State the domain, the range, and the intervals on which function is increasing decreasing, or constant in interval notation. State the domain and range using interval notation.

Answers

Answer 1

Answer:

[tex]Domain = (-\infty, \infty)[/tex]

[tex]Range = (-\infty, 4][/tex]

Increasing interval is: [tex](-\infty, 0)[/tex]

Decreasing interval is: [tex](0, \infty)[/tex]

Constant at no interval

Step-by-step explanation:

Given

See attachment for graph

Solving (a): The domain

From, the attached graph, we have:

[tex]y = -x^2 + 4[/tex]

The degree of the polynomial (i.e 2) is even.

Hence, the domain is the set of all real numbers, i.e.

[tex]Domain = (-\infty, \infty)[/tex]

Solving (b): The range

The curve of [tex]y = -x^2 + 4[/tex] opens downward, and the maximum is:

[tex]y_{max} = 4[/tex]

This means that the minimum is:

[tex]y_{mi n} = -\infty[/tex]

Hence, the range of the set is:

[tex]Range = (-\infty, 4][/tex]

Solving (c): Interval where the function increases/decreases/constant

In (a), we have:

[tex]Domain = (-\infty, \infty)[/tex]

Split to 2 (at vertex x = 0)

[tex](-\infty, 0)[/tex] and [tex](0, \infty)[/tex]

So:

The increasing interval is: [tex](-\infty, 0)[/tex]

The decreasing interval is: [tex](0, \infty)[/tex]

The function has a tangent at [tex]x = 0[/tex] but at no interval, was the function constant

State The Domain, The Range, And The Intervals On Which Function Is Increasing Decreasing, Or Constant

Related Questions

PLEASE HELP ME I WILL GIVE BRAINLIEST!!!

Answers

Answer:

Step-by-step explanation:

realtionship between distance and time is

distance=time/3

a.distance=time/3

129*3=time

387 s =time

Answer:

387

Step-by-step explanation:

129x3=387

Is the answer a b or c

Answers

Answer:

Step-by-step explanation: A

Answer:

B

Step-by-step explanation:

10 to 4

4 divided by 2 = 2, 2 x 5 = 10

15 to 6

6 divided by 2 = 3, 3 x 5 = 15

35 to 14

14 divided by 2 = 7, 7 x 5 = 35

4 1/2 plus 1 3/5 equal

Answers

Answer:

6 1/10

Step-by-step explanation:

459, 450, 441, ...
Find the 38th term.

Answers

Answer:

I am pretty sure it is 351

Cone 1 is congruent to cone 2 with dimensions given in units as shown below

What is the surface area of cone 2 ?



Please help !! ASAP giving 30 points too correct answer choice

Answers

The answer it is It’s the last one

Surface area of cone2 is equals to 96π.

What is surface area?

"Surface area is defined as the sum of the area of all the faces of given three dimensional shape."

Formula used

Surface area of the cone = πr² + πr l

According to the question,

Given,

'r' represents the radius of the cone

'h' represents the height of the cone

'l' represents the slant height of the cone

Cone1 and Cone2 are congruent cones.

⇒Radius of cone1 = Radius of cone2

  Slant height of cone1 = Slant height of cone2

As per the given dimensions we get,

Radius of both the cones 'r' = 6units

Slant height of both the cones 'l' = 10units

Substitute the values in the formula we get,

Surface area of the cone2 = π (6)² + π (6) (10)

                                            = 36π +60π

                                            = 96π square units

Hence, surface area of cone2 is equals to 96π.

Learn more about surface area here

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Solve: y = 2x. y = -x+3. Write the coordinates (__, __)

Answers

Answer:

(1,2)

Step-by-step explanation:

y = 2x. y = -x+3

Set the two equations equal

2x = -x+3

Add x to each side

2x+x = -x+x+3

3x = 3

Divide by 3

3x/3 = 3/3

x = 1

Now find y

y =2x = 2(1) = 2

(1,2)

Solve like how you solve the system of equations. System of Equations are to find the intercept of both graphs or to find which coordinate points are solution to both equations.

We are given the equations below:

[tex] \large{ \begin{cases} y = 2x \\ y = - x + 3 \end{cases}}[/tex]

Since both equations are y-isolated and we want to find the coordinate point that both equations have or the coordinate point that is a part of two equations.

