The function LaTeX: f\left(x\right)=-x^2+4f ( x ) = − x 2 + 4 defined on the interval LaTeX: -8\le x\le8− 8 ≤ x ≤ 8 is increasing on the interval LaTeX: \left[A,B\right][ A , B ] and decreasing on the interval LaTeX: \left[C,D\right][ C , D ]. Fill in the blanks below.

Answers

Answer 1

Given:

The function is

[tex]f(x)=-x^2+4[/tex]

It defined on the interval -8 ≤ x ≤ 8.

To find:

The intervals on which the function is increasing and the interval on which decreasing.

Step-by-step explanation:

We have,

[tex]f(x)=-x^2+4[/tex]

Differentiate with respect to x.

[tex]f'(x)=-(2x)+(0)[/tex]

[tex]f'(x)=-2x[/tex]

For turning point f'(x)=0.

[tex]-2x=0[/tex]

[tex]x=0[/tex]

Now, 0 divides the interval -8 ≤ x ≤ 8 in two parts [-8,0] and [0,8]

For interval [-8,0], f'(x)>0, it means increasing.

For interval [0,8], f'(x)<0, it means decreasing.

Therefore, the function is increasing on the interval [-8,0] and decreasing on the interval [0,8].


Related Questions

Each year, votes are cast for the rookie of the year in a softball league. The voting results for the top three finishers are shown in the table below. How many points is a third-place vote worth?

Answers

Answer:

A third place vote is worth 1 point

Step-by-step explanation:

Let the number of points for a first place vote be x, number of points for a second place vote be y and the number of points for a third place vote be z.

So, by multiplying the number of points by the number of what the point is worth and adding all together, we shall have the total points;

Hence, we have the following equation systems;

23x + 5y + z = 131

5x + 17y + 4z = 80

x + 5y + 15z = 35

These are the three equations we need to solve simultaneously to get the value of z

From equation 3, x = 35 -5y -15z

Insert this into the first two equations;

23 ( 35 -5y -15z) + 5y + z = 131

5(35-5y-15z) + 17y + 4z = 80

805 - 115y -345z + 5y + z = 131

805-131 = 115y + 345z -5y - z

674 = 110y + 344z ••••••••••(*)

The second equation now becomes the following;

5(35-5y-15z) + 17y + 4z = 80

175 -25y -75z + 17y + 4z = 80

175-80 = 25y + 75z -17y -4z

95 = 8y + 71z

8y + 71z = 95 •••••••••••(**)

So we have to solve x and xx simultaneously;

110y + 344z = 674

8y + 71z = 95

110/8 = 13.75 , so multiply equation xx by 13.75 and equation x by 1

110y + 344z = 674

110y + 976.25z = 1306.25

Subtract equation xx from x

(976.25z - 344z) = (1306.25 -674)

632.25z = 632.25

z = 632.25/632.25

z = 1

Use the Distance Formula to find the distance between (−3, 7) and (8, −6) , rounded to the nearest hundredth.

Answers

Answer:

d= 17.03

Step-by-step explanation:

[tex]d=\sqrt{ (x_{2}-x_{1})+(y_{2}-y_{1})^{2}}\\\\d=\sqrt{(8--3)+(-6-7)^{2}}\\\\d=\sqrt{(11)+(-13)^{2}} \\\\d=\sqrt{121+169}\\\\d= \sqrt{290} \\\\d=17.03[/tex]

Natalie budgets $146 for yoga training. She buys a yoga mat for $10 and spends $9 per day on yoga classes. Which inequality represents the number of days, d, that Natalie can take classes and stay within her budget?

Answers

5

explanation- hope this helped!

John’s truck used 22 gallons of gasoline while traveling 175 miles. Which expression can be used to determine the truck’s miles per gallon fuel consumption?

Answers

Mi/gal.

Or In this case, the correct answer would be:

22/175

Miles per gallon basically means how many miles in one gallon.

So miles dived by gallon

If this helped, please mark branliest.

Answer:

Mi/gal

Step-by-step explanation:

I think. I’m not sure.

Solve the equation.
-10x + 1 + 7x = 37
O x= -15
O x= -12
O x = 12
O x = 15

Answers

the awnser should be x = -12
the answer to this question is X=12

f(x)= |x|; translation 3 units to the right followed by a translation 2 units up

Answers

Answer:

What is the question??

Step-by-step explanation:

I am confused.

How can you tell if there will be more than one solution for the geometric means? Why does this happen with the geometric means?

Answers

Answer:

a. We can tell if there will be more than one solution for the geometric means if the set of numbers is an even number.

b. This happens because, there are two possible values for the nth root of a set of even numbers.

Step-by-step explanation:

a. How can you tell if there will be more than one solution for the geometric means?

We can tell if there will be more than one solution for the geometric means if the set of numbers is an even number.

Since geometric means of n numbers from x₁,x₂, x₃,...,xₙ is

GM = ⁿ√x₁,x₂, x₃,...,xₙ .

Now, if n is an even number, the geometric means would have both a positive and negative value.

