the height of the trapezoid [trapezium  :-)  ??].  If you can't, you can use the Pythagorean Theorem (image attached).  Draw a line from the upper right-hand corner down to the baseline--the 20m side.  You'll form a right triangle with one leg  h , hypotenuse 17m and the other leg  8m  (the difference between 20m and 12m).

(leg)^2 + (leg)^2 = (hypotenuse)^2

h^2 + 8^2 = 17^2

h^2 + 64 = 289

h^2 = 225

h = 15m

The area of the trapezium is [tex]A=\frac{1}{2}h\left(b_1+b_2\right)[/tex]  where the b's are the lengths of the two bases (upper and lower sides).

[tex]A=\frac{1}{2}(15)(12+20)=\frac{1}{2}(480) = 240[/tex] m^2

One can of weedkiller covers 100 m^2 of area.  You'll need 3 cans (2 cans isn't enough, and you can't buy a fraction of a can).  Tricky question!

Three cans will cost  3 x 19.75 pounds = £59.25

yoooooooooooooooo I need help

Answers

Answer:

13/5 which is 2.6 so A.

Step-by-step explanation: Reduce the expression, if possible, by cancelling the common factors.

The answer is A the other person is right

The figure below hows three quadrilaterals on a coordinate grid:
Which of the following statements is true about the three quadnlaterals?
O A and B are similar but not congruent.
O A and C are similar but not congruent.
O A and B are similar and also congruent.
O B and C are similar and also congruent.

Answers

A and C are similar but not congruent

PLEASE HELP NO LINKS PLEASE

Answers

Answer:

x < -2

Step-by-step explanation:

its less than x, open circle

Answer:

x < -2

Step-by-step explanation:

Okay, so the dot is at -2 and is facing left. Left means less than, so, we know x is less than -2.

But we don't know if it's equal to or less than or just less than.

The dot is hollow, which in graphing means that it is not equal to or less than.

Therefore, the answer is x < -2

Brainliest please?  

true or false pls answer

Answers

it's false because two lines cannot be horizontally parallel

This is incorrect the given picture is not a function. If we draw a vertical line through the graph we see that it touched the graph twice, meaning this is not a function.

(brainliest?)

The table shows the side length and area of several different squares. Complete the table using
exact values.
side length (cm)
5
V63
49
98
102
area (cm

Answers

Answer:

from left to right: 25cm², 7cm, 63cm², 9.90cm (2dp), 10.10cm (2dp), 125cm²

The area of a 2D form is the amount of space within its perimeter. The table that shows the side length and area of several different squares as shown below.

What is an area?

The area of a 2D form is the amount of space within its perimeter. It is measured in square units such as cm², m², and so on. To find the area of a square formula or another quadrilateral, multiply its length by its width.

The area of a square is the square of the length of the side of the square. Therefore, the area of the square and the length of the side of the square can be written as,

Length of the side                Area

         side                              Side²

   5                                  25    7                                  49√63                                 63√98                                 98√102                               102√125                               125

Hence, the table that shows the side length and area of several different squares as shown above.

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3.84761 to 3 decimal place

Answers

the answer is 3.848.

The number 3.84761 become 3.848 after round off to 3 decimal place or thousandths place.

What is rounding off number?

Rounding is a technique to reduce a large number to a smaller, more approachable figure which is very similar to the actual. Rounding numbers can be achieved in a variety of ways.

We have a number:

= 3.84761

It is required to round off to 3 decimal place.

= 3.848  (0.0076 = 0.008)

Rounded to the nearest 0.001 or the Thousandths Place.

Thus, the number 3.84761 become 3.848 after round off to 3 decimal place or thousandths place.

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PLEASE HELP LAST QUESTION IT NEEDS TO BE CORRECT (WILL GIVE 20 POINTS!)

Answers

Answer:

it's 20 IT NEEDS TO BE CORRECT

What fraction is equal to 75% of 1/3

Answers

Answer:

1/4

Step-by-step explanation:

1.) Take 75% and convert it to a decimal, which is 0.75

2.) Then multiply 1/3 by 0.75

3.) Your answer is 0.25, and when 0.25 is converted to a fraction it is 1/4.

75% of 1/3 can be expressed as the fraction 1/4 by convert the percentage to a decimal, multiply it by the original fraction, and simplify the resulting fraction

To find the fraction that is equal to a given percentage of another fraction, follow these steps:

Step 1: Convert the percentage to a decimal by dividing it by 100. In this case, 75% is equivalent to 0.75.

