(4x²+9x-7) - (-7x²+5x-1)

Answer:

The average rate of change of [tex]f(x) = x^2 +6x+13[/tex]  is 12

The average rate of change of [tex]f(x) =- x^2 +6x+13[/tex] is 10

Step-by-step explanation:

The  average rate of change  of f(x) over an interval between 2 points (a ,f(a)) and (b ,f(b)) is the slope of the  secant line  connecting the 2 points.

We can calculate the average rate of change between the 2 points  by

[tex]\frac{f(b) - f(a)}{b -a}[/tex]-------------------(1)

(1) The average rate of change of the function [tex]f(x) = x^2 +6x+13[/tex]  over  the interval 1 ≤ x ≤ 5

f(a) = f(1)

[tex]f(1) = (1)^2 +6(1) + 13[/tex]

f(1) =1+6+13

f(a) =  20---------------------(2)

f(b) = f(5)

[tex]f(5) = (5)^2 +6(5)+13[/tex]

f(5) = 25 +30 +13

f(5) = 68-----------------------(3)

The average rate of change between (1 ,20) and (5 ,68 ) is

Substituting eq(2) and(3) in (1)

=[tex]\frac{f(5) - f(1)}{5-1}[/tex]

=[tex]\frac{68 -20}{5-1}[/tex]

= [tex]\frac{48}{4}[/tex]

=12

This means that the average of all the slopes of lines tangent to the graph of f(x) between  (1 ,20) and (5 ,68 ) is 12

(2) The average rate of change of the function  [tex]f(x) = -x^2 +6x+13[/tex] over  the interval -1 ≤ x ≤ 5

f(a)  = f(-1)

[tex]f(1) = (-1)^2 +6(-1) + 13[/tex]

f(1) =1-6+13

f(1) = 8---------------------(4)

f(b) = f(5)

[tex]f(5) = (5)^2 +6(5)+13[/tex]

f(5) = 25 +30 +13

f(5) = 68-----------------------(5)

The average rate of change between (-1 ,8) and (5 ,68 ) is

Equation (1) becomes

[tex]\frac{f(5) - f(-1)}{5-(-1)}[/tex]

On substituting the values

=[tex]\frac{68 - 8}{5-(-1)}[/tex]

=[tex]\frac{60}{5+1}[/tex]

=[tex]\frac{60}{6}[/tex]

= 10

This means that the average of all the slopes of lines tangent to the graph of f(x) between  (-1 ,8) and (5 ,68 ) is 10

To rewrite the expression (y + 1) + 4 without using parentheses, we can distribute 4 to the terms inside the parentheses and then combine like terms.

To rewrite the expression without using parentheses, we can use the distributive property. The distributive property states that multiplying a number by a sum is the same as multiplying the number by each term in the sum and then adding them together. In this case, we have (y + 1) + 4, and we can distribute the 4 to both terms inside the parentheses. So, (y + 1) + 4 can be rewritten as y + 1 + 4.Next, we can combine like terms. The terms y and 1 do not have any common variable factors, so they cannot be combined. However, 1 and 4 are both constants, so they can be added together to give us 5. Therefore, y + 1 + 4 simplifies to y + 5.

So, the expression (y + 1) + 4 can be rewritten as y + 5.

https://brainly.com/question/35587796

#SPJ2

Answer:

Step-by-step explanation:

3/8

Answer:

Step-by-step explanation:

40%

The formula is

Old-new/old *100

115-69/115*100

The percentage decrease is 40% if the price of an item yesterday was 115. Today the price fell to 69.

It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.

We have:

The price of an item yesterday was 115. Today the price fell to 69.

The difference in price = 115 - 69 = 46

Percentage decrease = (46/115)×100 = 40%

Thus, the percentage decrease is 40% if the price of an item yesterday was 115. Today the price fell to 69.

Learn more about the percentage here:

brainly.com/question/8011401

#SPJ2

To evaluate the expression 24/b+8 for b=9, substitute 9 for b to get 24/9 + 8, which simplifies to approximately 10.67.

To evaluate the expression 24/b+8 when b=9, we substitute the value of b into the expression and perform the arithmetic operation.

First, we replace b with 9:

24/9 + 8

Then, we divide 24 by 9:

2.666... + 8

Next, we add 8 to the quotient:

2.666... + 8 = 10.666...

The result of evaluating the expression 24/b+8 for b=9 is approximately 10.67.

The series in sigma notation is:  representing terms increasing by 4 starting from -5.

To represent the series in sigma notation, let's first examine the pattern of the terms.

The given series starts with -5 and each subsequent term increases by 4. We can express this pattern using the formula:

[tex]\[ a_n = -5 + (n - 1) \times 4 \][/tex]

Here, [tex]\( a_n \) represents the \( n \)th term of the series[/tex].

