A functionf(x) is graphed on the coordinate plane.
What is the function rule in slope-intercept form?
Enter your answer in the box.
f(x)=

The absolute maximum value occur (3, 4.033) at point x = 3

The function given in the problem is g(x) = 3x³e⁻ˣ

differentiating the function

g(x) = 3x³e⁻ˣ

g'(x) = 3x³(-e⁻ˣ) + e⁻ˣ(9x²)

g'(x) = e⁻ˣ(-3x³ + 9x²)

equating to zero

0 = e⁻ˣ(-3x³ + 9x²)

0 = -3x³ + 9x²

3x³ = 9x²

x = 3

checking intervals close to 3: the check is done using numbers at the left and right to 3 and this numbers will be sufficiently close.

We choose 1 and 5, when the value of g'(x) increases from positive to negative then maximum value occurs

at x = 1, g'(1) = e^(-1)(-3(1)³ + 9(1)²) = 2.2073

at x = 3, g'(3) = e^(-3)(-3(3)³ + 9(3)²) = 0

at x = 5, g'(5) = e^(-5)(-3(5)³ + 9(5)²) = -1.0107

We can say that x = 3 is point of local maxima

g(3) = 3(3)³e^(-3) = 4.03275 = 4.033

from calculation the absolute maximum value occurs at (3, 4.033)

From the graph the absolute maximum value for the domain -1 ≤ x ≤ 5 occurs at (3, 4.033)

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Answer:

∠ BDC = 29°

Step-by-step explanation:

the sides of a rhombus are congruent, so CD = ED and Δ EDC is therefore isosceles with base angles congruent , then

∠ BCD = ∠ BED = 61°

• the diagonals are perpendicular bisectors of each other , then

∠ CBD = 90°

the sum of the 3 angles in Δ BCD = 180°

∠ BDC + ∠ CBD + ∠ BCD = 180°

∠ BDC + 90° + 61° = 180°

∠ BDC + 151° = 180° ( subtract 151° from both sides )

∠ BDC = 29°

Answer:

x=80°

Step-by-step explanation:

Straight line=180°

therefore,

180=2x-30+50

minus 50 on both sides

130=2x-30

plus 30 on both sides

160=2x

divide 2 on both sides

x=80

Answer:

m∠A = 130

Step-by-step explanation:

Here, In a given figure

m∠A = 2x - 30°

Now, we know that the sum of all angle is 180° on a straight line

So,

2x - 30° + 50° = 180°

2x + 20° = 180°

2x = 180° - 20°

2x = 160°

x = 160° ÷ 2

x = 80°

Here, we get the value of x is 80°

Now,

m∠A = 2x - 30°

m∠A = 2(80°) - 30°

m∠A = 160° - 30°

m∠A = 130

Thus, m∠A = 130

-TheUnknownScientist

Answer:

x≤20

Step-by-step explanation:

x+5≤25

 -5.  -5

x≤20

Hopes this helps please mark brainliest

Answer:

The answer is B

Step-by-step explanation:

20+5=25 and x can be greater than or equal to 25

Answer: 3 times 3 equals 9 times 4 equals 36

Step-by-step explanation:

Answer:

36cm^3 for volume 12cm^2 area

Step-by-step explanation:

theres only 3 sides here ill assume that these are the three sides to the solid. multiply all 3x4x3

im assuming the 3cm and 4cm will make a surface area so 3x4

The volume of the sphere can be calculated using the formula V = 4/3πr³

A sphere is a geometrical object that is a three-dimensional analogue to a two-dimensional circle. A sphere is the set of points that are all at the same distance r from a given point in three-dimensional space. It is a perfectly-round 3D shape with one continuous curved surface

We have a sphere.

Since the dimensions of a sphere are not given, we will assume it. Assume the radius of sphere be [r]. Then the approximate value of the volume of the sphere can be calculated using the formula -

V = 4/3πr³

Where -

[r] is the radius of sphere

Therefore, the volume of the sphere can be calculated using the formula V = 4/3πr³

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It takes time of near about 35 year.

Given that,

Storage capability of computers has been doubling every 5 years

The date of 1st computer made = 1980

computer could store 5 megabytes,

Now,

We can use the following calculation to determine how long it took computers to store 100 megabytes:

Therefore,

Log₂ (final amount / beginning amount)

=  Log₂ (100 / 0.5)

= log₂ (200)

= 7.64 is the number of doublings.

If each doubling takes five years, then it would take computers just over seven doublings or almost 35 years to store 100 megabytes.

