Mathematics High School

Find the point(s) at which the function f(x) = 5 - 2x equals its average value on the interval [0,4]. The function equals its average value at x=

Answers

Answer 1

Thus, the point(s) at which f(x) = 5 - 2x equals its average value on the interval [0,4] is x=5/2.

To find the point(s) at which the function f(x) = 5 - 2x equals its average value on the interval [0,4], we first need to find the average value of the function on this interval. The formula for the average value of a function f(x) on an interval [a,b] is:

average value = (1/(b-a)) * ∫[a,b] f(x) dx

In this case, a=0 and b=4, so the average value of f(x) on [0,4] is:

average value = (1/(4-0)) * ∫[0,4] (5-2x) dx
average value = (1/4) * [5x - x^2] from 0 to 4
average value = (1/4) * [(5(4) - 4^2) - (5(0) - 0^2)]
average value = (1/4) * (0)
average value = 0

So the average value of f(x) on [0,4] is 0. Now we need to find the point(s) where f(x) equals 0. We can set the function equal to 0 and solve for x:

5 - 2x = 0
2x = 5
x = 5/2

So the function f(x) equals its average value of 0 at x=5/2. Therefore, the point(s) at which f(x) = 5 - 2x equals its average value on the interval [0,4] is x=5/2.

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Related Questions

Susan graphed a system of equations for the lines y = 3x + 1 and y = 3x - 10. Which statement is true about Susan's lines?
The lines intersect once at a right angle because they are perpendicular.
The lines intersect at all points because they are the same line.
The lines intersect three times because each has a slope of three.
The lines do not intersect because they are parallel and have different y-intercepts.

Answers

Answer: The lines do not intersect because they are parallel and have different y-intercepts.

Step-by-step explanation:

I need help getting started

Answers

1. 3/4
2.-7/6
3.3/4
4.-1/4
5.-5/4
6.-1/2
7.-3/4
8.-5/3

Santino pays $36.85 for eleven 10-count boxes of granola bars. How much does 1 box of granola bars cost?

Answers

Answer:

One box of granola bars costs $3.35.

Step-by-step explanation:

36.85/11=3.35

what are all the sums and differences of 3/4?​

Answers

Answer:

1/2 + 2/4

11/12 - 1/6  

3/5 + 3/20  

7/8 - 1/2

Step-by-step explanation:

choose the answer that represents the product below as an exponential expression*​

Answers

Answer:

B

Step-by-step explanation:

the bases are the same and according to exponential laws exponents of the same base are added

Answer:

B

Step-by-step explanation:

Write the linear equation in slope-intercept form given the following:
(-3, 7) and (6, -8)

Answers

Answer:

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

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 3, 7) and (x₂, y₂ ) = (6, - 8)

m = [tex]\frac{-8-7}{6+3}[/tex] = [tex]\frac{-15}{9}[/tex] = - [tex]\frac{5}{3}[/tex] , then

y = - [tex]\frac{5}{3}[/tex] x + c ← is the partial equation

To find c substitute either of the 2 points into the partial equation

Using (6, - 8) , then

- 8 = - 10 + c ⇒ c = - 8 + 10 = 2

y = - [tex]\frac{5}{3}[/tex] x + 2 ← equation of line

PLEASE HELP URGENT
Hank's age is 5 more than three times John's age. Hank
is 29 years old. How old is John?

Answers

8. Because 29-5 =24 and 24/3 =8

broooo plzzz helpppp

Answers

Answer:

3 3/5 + 1 1/4 = 4 17/20

7/8 + 1/12 = 23/24

8/9 - 2/5 = 22/45

5 1/4 - 2 2/3 = 2 7/12

Step-by-step explanation:

3 3/5 + 1 1/4

First convert into improper fractions

= 18/5 + 5/4

Now find the common denominator

72/20 + 25/20 =

97/20

Now simplify

4 17/20

Next problem:

7/8 + 1/12

find the common denominator

21/24 + 2/24 =

23/24

Next problem:

8/9 - 2/5

find the common denominator

40/45 - 18/45 =

22/45

Next problem:

5 1/4 - 2 2/3

First convert into improper fractions

21/4 - 8/3

find the common denominator

63/12 - 32/12 =

31/12

Now simplify

2 7/12

Decide wether the function is linear or nonlinear.
Linear function
Nonlinear function

Answers

the function is NONLINEAR

it does not follow a constant rate of change

(Look at photo for reference)

Answers

Answer:

B

Step-by-step explanation:

6% is usually represented by 0.06

Hope this helped :)

I need help plz......I'll give brainliest:
The sum of two numbers is 44. The smaller number is 12 less than the larger number. What are the numbers?

Answers

x+(12+x)=44

2x+12=44

2x=32

x=32/2

x=16  

The two numbers are 16, 28  

Hope I helped :)

If the cos 90° = 0, then the sin 0° = _____.


pls help

Answers

Answer:

I think its 0

Step-by-step explanation:

Answer:

This one too clicked by me

Are 0.34 and 3/4 equivalent? Please explain your answer In complete sentences.

Answers

no

when 3 divided by 4 is converted into a decimal, it is 0.75 which does not equal 0.34

0.34 can also be written as 34/100
and 3/4 can be written as 75/100

therefore 0.34 and 3/4 are not equivalent

Radium-226 has a half-life of 1660 years. How many years does it take a radium sample to decay to 55% of the original amount? Round your answer to the nearest year.