Step 2: Multiply the decimal by the original fraction. In this case, 0.75 * 1/3 = 0.25/1.

Step 3: Simplify the resulting fraction, if possible. In this case, the fraction 0.25/1 can be simplified to 1/4.

Therefore, 75% of 1/3 is equal to the fraction 1/4.

To find the fraction that represents a given percentage of another fraction, convert the percentage to a decimal, multiply it by the original fraction, and simplify the resulting fraction if necessary. In this case, 75% of 1/3 is equal to the fraction 1/4.

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Simplify the following expression:
4x - 5.2y + 6y + 7.0x - 8x
Pleas i really need help this is confusing

Answers

Answer: 3x +1.2y

Step-by-step explanation:

you have to add the like terms together (the x’s plus the x’s, the y’s plus the y’s)

4x+7x=11x

11x-8x=3x

-5.2y+6y= 1.2y

Then you combine the x and the y for your answer.

3x+1.2y

Answer:

3x+0.8y

Step-by-step explanation:

4x-5.2y+6y+7x-8x

4x+7x-8x-5.2y+6y ( 4x+7x-8x → 3x)

3x-5.2y+6y ( -5.2y+6y → 0.8y)

3x+0.8y

Hope it helps! :)

If 1 inch represents 68 miles on a map, then how many inches will represent 8600 miles

Answers

Answer:

126.470588235

Step-by-step explanation:

I like to set these up like how I set up my radian conversions so what I do is I have one unit on top of a fraction and another on the bottom so it would look like this 1/68 = x/8600 this equation will let us solve for x which would be our inches to get 8600 so we just times 1/68 by 8600 and get 126.470588235 and just to check 126.470588235 * 68 = 8600

Determine if the sequence below is arithmetic or geometric and determine the common difference/ratio in the simplest form 2,8,32,…
I need this filled out in this format;
This is a____ sequence and the common ratio/common difference(choose one) is equal to___

Answers

Notice:

2 is first term

2*4 = 8 is second term

8*4 = 32 is third term

and so on


Each term is multiplied by 4 to get the next term, so it’s geometric. The “common ratio” is whatever you’re multiplying by, which is 4.

7) Solve the equation for the variable given.

Solve for x.

m=2x+b/3

Answers

Answer:

x= m/2 - b/6

(its a lot of work...)

Step-by-step explanation:

1. Subtract 2x from both sides

-2x=2x+b/3-2x

2. Simplify

-2x=b/3

3. Factor

x(m-2)=b/3

4. divide both sides by m-2; m≠2

x(m-2)/m-2=b/3/m-2 m≠2

5. Simplify again...

x=b/3(m-2); m≠2

The length of a
rectangle is represented by
4a + 3b, and its width is
represented by 7a – 2b. Write
a polynomial for the perimeter
of the rectangle.

Answers

Solution:

Given:

Length of rectangle = 4a + 3bWidth of rectangle = 7a - 2bPerimeter of rectangle = 2W + 2L

Let's simplify the perimeter of the rectangle by using the expression for the perimeter.

=> 2W + 2L=> 2(7a - 2b) + 2(4a + 3b)=> 14a - 4b + 8a + 6b=> 22a + 2b

Hence, the polynomial that represents the perimeter of the rectangle is 22a + 2b.

HELP MEEEEEEE :((((((((

Answers

Compound interest are used to determine interest on deposits

The balance as a function of time is [tex]y = 2000 * (0.2625)^{4t}[/tex]

How to determine the function

The given parameters are:

Principal, P = $2000

Rate, r = 5%

n = 4, (quarterly)

The amount remaining is calculated as:

[tex]A = P * (1+ r/n)^{nt}[/tex]

So, we have:

[tex]A = 2000 * (1+ 5\%/4)^{4t}[/tex]

Simplify

[tex]A = 2000 * (0.2625)^{4t}[/tex]

Rewrite as:

[tex]y = 2000 * (0.2625)^{4t}[/tex]

Hence, the balance as a function of time is [tex]y = 2000 * (0.2625)^{4t}[/tex]

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Which formula should be used to calculate the variance?.