[tex] \large{2 x = - x + 3}[/tex]

Isolate the x-term by adding both sides by x.

[tex] \large{2x + x = - x + 3 + x} \\ \large{3x = 3}[/tex]

Divide both sides by 3 so we can finally get the x-isolated equation.

[tex] \large{ \frac{3x}{3} = \frac{3}{3} \longrightarrow x = 1 }[/tex]

Next step is to find the value of y. x-term and y-term both have relations. That means when substituting x-term, we get y-term. Therefore, substitute x = 1 in any given equations. It is not necessary to substitute both, only one is fine. I will choose the first equation to solve for y-value.

[tex] \large{y = 2x}[/tex]

Substitute x = 1:

[tex] \large{y = 2(1) \longrightarrow y = 2}[/tex]

The value of y is 2 when x is 1. Since we want the answer to be in coordinate form or ordered pair. From (x,y) - we get (1,2).

Answer

(1,2) is the solution.

I hope this helps! Let me know if you have any questions or doubts. Do not hestitate to ask if you've got a question. Good luck on your assignment and have a great day!

Show that triangle FUN is isosceles.

Answers

an isosceles triangle is a triangle that has two sides of equal length

FU = 7 units

UN = 5 units

FN = 7 units

FU = FN

FU ≠ UN

FN ≠ UN

FUN is an isosceles triangle.

Given that tanx=-3/4 find sinx and cos x

Answers

HOPE IT HELPS MUCH

[tex]{{clickphoto2see}}the \: arnswer}}[/tex]

the three points A(0,0,0), B(2,-3,3) C(-2,3,-3) are collinear. find in what ratio each point divides the segment joining the other two.​

Answers

Answer:

pls provide diagram

it will hep

Do the ratios 11/6 and 23/9 form a proportion

Answers

NO

11/6 = 1. 8333

23/9= 2. 555

[tex]{hope it helps}}[/tex]

#CarryOnLearning

En el cumpleaños de Manolito se inflaron 144 globos. Los 2/9 de los globos eran rojos; los 5/18, verdes y 1/6 eran amarillos. ¿Cuántos globos eran de otros colores?

Answers

Answer:

48 globos

Step-by-step explanation:

De la pregunta anterior, se nos dice que:

En el cumpleaños de Manolito se inflaron 144 globos.

Por eso:

Para globos rojos

2/9 de los globos eran rojos

Número de globos rojos = 2/9 × 144 globos

= 32 globos

Para globos verdes

5/18 eran verdes

Número de globos verdes = 5/18 × 144 globos

= 40 globos

Para globos amarillos

1/6 eran amarillas

Número de globos amarillos = 1/6 × 144 globos

= 24 globos

Tenga en cuenta que:

Número total de globos =

Globos rojos + Globos verdes + Globos amarillos + Otros colores

Otros colores = 144 globos - (globos rojos + globos verdes + globos amarillos)

Otros colores = 144 globos - (32 + 40 + 24) globos

= 144 globos - 96 globos

= 48 globos

Por lo tanto, la cantidad de globos que son de otros colores = 48 globos

From $16 to $4
Percent decrease

Answers

Answer:

75%

Step-by-step explanation:

Answer:

75%

Step-by-step explanation:

The difference is $12 so let's calculate the percent of 12 to 16:

12/16 = 0.75 = 75%

What is the cost of 2 kilograms of flour if 3 kilograms cost $4.86 and the unit price for each package of flour is the same?

Answers

Answer: Your answer is on the bottom of the photo I used an online note table

Step-by-step explanation:

Answer:

I think the answer is $3.24.

Step-by-step explanation:

4.86 / 3 = 1.62

$1.62 is equal to how much 1 kilogram of flour would cost.

1.62 x 2 = 3.24

Hope this helped.

(75 points) need help now

Answers

Answer:

A is not a function

Step-by-step explanation:

In table A, the x value of 4 goes to two different y values

To be a function each x value can only go to one y value

A is not a function

Answer:

27 is the answer

Step-by-step explanation:

We have this proportion....