Answers

Answer:

1432 years

Step-by-step explanation:

A(t) = I(0.5)^t/t1/2

Where t1/2 = half life = 1660

Final amount, A(t) = 0.55 of its original amount =. 0.55I

Hence, we have

0.55I = I(0.5)^t/1660

Take the log of both sides

Log(0.55) = log(0.5)^t/1660

t/1660 = log(0.55) / log(0.5)

t/1660 = 0.8624964

t = 0.8624964 * 1660

t = 1431.7441

t = 1432(nearest whole number)

A cone has a volume of 47.1 cm³ and a radius of 3 cm what is its height?

Answers

Radius of cone ( r ) = 3 cm,

Curved surface area of a cone= 47.1 cm²

Curved surface area of a cone= πrl

47.1 = πrl

47.1 = 3.14 × 3 × l

l = 47.1 / (3.14 × 3)

l = 15.7 / 3.14= 1570/314= 5 cm

slant height (l) = 5 cm

Height of a cone (h) = √(l²) - (r²)

h = √ 5² -3²

h = √ 25 - 9 = √ 16 = 4 cm

h = 4 cm

Volume of cone= ⅓(πr²h)

= ⅓(3.14 × 3 × 3 × 4)

= 3.14 × 12= 37.68 cm³

Hence, the volume of a cone is 37.68 cm³.

A spinner has 3 sections of different sizes. The sections are orange, purple, and green. 1/4 of the spinner is orange. 7/12 of the spinner is purple. Which fraction of the spinner is green?

Answers

Answer: it would be 2/3

Step-by-step explanation:

2/3z=-6

Help please!!

Answers

Answer:

z = -9

Step-by-step explanation:

if 2x + 16 = -6x what is x

Answers

Answer:

x = -2

Step-by-step explanation:

Answer:

x is -2

Step-by-step explanation:

8x+16=0

subtract 16 from both sides

8x=-16

Divide each term by 8 and simplify

x=-2

what is the median of 9.3 an 6.8?????

Answers

Answer:

Désolé mec mais je n'ai pas compris ta question

Find the missing length indicated.

Pls Help

Answers

none of them are correct


On a certain hot summer's day, 234 people used the public swimming pool. The
daily prices are $1.25 for children and $2.00 for adults. The receipts for admission totaled
$435.00. How many children and how many adults swam at the public pool that day?

Answers

Answer44 children and 190 adults

Step-by-step explanation:

Combine any like terms in the expression. If there are no like terms, rewrite the expression.
7j2 + 3j2 + j?

Answers

Answer:

10j^2 +j

Step-by-step explanation:

I added the first two terms since they have the same exponent and then left the j because its not squared or anything

Which of the following is a rational number? Select all that apply.

A. √1
B. √3
C. √4
D. √5
E. √8
F. √9

Answers

Answer: The numbers that are rational numbers are A, C, and F.

Step-by-step explanation: This is because all non-perfect square roots are always irrational. Also, perfect square roots are always RATIONAL. Therefore, the rational numbers of the choices given are [tex]\sqrt{1} , \sqrt{4}, \sqrt{9}[/tex]

Answer:  A, C, and F. √1 √4 √9

Which represents the solution(s) of the graphed system of equations, y = x2 – 2x and y = –2x – 1?



(1, –1)
(0, 0) and (0, –1)
(0, 0) and (2, 0)
no solutions

Answers

Hopefully someone comes along and helps, 0,0 - 732 + 3

Answer:

D) no solutions :D

What is the multiplicative rate of change for the exponential function f(x)= 3 (2/3)^-x
A. 0.4
B. 2.5
C. 0.6
D. 1.5

Answers

Answer:

C basta Yan ang sagot HAHAHA dko mapicturan solution ko e

Step-by-step explanation:

ano ba yan arte nyo sabing yan ang sagot e

Answer:

c 0.6

Step-by-step explanation:

lol

PLS PLS HELP ASAP I WILL MARK BRAINLIEST
Using the given equation find the missing coordinates of the points and then find the slope of the line for the equation.
y=3.5x+4; A(...;5), B(10;...)

Answers

Okay so,

A (0.2875; 5), B (10; 39)

THE SLOPE IS 3.5

There are three rows of VIP seats in each section. Each row
has 12 seats and there are 16 sections. How many VIP seats
are there in all?

Answers

Answer:

The answer is 576 seats

Step-by-step explanation:

3 rows x 12 seats = 36 seats in one section

36 seats in one section x 16 sections = 576 seats

Solve for n:
1-5|n-9|=-74

I need answer by 12:10, please help!!!

Answers

Answer:

[tex]n=-6, 24[/tex]

Step-by-step explanation:

We are given:

[tex]1-5|n-9|=-74[/tex]

Subtract 1 from both sides:

[tex]-5|n-9|=-75[/tex]

Divide both sides by -5:

[tex]|n-9|=15[/tex]

By definition of absolute value:

[tex](n-9)=15\text{ or } -(n-9)=15[/tex]

Solve for each case:

[tex]n=24\text{ or } n=-15+9=-6[/tex]

Therefore, our two solutions are:

[tex]n=-6, 24[/tex]

How do I write a phrase in words as an algebraic expression for 8/d?

Answers

Answer:

The quotient of 8 and d.

Step-by-step explanation:

I hope this helps you have a wonderful day! :D

It took Hank 3.4 hours to travel 124 miles. At that rate, how long will it take Hank to travel 310 miles?

Answers

Answer: Time = 8.5 hours

Step-by-step explanation:

Step 1

Speed = distance / time

Distance  traveled by  Hank = 124 miles

Time = 3.4 hrs

Speed= Distance / Time

= 124/ 3.4 = 36.47 miles per hour

Step 2

At this same rate of speed =36.47 miles per hour, if he travels 310 miles, he will spend=

Time = Distance / Speed

Time = 310/ 36.47

Time =8.5 hours

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