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Answer:

39364

Step-by-step explanation:

You can simplify the equation to make 4(1+3+9...) The nth term is therefore \(3^{n-1}\) so u can substitute that into the equation so 4(\(3^{n-1}+ 3^{n} + 3^{n+1}\)..). This would simplify to 4(\(3^0 +3+3^2\)+\(3^3+3^4+3^5+3^6+3^7+3^8\)). By simplifying this, you can make it so 4(\(2^2+6^2+18^2+42^2+81^2\)) = 4(4+36+324+2916+6561) =39364

3rd one

25. 2/11 yvyvybyivyvtcyvjjvyvyvufugucyftcyf

Answer:

Yes, it'd be the red and green one, along with the top left blue portion if that is allowed to be picked too.

Step-by-step explanation:

Top left Blue Portion: (-infinity, -3]

Red Portion: [-3, 0]

Green Portion: [3, infinity)

Answer:

The numbers are 6 and 7.

Step-by-step explanation:

4² = 16

5² = 25

6² = 36

7² = 49

√36 = 6

√42 = ?

√49 = 7

The numbers are 6 and 7.

Answer:  Multiply the original price by the decimal form of the percent and subtract that from the original price.

37*0.85=31.45

37-31.45=5.55

Answer: New price is $5.55

The two integers are equal to 1 and 7 respectively.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Let x represent the smaller number. Then the given relationships say ...

1/x + 2/(x+6) = 9/7

Multiplying by 7x(x+6), we have ...

7(x+6) +14x = 9x(x+6)

9x² +54x = 21x +42 . . . . .eliminate parentheses, swap sides

9x² +33x = 42 . . . . . . . . ...subtract 21x

3x² +11 -14 = 0 . . . . . . . . . .subtract 42 and divide by 3

(3x +14)(x -1) = 0 . . . . . . . . factor

Values of x that make this true are x = 1 and x = -14/3. Then for the positive integer x=1, the other integer is x+6=7.

Therefore, the two integers are equal to 1 and 7 respectively.

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The ratio of the given 240 kg to 6 kg will be 40:1.

What is Ratio?

Comparing two amounts of the same units and determining the ratio tells us how much of one quantity is in the other. Two categories can be used to categorise ratios. Part to whole ratio is one, and part to part ratio is the other. The part-to-part ratio shows the relationship between two separate entities or groupings. Mathematicians use the term "ratio" to compare two or more numbers. It serves as a comparison tool to show how big or tiny an amount is in relation to another. Two quantities are compared using division in a ratio. In this case, the dividend is referred to as the "antecedent" and the divisor as the "consequent."

the ratio 240 kg to 6 kg.

It will be simple 240/6 :: 40 :1

Hence the ratio of the given data will be 40:1

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The best representation of the number of tiles that will be needed to cover the Floor is 80 tiles.

The number of tiles needed to cover the floor, we can calculate the total area of the floor and divide it by the area of each tile.

The area of the floor is given by the product of its length and width: 15 feet * 12 feet = 180 square feet.

The area of each tile is given by the product of its length and width: 1.5 feet * 1.5 feet = 2.25 square feet.

To find the number of tiles needed, we divide the total area of the floor by the area of each tile:

Number of tiles = (Total area of the floor) / (Area of each tile) = 180 square feet / 2.25 square feet = 80 tiles.

therefore, the best representation of the number of tiles that will be needed to cover the floor is 80 tiles.

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Answer:

50126.978033

Step-by-step explanation:

12000(1.10)^15

12000 is your starting amount.

You earning 10% investment so add 1 to that 10% and make it a decimal = 1.10

Raise is to 15 years because it's compounded for 15 years.

Answer:

$88,292

Step-by-step explanation:

answer was asked to my teacher she told me it was that   hope this helps you :)

Answer:

n = 19

Step-by-step explanation:

2n > 36 ( divide both sides by 2 )

n > 18

and

5n < 100 ( divide both sides by 5 )

n < 20

so n > 18 and n < 20

thus n = 19

To match the graphs of cylinders a and b to cylinders P and Q, we need to analyze the relationship between the height of the water and the volume of water in each cylinder.

Cylinder P would correspond to graph b, while Cylinder Q would correspond to graph a.

The reasoning behind this is as follows:

Cylinder P, corresponding to graph b, shows a steeper increase in height with increasing volume. This indicates that the water level rises quickly as more volume is added, suggesting that the cylinder has a smaller cross-sectional area. Since height is directly proportional to volume for a cylinder, a smaller cross-sectional area would result in a higher rise in height for the same volume of water.

Cylinder Q, corresponding to graph a, shows a slower increase in height with increasing volume. This implies that the water level rises more gradually as more volume is added, indicating a larger cross-sectional area. A larger cross-sectional area would result in a smaller increase in height for the same volume of water.