36 / 12 = x / 9 where x is the model door height

Cross-multiply

36*9 = 12 * x

324 = 12 *x divide both sides by 12

27 = x and that's the model height in centimeters

The Really Spicy Hot Sauce Company decides to make a special-edition, extra-spicy version of its Really Spicy Hot Sauce. Expected demand for the special-edition version of their hot sauce is estimated to be 5000, normally distributed with a standard deviation of 1200. It will cost $2.50 to make each bottle; the bottles are intended to sell for $20. Whatever doesn't sell will be given to employees as a gift, thus earning $0 in revenue. Because it takes 3 years for the hot sauce to fully ferment and mature, the Really Spicy Hot Sauce Company can only make one batch of the special-edition hot sauce. How many bottles should the company make in order to maximize their expected profit? ______________

Answers

$32,00 because it is a lot of money

please helpp due soon!! 10 points :)

Answers

Answer:

[tex]2.3\:\mathrm{in^3},\\1.3\:\mathrm{fl\:oz}[/tex]

Step-by-step explanation:

The volume of a cone with radius [tex]r[/tex] and height [tex]h[/tex] is equal to [tex]V=\frac{1}{3}\cdot r^2\pi\cdot h[/tex].

What we're given:

Since radius is half the diameter, [tex]r[/tex] is [tex]1.1[/tex] Height of [tex]1.8[/tex]

Substituting given values, we get:

[tex]V=\frac{1}{3}\cdot 1.1^2\pi \cdot 1.8=0.726\pi\approx \boxed{2.3\:\mathrm{in^3}}[/tex]

Convert to fluid ounces using the conversion given in the question:

[tex]0.726\pi}\cdot \frac{0.554}{1}\approx \boxed{{1.3\:\mathrm{fl\:oz.}}}[/tex]

Factor x3 – 7x2 – 5x + 35 by grouping. What is the resulting expression?

(x2 – 7)(x – 5)
(x2 – 7)(x + 5)
(x2 – 5)(x – 7)
(x2 + 5)(x – 7)

Answers

Answer:

Factor x3 – 7x2 – 5x + 35 by grouping. What is the resulting expression?

(x2 – 7)(x – 5) (x2 – 7)(x + 5) (x2 – 5)(x – 7)  <<<CORRECT (x2 + 5)(x – 7)

Step-by-step explanation:

Edge 2021

Polynomial is an expression that consists of indeterminates(variable) and coefficients. The correct option is A.

What are polynomials?

Polynomial is an expression that consists of indeterminates(variable) and coefficient, it involves mathematical operations such as addition, subtraction, multiplication, etc, and non-negative integer exponentials.

For the given expression x³ – 7x² – 5x + 35 the factorisation by grouping can be done as,

x³ – 7x² – 5x + 35

Take x² as common from the first two terms, while -5 as common from the last two terms,

= x²(x – 7) –5(x  – 7)

Take (x–7) as the common term from the two terms,

= (x² – 5)(x – 7)

Hence, the correct option is A.

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Which expression is equivalent to 16 - 4x^2?

Answers

Answer:

4(2 - x)(2 + x)

Step-by-step explanation:

16 - 4x² ← factor out 4 from each term

= 4(4 - x²) ← difference of 2 squares

= 4(2 - x)(2 + x) ← in factored form

can someone help me identify c(6)=

Answers

Answer and Step-by-step explanation:

To solve, simply plug 6 in for m in the equation.

C(6) = 50(6) + 79.50

6 times 50 is 300.

300 + 79.50 = 379.50 = C(6)

The answer is 379.5

(Looking at the question again, I don't think what I said is what it is asking for, soo)

The slope of the function given represents the amount that needs to be paid every month. The y-intercept (79.50) represents the initial cost (starting amount) for paying the membership.

#teamtrees #PAW (Plant And Water)

What is the value of a in the equation 3 a plus b equals 54, when b equals 9?

Answers

Answer:

a + b = 54

a + 9 = 54

Use inverse operations to solve

Step-by-step explanation:

Please look at the image

Answers

Answer:

3=1+2 because An exterior angle of a triangle is equal to the sum of the opposite interior angles

when 2=1

we can also write it as

3=1+1

3=21(this means twice of angle 1)

what are the factors of the expression below? 2bx+4by-3ax-6ay​

Answers

Answer:

Step-by-step explanation:

2bx + 4by -3ax -6ay

= 2b (x +2y) - 3a (x +2y)

= (x +2y) (2b-3a)

A baseball card was worth $120. Each year for x years, the card’s value, y, in dollars, decreased by $10. The owner sold the card after 5 years.

The value of the card can be modeled using a linear function. What is the domain of the function?

