For the function below, find a) the critical numbers; b) the open intervals where the function is increasing; and c) the open intervals where it is decreasing. f(x)=4x3−33x2−36x+3 a) Find the critical number(s). Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The critical number(s) is/are (Type an integer or a simplified fraction. Use a comma to separate answers as needed.) B. There are no critical numbers. b) List any interval(s) on which the function is increasing. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The function is increasing on the interval(s) (Type your answer in interval notation. Simplify your answer. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.) B. The function is never increasing. c) List any interval(s) on which the function is decreasing. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The function is decreasing on the interval(s) (Type your answer in interval notation. Simplify your answer. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.) B. The function is never decreasing.

Answer:

100+80+9+0.2+0.07+0.001

Answer:

the slope is -3

Step-by-step explanation:

down 6 and over 2 = -6/2 = -3

Answer:

slope = -3

Step-by-step explanation:

Line pass (1,2) and (3,-4)

slope = difference of y/difference of x

m = (-4 - 2)/(3 - 1) = -6/2 = -3

Answer:

X = 7

Step-by-step explanation:

Answer: D - 6x^2 + 5x - 4/15

Step-by-step explanation:

To simplify the expression (8x^2 - 3x + 1/3) - (2x^2 - 8x + 3/5), we can combine like terms within the parentheses

8x^2 - 3x + 1/3 - 2x^2 + 8x - 3/5

Next, we can combine the like terms

(8x^2 - 2x^2) + (-3x + 8x) + (1/3 - 3/5)

Simplifying

6x^2 + 5x + (5/15 - 9/15)

The fractions can be simplified further

6x^2 + 5x + (-4/15)

Thus, the simplified expression is 6x^2 + 5x - 4/15

Answer:

$4,351.48

Step-by-step explanation:

This is because if you take 6,000 and use the part over whole method, 6,000 x 100 = 600,000 divided bt 105.5 = 5,687.20, continue that with the same numbers, except you replace the part with the last answer you got.

6,000 after 6 months

5,687.20 after 5 months

5,390.72 after 4 months

5,109.68 after 3 months

4,843.30 after 2 months

4,590.81 after 1 month

4,351.48 as the initial deposit.

when you click on the tutoring tab it will show you all the details

Answer:

3

Step-by-step explanation:

y+3=-y+9

Move -y to the left and move +3 to the right and change the + into a -

y+y=-3+9

Calculate

2y=6

Divide both members by 2

y=3

Answer:

Hey there!

g(x) is 4x-1

f(g(x) is f(4x-1)

f(4x-1)=2(4x-1)-5

f(4x-1)=8x-2-5

f(4x-1)=8x-7

The answer is 8x-7

Let me know if this helps :)

In the given triangle, one side is 4 cm longer than another side, and the angle bisector divides the opposite side into 5-cm and 2-cm segments. The perimeter of the triangle is 20 cm. If the first side of the triangle is x cm longer than the second side, the perimeter of the triangle can be expressed as 2x + 18 cm.

Let the second side of the triangle be y cm. According to the given information, the first side is 4 cm longer than the second side, so its length is y + 4 cm. The ray bisecting the angle divides the opposite side into segments of length 5 cm and 2 cm.
By applying the angle bisector theorem, we can set up the following proportion:
(5 cm) / (y + 4 cm) = (2 cm) / y
Cross-multiplying and simplifying, we get:
5y = 2(y + 4)
5y = 2y + 8
3y = 8
y = 8/3 cm
Now, we can calculate the lengths of the other sides of the triangle:
First side = y + 4 = 8/3 + 4 = 20/3 cm
Third side = 5 cm + 2 cm = 7 cm
The perimeter of the triangle is the sum of the lengths of all three sides:
Perimeter = (20/3) cm + (8/3) cm + 7 cm = (2/3)(20 + 8) cm + 7 cm = 20 cm
If the first side is x cm longer than the second side, then the length of the first side would be y + x cm. The perimeter of the triangle can be expressed as the sum of all three sides:
Perimeter = (y + x) cm + y cm + 7 cm = 2x + 2y + 7 cm = 2x + 18 cm, since y = 8/3 cm as determined earlier.
Therefore, the perimeter of the triangle in terms of x is 2x + 18 cm.

Learn more about triangle here
https://brainly.com/question/29083884



#SPJ11

The probability that a teenager plays varsity sports, given that they play a team sport, is approximately 0.4884 or 48.84%.

To find the probability that a teenager plays varsity sports given that they play a team sport, we can use conditional probability.

Let's denote:

A: Playing varsity sports

B: Playing a team sport

We are given:

P(B) = 43% = 0.43 (Probability of playing a team sport)

P(A) = 21% = 0.21 (Probability of playing varsity sports)

We need to find PA(|B), which represents the probability of playing varsity sports given that the teenager plays a team sport.

The conditional probability formula is:

P(A|B) = P(A ∩ B) / P(B)

P(A ∩ B) represents the probability of both A and B occurring simultaneously.