In summary, the steeper graph b matches Cylinder P with a smaller cross-sectional area, while the gentler graph a matches Cylinder Q with a larger cross-sectional area.

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Answer:

Step-by-step explanation:

$2.12 - $1.65 = $0.47
$0.47 x 65 = $30.55 profit.

This is an exercise in the formula to calculate the profits obtained from the sale of a product, it is an essential tool in the management of any business. By knowing the profits obtained from the sale of a product, business owners and managers can make informed decisions and adjust their business strategies to maximize their profitability.

Profit is calculated by subtracting the total costs of production from the total revenue earned from the sale of a product. Total production costs include not only the direct costs associated with manufacturing the product, but also indirect costs, such as advertising and marketing costs, the cost of packaging materials, and other overhead.

The total income obtained from the sale of a product is the product of the number of units sold by the sale price per unit. It is important to remember that the selling price per unit must be sufficient to cover both the direct and indirect costs of production, and to provide a reasonable profit.

Once the profit earned from the sale of a product has been calculated, business owners and managers can use this information to improve their profitability. If profits are low, they might consider lowering production costs, raising the selling price, or finding ways to sell more units. On the other hand, if profits are high, they might consider increasing their investment in advertising and marketing to attract more customers and expand their business.

In addition, profit calculation can also help business owners and managers assess the feasibility of launching a new product or expanding into new markets. By calculating total production costs and potential total revenue, they can determine if the new product or market is profitable and make informed decisions about whether to proceed with the launch or expansion.

The total cost of making the handles is the product of the number of handles times the cost per unit:

Total cost = 65 potholders × $1.65/potholder = $107.25

The total revenue from selling the handles is the product of the number of handles times the selling price per unit:

Total revenue = 65 potholders x $2.12/potholder = $137.8

Elmo's profit is the difference between total revenue and total cost:

Profit = Total Revenue - Total Cost

Profit = $137.8 - $107.25 = $30.55

Profit = $30.55

The solution set of f(x) > 0 is x ∈ (-2, 8).

To find the solution set of f(x) > 0, we need to first determine the critical values of x where f(x) changes sign.

Let's start by finding the domain of the function:

x² - 6x - 16 ≠ 0

We can solve for x by using the quadratic formula:

x = [6 ± √(6² + 4(16))]/2 = [6 ± √52]/2 = 3 ± √13

So the domain of f(x) is (-∞, 3 - √13) U (3 + √13, ∞).

Now let's factor the numerator and denominator of f(x):

f(x) = (x + 10)/[(x - 8)(x + 2)]

The critical points occur where the numerator or denominator of f(x) changes sign.

The numerator changes sign at x = -10, and the denominator changes sign at x = -2 and x = 8.

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The number of fidgets and pop bought was 15 each

From the information given, we have that;

1 fidget costs $3

1 Pop cost $4

Let the number of Fidgets be x

Let the number of Pop be y

Then, we have that a total of 20 fidgets and Pop cots $75

We have that;

20x + y = 75

Now, substitute the value of x as 3, we get;

20(3) + y= 75

expand the bracket

y = 75 - 60

y = 15

The number of fidgets is expressed as;

20x/4 = 20(3) /4 = 15

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Answer:

The location of Phoenix is (-7, -9)

Step-by-step explanation:

Hope this helps!

Answer:

81 days

Step-by-step explanation:

Formula to solve this type of equation \(t=\frac{k}{p}\)

t is time

k is a constant

p is people

We must substitute the values into the equation

\(54=\frac{k}{9}\)

\(k=486\)

Now we must substitute it to find the time

\(t=\frac{486}{6}\)

you get 81

It would take \(6\) builders  \(36\) days to complete the same house.

Builders are those person whose job is to build or repair houses and other buildings.

We have,

\(9\) builders take \(54\) days to complete a house.

So,

\(1\)  builder will take  \((\frac{54}{9})\)  days to complete a house,

In the same way,

\(6\)  builder will take  \((\frac{54}{9}*6)\)  days to complete a house,

i.e.

\(6\)  builder   \(=(\frac{54}{9}*6)= 36\) days.

Hence, we can say that it would take \(6\) builders  \(36\) days to complete the same house.

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Answer:

\(6\sqrt{3}\)

Step-by-step explanation:

because of the 90-60-30 theorem

which \(6*\sqrt{3}=6\sqrt{3}\)

Answer:A school bus provides a safe way of transportation for your child. Learn resources to talk to your child about school bus and bus stop safety.

Step-by-step explanation:

Answer:

30

Step-by-step explanation:

150/5 = 30

30+30+30+30+30 = 150