Answers

y = $120 - $10(5)
y = $150
domain = x or 5

The value of the card can be modeled using a linear function. The domain of the function is 5.

What is a linear equation?

A linear equation is an equation that has the variable of the highest power of 1. The standard form of a linear equation is of the form Ax + B = 0.

A baseball card was worth $120.

Each year for x years, the card’s value, y, in dollars, decreased by $10. The owner sold the card after 5 years.

y = $120 - $10(5)

y = $150

domain = x or 5

Learn more about linear equations;

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A basketball free throw can be modeled by a parabolic path, which can be represented by the function b(x) = - 0.25 x^2 + 4x, where x is time, in seconds, and b(x) is the height of the ball off the ground in feet.
What is the VERTEX and what do the coordinates mean in the context of the problem?

please solve algebraically

Answers

Answer:

The vertex of this problem is (8,16). This means that the highest height the ball reaches is at t = 8s, and this maximum height is of 16 feet.

Step-by-step explanation:

Vertex of a quadratic function:

Suppose we have a quadratic function in the following format:

[tex]f(x) = ax^{2} + bx + c[/tex]

It's vertex is the point [tex](x_{v}, y_{v})[/tex]

In which

[tex]x_{v} = -\frac{b}{2a}[/tex]

[tex]y_{v} = -\frac{\Delta}{4a}[/tex]

Where

[tex]\Delta = b^2-4ac[/tex]

If a<0, the vertex is a maximum point, that is, the maximum value happens at [tex]x_{v}[/tex], and it's value is [tex]y_{v}[/tex].

b(x) = - 0.25 x^2 + 4x

Quadratic equation with [tex]a = -0.25, b = 4[/tex].

Vertex:

[tex]x_{v} = -\frac{4}{2(-0.25)} = 8[/tex]

[tex]\Delta = 4^2-4(-0.25)(0) = 16[/tex]

[tex]y_{v} = -\frac{16}{4(-0.25)} = 16[/tex]

The vertex of this problem is (8,16). This means that the highest height the ball reaches is at t = 8s, and this maximum height is of 16 feet.

Both Eli Manning and Peyton Manning won 2 super bowls-
True
or
False

Answers

Answer:

-true

Step-by-step explanation:

I'm correct if I'm rwong

ckdksksksk i need hellll yal plsss

Answers

I think it’s -3,-4 if i’m not mistaken becuase when you rotate 180 degrees you are going to end up in the negative section.

Answer:

Its B (3,-4)

When rotating at point 180 degrees the equation for that is (-x,-y) so in this case (-3,4)

3 turns into a positive because two negatives equal a positive

and 4 turns into a negative

have a nice day :)

Kendra spent ⅓ of her allowance on a book and ⅖ on a snack. If she had four dollars remaining after purchasing a book and snack, what was the total amount of her allowance?

Answers

Answer: 15$

Step-by-step explanation:

Given

Kendra spent one-third of allowance on a book and two-fifth on snack.

If she had four dollar remaining after purchase

Suppose x is the original amount

[tex]\therefore x-\dfrac{x}{3}-\dfrac{2x}{5}=4\\\\\Rightarrow \dfrac{15x-5x-6x}{15}=4\\\\\Rightarrow 4x=60\\\Rightarrow x=15[/tex]

Thus, 15$ was her total allowance.

2. The Vasco da Gama Bridge in Lisbon, Portugal, includes a trapezoid as part of
its structure (pictured above). The bridge's roadway goes through the median of
the trapezoid. If the bases of the trapezoid measure 22 m and 38 m, what is the
approximate width of the bridge's roadway? Explain how you got your answer.

Answers

Answer:

30 m

Step-by-step explanation:

Midsegment of a Trapezoid

[tex]\frac{(Base_{1}) +( Base_{2}) }{2}[/tex]

[tex]\frac{12 + 38}{2}[/tex]

[tex]\frac{60}{2}[/tex]

30

Average of the top and bottom = the middle  

What is the longest math problem in the world?

Answers

I think it’s conjecture

If f(x) = 3x + 3, then f^-1 (x)=

Answers

Hello,

[tex]f(x)=3x+3 \Longleftrightarrow y=3x+3\\\\x=3*y+3 \Longleftrightarrow y=\dfrac{x-3}{3} \\\\\boxed{f^{-1}(x)=\dfrac{x-3}{3}}[/tex]

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