In this case, the probability of a teenager playing varsity sports and a team sport simultaneously is not given directly. However, we can make an assumption that all teenagers who play varsity sports also play a team sport. Under this assumption, we can say that P(A ∩ B) = P(A) = 0.21.

Now we can calculate P(A|B):

P(A|B) = P(A ∩ B) / P(B)

       = 0.21 / 0.43

      ≈ 0.4884

Therefore, the probability that a teenager plays varsity sports, given that they play a team sport, is approximately 0.4884 or 48.84%.

To learn more about probability click here:

brainly.com/question/22946813

#SPJ11

The piecewise functions that are represented by the graph are; g(x) = −2, x < −2; g(x) = −2x + 6, x ≥ 1; g(x) = x/2 + 1, –2 ≤ x < 1

From the attached graph of the piecewise function, we can access each option as follows;

A) g(x) = −2x, −2 < x < 0

This is not represented by the graph because g(x) = −2x has negative slope which means it goes downward. There's also no y-intercept in g(x) = −2x.

B)  g(x) = −2, x < −2;

This is represented by the graph because g(x) = −2 is a horizontal line which is only on the left side of x = -2.

C) g(x) = x − 2, −2 < x < 1;

This is not represented by the graph because g(x) = x − 2 has y-intercept at y = -2 and slope of 1 which means that graph of g(x)= x - 2 must be going upward and crossing at y = -2.

D) g(x) = −2x + 6, x ≥ 1

This is represented by the graph because g(x) = −2x+6 satisfies the graph which is going downward.

E) g(x) = x/2 + 1, –2 ≤ x < 1

This is represented by the graph because g(x) = (x/2) + 1 satisfies the graph which is going downward.

The options are;

g(x) = −2x, −2 < x < 0

g(x) = −2, x < −2

g(x) = x − 2, −2 < x < 1

g(x) = −2x + 6, x ≥ 1

g(x) = x/2+ 1, –2 ≤ x < 1

Read more about Piecewise Function at; https://brainly.com/question/3628123

#SPJ1

Answer:

x=-2 and x = 5

Step-by-step explanation:

The solutions to the equation are where the graph crosses the x axis

We can see that the graph crosses at x=-2 and x = 5

Answer:

x = -2

x = 5

Step-by-step explanation:

The answer is found when the graph crosses the x-axis

Hope this helps :D

Answer: I

Step-by-step explanation:

A new sample size of at least 537 fish to estimate the true mean length with a margin of error of 0.5 centimeters and 95% confidence.

To determine the size of a new sample so that the true mean length is estimated with a margin of error of 0.5 centimeters with 95% confidence, we need to find the standard error of the mean and use it in the formula for the margin of error.

The formula for the margin of error is: ME = z * (σ/√n)

where z is the z-score corresponding to the desired confidence level, σ is the standard deviation of the population, and n is the sample size.

We can estimate the standard deviation of the population using the sample variance, which is given as 34.9.

The standard deviation is the square root of the variance, so σ = √34.9

= 5.91.

To find the standard error of the mean, we divide the standard deviation by the square root of the sample size:

SEM = σ/√n

= 5.91/√n We want the margin of error to be 0.5 centimeters, so we can set up the equation:

0.5 = z * (5.91/√n)

To solve for n, we need to know the value of z for a 95% confidence level.

This corresponds to a z-score of 1.96. Substituting this into the equation gives: 0.5 = 1.96 * (5.91/√n)

Simplifying and solving for n gives: √n = 1.96 * (5.91/0.5) √n

n =(23.18)

n = 537

To know more about centimeters visit:

https://brainly.com/question/9133571

#SPJ11

Step-by-step explanation:

Male=60kg

female=45kg

accelerate= 2.0 m/s

solution,

Here,

a= v-u

2.0= 60-45

2.0 = 15

= 15-2.0

Accelerate = 13 m/s is a male skater .

The acceleration of the male skater will be 13 meters per second.

The rate at which an object's velocity with respect to time changes is referred to as acceleration in mechanics. They are vector quantities and accelerations.

Given that in the pair competition of Olympic figure skating, a 60-kg male skater pushes a 45-kg female skater.

Male=60kg

female=45kg

accelerate= 2.0 m/s

The value of the acceleration will be calculated as:-

a + m = v-u

2.0 + m= 60-45

2.0 + m  = 15

m = 15-2.0

m =13 meters per second

Therefore, the acceleration of the male skater will be 13 meters per second.

To know more about acceleration follow

https://brainly.com/question/460763

#SPJ5

Answer:

Part A

The height to which the projectile reaches is given by the following formula;

\(\Delta y = y-y_0 = v_{0y} \times t-\dfrac{1}{2} \times g \times t^2\)

Where;

\(v_{0y}\) = The initial velocity of the projectile = Stays the same

y = The height the projectile reaches

y₀ = The height from which the projectile is launched

g = The acceleration due to gravity

t = The time taken

Given that the projectile has the same initial velocity, the variation of Δy with time, 't', will be the same when the project is launched from a different height, and the time change that it takes for the projectile to reach the maximum height will be the same for the previous launch height

Part B

From the change in eight of the projectile, Δy = y - y₀, the maximum height reached, 'y', is therefore given as follows;

y = Δy + y₀

The maximum height will increase by 'y₀', where 'y₀' is the difference between new height and the previous height, \(y_i\)

That is, if y₀ > \(y_i\), the maximum height reached increases and if y₀ < \(y_i\), y₀ will be added as y = Δy - y₀ and the maximum height reached decreases

Step-by-step explanation:

Answer:

(a) The strip should be 5ft wide

(b) The strip around the outside field is 10ft wide.