Now, let's break down the components of the formula:

-[tex]\( -5 \) is the initial term of the series.- \( (n - 1) \) accounts for the position of each term in the series. When \( n = 1 \), \( (n - 1) = 0 \), so the first term is \( -5 \). As \( n \) increases, \( (n - 1) \) increases by 1, causing the series to increase by 4 each time.- \( 4 \) is the common difference between consecutive terms in the series.[/tex]

Next, we represent the series using sigma notation:

[tex]\[ \sum_{n=1}^{5} (-5 + (n-1) \times 4) \][/tex]

This notation indicates that we sum up the expression [tex]\( -5 + (n-1) \times 4 \) for \( n \)[/tex] ranging from 1 to 5, which covers all the terms of the given series.

In summary, the series is represented in sigma notation as described above, capturing the pattern of increasing terms starting from -5.

Answer:

B shows 50% shaded

Step-by-step explanation:

Count how many triangles are in it (4) then see how many are shaded (2/4).

Simplify it to 1/2=50% then you got your answer.

Answer:

B

Step-by-step explanation:

because there is 2 trangle shaded and 2 trangle remain blank

The relationship between the distance traveled by a car and the amount of gas in the car is inverse. As the distance increases, the gas decreases

The relationship between the distance traveled by a car and the amount of gas in the car is inverse. This means that as one quantity increases, the other decreases. In this case, as the distance traveled by a car increases, the amount of gas in the car decreases, because the car uses gas to move. In other words, the more you drive, the less gas you have left in your car.

https://brainly.com/question/10025284

#SPJ2

Answer:

The vaues to the given equations are x=-2 and y=-4

Therefore the solution set is (-2,-4)

Step-by-step explanation:

Given equations are [tex]3x+3y=-18\hfill (1)[/tex]

[tex]-2x+2y=-4\hfill (2)[/tex]

To solve the given equation to find the solution set :

Multiply the equation (1) into 2 we get

[tex]6x+6y=-36\hfill (3)[/tex]

Multiply the equation (2) into 3 we get

[tex]-6x+6y=-12\hfill (4)[/tex]

Now adding the equations (3) and (4) we get

[tex]6x+6y=-36[/tex]

[tex]-6x+6y=-12[/tex]

________________

[tex]12y=-48[/tex]

[tex]y=\frac{-48}{12}[/tex]

Therefore y=-4

Substitute the value of y=-4 in the equation (1) we get

[tex]3x+3y=-18[/tex]

[tex]3x+3(-4)=-18[/tex]

3x-12=-18

3x-12+12=-18+12

3x=-6

[tex]x=\frac{-6}{3}[/tex]

Therefore x=-2

The vaues to the given equations are x=-2 and y=-4

Therefore the solution set is (-2,-4)

Final answer:

Buying the least expensive car can save $85, and the average price of the car from the three dealers is $14,250.

Explanation:

To address the question concerning the savings and the average price of a car being advertised by three different dealers, we perform the following calculations:

Answer:  8 miles

Step-by-step explanation:

24/3=8

Answer:

The answer is NOT D, because clearly the angle measurements are not EQUAL. So cross that off. My best guess would be A, acute triangle. Usually for that the two angles are shown as the same and the top angle is usually smaller. That's just from picturing it in the head.

Step-by-step explanation:

Can I have brainliest

Answer: The Answer is acute triangle

to know if something is linear when you graph it it is always going to be in a straight line. if it isn't then it is not linear

Answer:

D

Step-by-step explanation:

i got it right on E2020

Answer: According to the pattern i think its 66

Step-by-step explanation:

The correct statement is that the terms are

A. The next three numbers are 1/8, 1/32, and 1/128.

B. The next three-term will be 9, 13.5, and 20.5.

A sequence is a list of elements that have been ordered in a sequential manner, such that members come either before or after. A series is a sum of sequence terms. That is, it is a list of numbers with adding operations between them.

Given

A. 32, 8, 2, 1/2, ...

B. 16/9, 8/3, 4, 6, ...

A.  32, 8, 2, 1/2... can be expressed as [tex]2^{2n - 1}[/tex]

Then For n= -1, -2, and -3, Then the next three numbers will be

[tex]2^{-2 - 1} \ \ \ \ \ , \ 2^{-4 - 1} \ \ \ \ \ , \ 2^{-6 - 1}\\\dfrac{1}{8} \ \ \ \ \ \ \ \ \ \ \ , \dfrac{1}{32} \ \ \ \ \ \ \ \ \ \ , \dfrac{1}{128}[/tex]

The next three numbers are 1/8, 1/32, and 1/128.