For example, if n = 2,

GM = ±√x₁,x₂ which is

GM = +√x₁,x₂ or -√x₁,x₂.

b. Why does this happen with the geometric means?

This happens because, there are two possible values for the nth root of a set of even numbers. For example if n = 2,

GM = ±√x₁,x₂ which is

GM = +√x₁,x₂ or -√x₁,x₂.

So, we have two possible values for the geometric means.

0.02 divided by 924.3

PLEASE HELP

Answers

Answer:

0.00002163799

Step-by-step explanation:

Answer:

0.00002163799

Step-by-step explanation:

What is z?
A. 54
B. 92
C. 88
D. 93
117 87 39 48 44 87

Answers

z is obviously c which is 88

At top speed, a rabbit can cover 6 miles in 12 minutes. If a rabbit could
continue at this rate indefinitely, how long would it take the rabbit to
cross the 220-mile expanse of the Mojave Desert?

Answers

Answer:

440 minutes

Step-by-step explanation:

i just multiplied by 2

Evaluate the following expression when t= 2 .
t² – 44 - 4
Help please

Answers

Answer:

-44

Step-by-step explanation:

So you want to plug 2 in for t, so the equation should now look like:

[tex]2^{2}[/tex] - 44 - 4

No all you have to do is solve

[tex]2^{2}[/tex] = 4

4 - 44 = -40

-40 - 4 = -44

Answer:

-44

Step-by-step explanation:

t=2, t² - 44 - 4

1. substitute in the value to the variable: 2² - 44 - 4

2. using PEMDAS, solve the equation: 2² - 44 - 4 = 4-44-4 = -40-4= -44

(evaluate the exponent, then subtract)

If (72)x = 1, what is the value of x?

Answers

Answer:

x= 1/72  or in decimal form 0.0138

Step-by-step explanation:

the 8 is repeating

Answer:

1/72

Step-by-step explanation:

Given the following functions f(x)

Answers

Answer:    x

============================================

Work Shown:

[tex]g(x) = \frac{(x-1)^2}{3}\\\\g(f(x)) = \frac{(f(x)-1)^2}{3}\\\\g(f(x)) = \frac{(1+\sqrt{3x}-1)^2}{3}\\\\g(f(x)) = \frac{(\sqrt{3x})^2}{3}\\\\g(f(x)) = \frac{3x}{3}\\\\g(f(x)) = x\\\\[/tex]

The idea is to start with g(x) and then replace every x with f(x). From there you plug in f(x) = 1+sqrt(3x) and simplify.

Juno and his 3 friends are evenly dividing the group rate cost for entrance to the zoo.
The group cost is n dollars. Write the expression that tells how much Juno will pay.

Answers

Answer:

1) Are dividing the group rate cost.

2) Multiplication.

3) Action is being performed on the variable.

4) n/4 or n [divided sign] 4

Step-by-step explanation:

Atleast this book tells you. but most times its a multi questioning test like online.

Help please I will give brainliest!

Answers

Answer:

I believe it would be $1.25

Step-by-step explanation:

Since a lot of people bought doughnuts, that would probably be what most of them are spending their money on.

Look at the attachment for the question please hurry!!!

Answers

Answer:

Neither

Step-by-step explanation:

The two lines going through those points to not intersect at a 90-degree angle.

For each sequence, find the first 4 terms and the 10th term.
A) n+5
B)2n-1

Answers

Answer:

see explanation

Step-by-step explanation:

(a)

To find the first 4 terms substitute n = 1, 2, 3, 4 into the n th term formula.

a₁ = 1 + 5 = 6

a₂ = 2 + 5 = 7

a₃ = 3 + 5 = 8

a₄ = 4 + 5 = 9

For the 10 th term substitute n = 10, that is

a₁₀ = 10 + 5 = 15

The first 4 terms are 6, 7, 8, 9 and the 10 th term is 15

(b)

Substitute n = 1, 2, 3, 4 and 10 into the n th term formula

a₁ = 2(1) - 1 = 2 - 1 = 1

a₂ = 2(2) - 1 = 4 - 1 = 3

a₃ = 2(3) - 1 = 6 - 1 = 5

a₄ = 2(4) - 1 = 8 - 1 = 7

a₁₀ = 2(10) - 1 = 20 - 1 = 19

The first 4 terms are 1, 3, 5, 7 and the 10 th term is 19

What are the y-intercept and the x-intercept:

y=4x-4​

Answers

Answer:

X=1

Step-by-step explanation:

0=4x-4

-4x=-4

-4x/-4=-4/-4

x=1

the y intercept can be found by setting x equal to 0. so the equation becomes:
y = 4(0)-4
y = 0-4
y = -4

the y intercept is -4

to find the x intercept, do the same thing but with y (set y to 0)to get:
0 = 4x - 4
4x = 4
x = 1

the x intercept is 1


Solve each equation algebraically. Show work. #1,#4,and #6

Answers

Answer:

In order to solve these, you must combine your variable terms and move them till they are isolated from your constants. Divide until the variable is alone on one side.