Step-by-step explanation:

Given:

Length of the rectangular field, L= 200 ft

width of the rectangular field, w = 100 ft

Area of the rectangular field, A = 200ft x 100ft = 20000 ft^2

let the width of the strip = x

The strip around the outside field = 2x

If the field is increased by 15.5%

New area of the field = 1.155 x 20000 = 23,100 ft^2

The increase in area of the field = 3,100 ft

3,100 = New area of field - old area of the field

3100 = (200 + 2x)(100 + 2x) - 20000

3100 = 20000 + 400x 200x + 4x^2 - 20000

3100 = 600x + 4x^2

Divide through by 4

775 = 150x + x^2

x^2 + 150x - 775 = 0

Factorize

(x + 155)(x-5) = 0

x = 5 ft

The strip should be 5ft wide.

The strip around the outside field = 2 x 5 ft = 10 ft

Thus, the strip around the outside field is 10ft wide.

Answer:

338.64

Step-by-step explanation:

set up a proportion x/408=83/100 cross multiply you get 338.64

Answer: 338.64 is the Answer.  

Step-by-step explanation:

83 x 408/100  (First do 83 x 408, then divide the answer by 100.)  

= 338.64

Answer:

26 inches.

Step-by-step explanation:

Lilly: 12 x 2 + 2 = 26

Anita: 12

Answer:

6.1

Step-by-step explanation:

Answer:

6.164? idkr sorry

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

The answer would be B

Step-by-step explanation:

From 1 second to 3 seconds Denise had stopped

We can tell that this is true because looking at the graph we can see that from 1 to 3 seconds the distance stayed the same which indicates that Denise was not walking

Answer:

I think it is B  between 1 and 3 bc a flat line shows no progress and the only area where is show a flat line is between 1 and 3 so he stopped walking at that point

Step-by-step explanation:

Answer:

y = 2x + 1

Step-by-step explanation:

formula for equation of graph:

\(y = mx + c\)

substitute m = 2 and c = 1 into the equation

\(y = 2x + 1\)

Step-by-step explanation:

please see it my step work solution

Answer:

x + 5

Step-by-step explanation:

Step 1: Write expression

x + 2 + 3

Step 2: Combine like terms (constants)

x + 5

Answer:

i think A

Step-by-step explanation:

Answer:

The answer is c, I don't know how I'm supposed to show a graph, if that's what you wanted

Step-by-step explanation:

The product of the given polynomials is -2x² + 5x - 2.

Given two polynomial functions, f(x) and g(x).

f(x) = 2x - 1 and g(x) = -x + 2

We have to find the product of these polynomials.

Numerically, we can find the area as,

f(x) g(x) = (2x - 1) (-x + 2)

            = -2x² + x + 4x - 2

            = -2x² + 5x - 2

Area model can be done by drawing a rectangle and then marking the length of the rectangle as 2x - 1 and the width of the rectangle as -x + 2.

Area of the rectangle = length × width                                                                                                      

Hence the product of the given polynomials is -2x² + 5x - 2.

Learn more about Product of Polynomials here :

https://brainly.com/question/1603555

#SPJ1

The slope-intercept form of the equation 8x + 6y = 5 is y = (-4/3)x + 5/6, and the slope is -4/3, while the y-intercept is 5/6.

To write the equation 8x + 6y = 5 in slope-intercept form, we need to isolate the y variable on one side of the equation.

8x + 6y = 5

Subtract 8x from both sides:

6y = -8x + 5

Divide both sides by 6 to solve for y:

y = (-8/6)x + 5/6

Simplifying the equation further:

y = (-4/3)x + 5/6

Now we can identify the slope and y-intercept of the line:

The slope (m) is the coefficient of x, which is -4/3.

The y-intercept (b) is the constant term, which is 5/6.

Leran more about slope-intercept here: https://brainly.com/question/30216543

#SPJ11

The expression for the area of the rectangle is (5 + 4)t or 9t.

Options C and E are the correct answer.

A rectangle is a 2-D shape with length and width.

The length and width are different.

If the length and width are not different then it is a square.

The area of a rectangle is given as:

Area = Length x width

We have,

From the figure,

Length = 5 + 4

Width = t

Now,

The area of the rectangle.

= Length x Width

= (5 + 4) t

= 9t

Thus,

The area of the rectangle is (5 + 4)t or 9t.

Learn more about rectangles here:

https://brainly.com/question/15019502

#SPJ1