Answers

Answer:

C is the formula you should use and the rest of the answers are below

Step-by-step explanation:

Hence, the formulae to calculate the variance are -

[tex]\sigma^2 = \frac{\displaystyle\sum_{i=1}^{n}(x_i - \mu)^2} {n}[/tex]     for a complete population and [tex]s^{2} = \frac{\displaystyle\sum_{i=1}^{n}(x_i - \mu)^2} {n-1}[/tex]  for a sample population.

We have Variance.

We have to specify the formula of variance.

What is Variance?

Variance is a measure of dispersion that takes into account the spread of all data points in a data set.

According to the question, the following formulae for variance are used according to the need.

For a Complete Population divide by the size n -

[tex]\sigma^2 = \frac{\displaystyle\sum_{i=1}^{n}(x_i - \mu)^2} {n}[/tex]

For a Sample Population divide by the sample size minus 1

[tex]s^{2} = \frac{\displaystyle\sum_{i=1}^{n}(x_i - \mu)^2} {n-1}[/tex]

Hence, the the formulae to calculate the variance are -

[tex]\sigma^2 = \frac{\displaystyle\sum_{i=1}^{n}(x_i - \mu)^2} {n}[/tex]     for a complete population and [tex]s^{2} = \frac{\displaystyle\sum_{i=1}^{n}(x_i - \mu)^2} {n-1}[/tex]  for a sample population.

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Please help! 10 points! It costs $60 to rent a car for a day, and each mile you drive costs $40. Write an expression for the daily cost to rent the car and drive D miles. How much will it cost if you drive 37 miles?

Answers

For you to drive 37 miles at $40 a mile it’ll be $1480. 60+(37•40)=$1540

Answer:

$1540

Step-by-step explanation:

base cost = $60
1 mile = $40
$40 x 37m = $1480
$1480 + $60
= $1540

Which equation is the inverse of y = 16x2 + 1?

Answers

D would be the best answer

Answer :

± [tex]\frac{\sqrt{x-1} }{4}[/tex]

There is a bag filled with 3 blue and 5 red marbles.
A marble is taken at random from the bag, the colour is noted and then it is not replaced.
Another marble is taken at random.
What is the probability of getting 2 that are different in colour?

Answers

Answer:

15/28

Step-by-step explanation:

There are 3 blue, 5 red and the total of 8 marbles.

Two different colored marbles are:

blue, then red or red, then blue

Find the probability of each case:

P(b, r) = 3/8*5/7 = 15/56P(r, b) = 5/8*3/7 = 15/56

Required probability is:

P(different color) = 15/56*2 = 15/28

Answer:

15/28 is the probability of getting 2 that are different in colour.

Step-by-step explanation:

3 blue and 5 red marbles

He is going to pick any marble, in second try, it must be a different colour marble.

total marble: 3 + 5 = 8 marbles

For blue marble:

In first try for blue marble: 3/8

total marble will decrease by 1, 7 marbles.

second try for red marble: 5/7

probability then: 5/7 *  3/8 = 15/56 is the probability for blue marble.

For red marble:

In first try for red marble: 5/8

total marble will decrease by 1, 7 marbles.

second try for blue marble: 3/7

probability then: 5/8 * 3/7 = 15/56

**

total probability of getting different in colour:

15/56 + 15/56

15/28  **

Help!! I don’t want to get this wrong ! Thank u

Answers

Answer:

95 degrees!!!

Step-by-step explanation:

add 5 to 90. or if you look at the protractor, after the 90, its on the 5 marker, which is why you add 5.

Convert 525 to a percent. helpppppppppppppp pleaseeeeeeeeeeeeeeee

Answers

Answer:

525 into a percent is 525%. Or 5.25.

Step-by-step explanation:

It's pretty simple.

All you have to do is this:

525 ⇒ 525%

All we did was put a percentage sign at the end at the number.

If you want to do it the hard way,

Do this:

525 ⇒ 5.25.

What we did was move a decimal point 2 spaces to the left.

This also counts as a percentage.

help i need help math is hard hard

Answers

Answer:

0.5, 7

Step-by-step explanation:

y=mx+b

-2y=0.5x+7

slope is m

yintercept is b

slope= 0.5

yintercept= 7

PLEASE ANSWER FAST SORRY IM IN A RUSH
72t^2+225

Answers

Answer:

9(8t^2+25)

Step-by-step explanation:

Which of the following are exterior angles? Check all that apply.

Answers

Answer:

2, 3, 5, 6

Step-by-step explanation:

because the angles are outside

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