Answer:

1. 7

Step-by-step explanation:

1. 8y= 37+ 35

Subtract 3y from both sides of the equation:

8y - 3y = 3y + 35 - 3y

simplify:

combine like terms

than combine like terms again

5y= 35

Divide both sides of the equations by the same term:

5y = 35

[tex]\frac{5y}{5} = \frac{35}{5}[/tex]

simplify:

cancel terms that are in both the numberator and denominator

divide numbers

7

 

Mario is walking away from a motion detector at a rate of 1.5 feet per second. He started recording his distance from the motion detector when he was 2 feet in front of the motion detector. Fill in the blank in the sentence below. Mario is 11 feet from the motion detector at ____ a seconds

Answers

Answer:

6 seconds

Step-by-step explanation:

Initial distance of Mario from motion detector = 2 ft

Speed of Mario = 1.5 ft/sec

Total distance of Mario from motion detector = 11 ft

Total distance moved by Mario while walking at the rate of 1.5 ft/sec = 11 - 2 = 9 ft

Given that:

Distance = 9 ft

Speed = 1.5 ft/sec

Formula:

[tex]Distance = Speed \times Time[/tex]

[tex]\Rightarrow 9 =1.5 \times Time\\\Rightarrow Time = \dfrac{9}{1.5}\\\Rightarrow Time = \bold{6\ sec}[/tex]

So, at 6 seconds, Mario will be 11 ft from the motion detector.

5x - 3(x+1) = 2x - 3

Answers

Step-by-step explanation:

taking L.H.S

5x-3(x+1)

5x-3x-3

2x-3

proved

Answer:

True for all x

Step-by-step explanation:

Add similar elements 2x-3=2x-3

Add 3 to both sides

Simplify 2x=2x

Subtract 2x from both sides

Simplify 0=0

Both sides are equal True for all x

What is the slope of the line passing through (16, -2) and (-30, 6)?

Answers

[tex]m=\frac{\Delta y}{\Delta x}=\frac{-2-6}{16-(-30)}=\frac{-8}{46}=\boxed{-\frac{4}{23}}[/tex].

Hope this helps.

- 4/23 is what i got

4 × (1,351 - 381)

Which of the following is true about the expression above?
A.
The given expression is 4 more than (1,351 - 381).

B.
The given expression is 4 times as large as (1,351 - 381).

C.
The given expression is 4 times smaller than (1,351 - 381).

D.
The given expression is 4 less than (1,351 - 381).

Answers

Answer:

B

Step-by-step explanation:

The multiplication symbol is often referred to as "____ times as large" when written in text form

what is a compound interest​

Answers

Answer:

Compound interest is the addition of interest to the principal sum of a loan or deposit, or in other words, interest on interest. It is the result of reinvesting interest, rather than paying it out, so that interest in the next period is then earned on the principal sum plus previously accumulated interest

Step-by-step explanation:

Please mark as brainliest

Answer:Compound interest is the addition of interest to the principal sum of a loan or deposit, or in other words, interest on interest.

Step-by-step explanation:

8 times 10^5 + 5 times 10^4 = ? In scientific notation

Answers

Answer:

It's 8.5*10^5

Step-by-step explanation:

Find f (2) - 4 using the following equation.
f(x) = 5x – 2
f (2) - 4 =

Answers

On this equation it would be 5(2)-2=f(2) which f(2)=8 then 8-4=4.

In a bag of trail mix, for every 9 peanuts there are 7 pieces of chocolate. Write the ratio
of chocolate to peanuts.

Answers

Answer:

9 /9 + 7

= 56.25%

5.444444444444444444

5 if rounded

Step-by-step explanation:

The stone's height (in meters above the water), I seconds after Ricardo threw it, is modeled by
w(x) = -5(x – 8)(x +4)
How many seconds after being thrown will the stone reach its maximum height?
seconds

Answers

Answer: 2 seconds

-5(x-8) (x+4)

x-8=0 or x+4=0

x=8. or x=-4

Now we now the 2 x.

8+ -4/2 = 2 seconds

Cost of microscope is $269.95 markup is 43%

Answers

Answer:

386.0285

Step-by-step explanation:

Ally works in a shop for $18 per hour. She is not allowed to work more than 40 hours a week but has to work at least 20 hours. State a reasonable domain for this problem.

Answers

Answer:

Hi there!

The domain is:

20<=x<=40

Step-by-step explanation:

This states that:

x>=20

x<=40

Which fits the problem!

Hope this helps

For a given function f(x) we define the domain as the set of possible values of x that we can use in the function.

Here we will find that the domain is D: [20h, 40h]

We know that Ally wins $18 per hour, and she has two restrictions:

She cant' work more than 40 hours.

She needs to work at least 20 hours.

Then her weekly salary can be written as:

s(x) = $18*x

Where x is the number of hours that she works each week.

With the above restrictions we have:

20h ≤ x ≤ 40h

Then the domain is:

D: [20h, 40h]

If you want to learn more, you can read:

https://brainly.com/question/16875632

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