B.  16/9, 8/3, 4, 6... each term increases by 2/4. So the next three-term will be 9, 13.5, and 20.5.

Thus, the terms are 9, 13.5, and 20.5.

More about the sequence and the series link is given below.

https://brainly.com/question/8195467

Answer:

  45 minutes

Step-by-step explanation:

  1.5 × (30 min) = 45 min

It took Kyle 45 minutes to run the race.

Answer:

45 minutes

Step-by-step explanation:

If it is one and a half it would be a whole so 30 but the half, is half of 30, so 15. 30+ 15= 45

Answer:

See attachment.

Step-by-step explanation:

The given inequality is -2 < x - 3 < 5.

We add 3 to each part of -2 +3< x - 3+3 < 5+3

We now simplify to get: 1 < x < 8.

To represent this on the number line, we have to draw open circles at 1 and 8 and connect them as shown in the attachment.

Answer

6,000x

Explanation

To work out how many times greater something is compared to another, we have to divide the larger number by the smaller

To put it more simply, imagine you had 30 apples and I had 6. To work out how many times greater your apple collection was than mine, you would divide your 30 by my 6, and find that you had 5 times as many apples as me (30 ÷ 6 = 5).

The principle is the same here, how many more viruses (3 x 10⁹) are there compared to protozoa (5 x 10⁵)?

We do 3 x 10⁹ ÷ 5 x 10⁵

3 x 10⁹ = 3,000,000,000

5 x 10⁵ = 500,000

3,000,000,000 ÷ 500,000 = 6,000 times more

Answer:

C

Step-by-step explanation:

12 divided by 3 is 4 and 30 divided by 3 is 10

30 cm on the smaller figure corresponds to 12 meters on the larger figure.

We can write the ratio   30 cm : 12 m

If we divide both parts by the GCF 6 then,

30/6 = 5

12/6 = 2

This means the ratio  30 cm : 12 m  reduces to 5 cm : 2 m

Telling us "2 meters on the real house correspond to 5 cm on the doll house"

Answer:

bruh dis ni gga should keep all his lemonade forget his friends

Step-by-step explanation:

The ball that reached the highest is Mario's because his reached past 10 whereas Jasmine's was 7.8. The ball that went the farthest is Jasmine's.

Answer:

14pqr+35pqr = pqr×(14+35)

The value of b in the equation [tex]\( 3.2 = \frac{4}{5}(b - 5) \)[/tex] is 9.

To solve for b in the equation [tex]\(3.2 = \frac{4}{5}(b - 5)\)[/tex], we'll first distribute [tex]\(\frac{4}{5}\)[/tex] across b - 5:

[tex]\[3.2 = \frac{4}{5}b - \frac{4}{5} \times 5\]\[3.2 = \frac{4}{5}b - 4\][/tex]

Next, let's isolate the term containing b by adding 4 to both sides:

[tex]\[3.2 + 4 = \frac{4}{5}b\]\[7.2 = \frac{4}{5}b\][/tex]

Now, to solve for b, we'll multiply both sides by [tex]\(\frac{5}{4}\)[/tex] to isolate b:

[tex]\[b = 7.2 \times \frac{5}{4}\]\[b = 9\][/tex]

So, the value of b is 9.

Answer: (i) 4x - 40 = 76

(ii) 29 questions

Step-by-step explanation:

Let the total number of questions be x.

Since he received 4 points for every correct answer and he got 10 answers wrong , this means he lost 40 points , the equation thus become

4x - 40 = 76

To find the value of x , add 40 to both sides

4x = 116

divide through by 4

x = 29

Therefore , there are 29  questions on his math test

Answer:

a) -3x^3 - 2x + y - 10 = 0

b) it a trinomial

c) not sure. sorry. :(

hope this helps.:)

Answer:

The best answer is 12.4 units.

Step-by-step explanation:

This is because, when I totaled all of the side lengths, I got an estimated result of 12 units. 12.4 is the next closest answer, so your answer is 12.4

I hope this helps!

- sincerelynini

Step-by-step explanation:

To get the right answer always you can use the save route: Pythagoras' theorem.

[tex] \sqrt{(x1 - x2)^{2} + (y1 - y2)^{2} } [/tex]

Answer:

3rd one

Step-by-step explanation:

Answer:

x=1, y=-1. (1, -1).

Step-by-step explanation:

y=-2x+1

y=x-2

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

-2x+1=x-2

-2x-x=-2-1

-3x=-3

3x=3

x=3/3

x=1

y=1-2=-1

Answer:

-3×3×-3×-3 is positive

Answer:

-3 x 3 x -3 x -3 because the answer is -81.

(Bottom Left)