Find the value of x
x=

There are no critical numbers for the function f(x) = 2x³ + x² + 4x. This is because the discriminant (b² - 4ac) is negative.

1. Calculate the derivative of the function with respect to x (f'(x)). This will help us identify where the function has a critical point (maximum, minimum, or inflection point).

f'(x) = [tex]\frac{d}{dx} (2x^{3} + x^{2} + 4x)[/tex]

2. Use the power rule for differentiation to find the derivative of each term.
f'(x) = (3 * 2)x² + (2 * 1)x + 4

3. Simplify the derivative.
f'(x) = 6x² + 2x + 4

4. To find the critical numbers, set the derivative equal to zero and solve for x.
6x² + 2x + 4 = 0

5. To solve for x, we can use the quadratic formula:
x = [tex]\frac{-b\sqrt{(b^{2} - 4ac) } }{2a}[/tex]
where a = 6, b = 2, and c = 4.

6. Plug the values of a, b, and c into the quadratic formula:
x = [tex]\frac{-2 +\sqrt{(2^{2} - 4(6)(4)) } }{2 * 6}[/tex]

7. Simplify the expression:
x =[tex]\frac{-2 +\sqrt{(92) } }{12}[/tex]

8. Since the discriminant (b² - 4ac) is negative, there are no real solutions for x, meaning there are no critical numbers for the given function.

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Answer: 230

Step-by-step explanation: The first thing you need to do is add 1 inch to the length and width. The starting lenght is 22, and that becomes 23. The starting width is 9, and that becomes 10. The new measurements are 23 by 10. To find area you multiply length by width. 23 times 10 gives you an answer of 230. I hope that helped!

Answer:

58

Step-by-step explanation:

We see that both sides around x are the same length, 6.2. This tells us our triangle is an isosceles triangle, which means two sides are the same lengths. This also tells us that two angles will be equal to each other.

The angle other than x and 61, will be equivalent to 61.

We also know that a triangle's angles equal 180. So,

180 - 61 = 119

119 - 61 = 58

x = 58

Sorry if my explaination isn't fully clear, it's hard to type it out and explain!

Answer:

Microorganism B is 2500 times wider than microorganism A.

Step-by-step explanation:

Microorganism B is 2500 times wider than microorganism A.

Answer:

59

Step-by-step explanation:

Let's begin by simplifying the expression:

[tex](y-4)^2-(6+y)(y-6) = y^2 - 8y + 16 - y^2 + 36 = -8y + 52[/tex]

Since we've found are final expression, we can plug in the value we are given:

[tex]-8y + 52 = 7 + 52 = \fbox{59}[/tex]

Expontial decay function, A(t) = A₀e⁻⁰·⁰²ᵗ

a) The decay rate of strontium 90 is equals to the 0.02.

b) The left strontium 90 after 40 years is equals to the 179.73 grams.

c)After approx 34.66 year, only 200 grams of strontium 90 will be left.

Expontial decay function is used to calculate the population decay, half-life,radioactivity decay, etc. Formula,

y(t) = a × eᵏᵗ --(1)

Where y(t) = value at time "t"

We have a Strontium 90, which is a radioactive material. Radioactive decay function of it is

A(t) = A₀e⁻⁰·⁰²ᵗ --(2)

where A₀ --> initial amount

A -> amount present at time t(in years)

Initaial amount, A₀ = 400 grams

(a) Comparing equation (1) and (2), we will results the decay constant, k = 0.02

Hence, decay rate of strontium = - 0.02.

(b) we have to determine strontium 90 is left after 40 years. That is t = 40 years

=> A(40) = 400×e⁻⁽⁰·⁰²⁾⁴⁰

=> A(40) = 400 ×0.377

=> A(40) = 179.73

So there will be around 179.73 grams of strontium 90 after 40 years.

c) For determine time there will be only 200 grams of strontium 90 left,

=> 200 = 400e⁻⁰·⁰²ᵗ

=> 1/2 = e⁻⁰·⁰²ᵗ

take natural logarithm both sides

=> ln(2) = ln( e⁰·⁰²ᵗ)

=> 0.02t = ln(2)

=> t = 34.6573

=> t≈ 34.66

So, there will be 200 grams left after approximately 34.66 years.

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Complete question :

Strontium 90 is a radioactive material that decays according to the function

A(t)=A0e−0.02t, where A0 is the initial amount present and A is the amount present at time t (in years). Assume that a scientist has a sample of 400 grams of strontium 90.

a) what is the decay rate of strontium 90?

b) how much strontium 90 is left after 40 years

c) when will only 200 grams of strontium 90 be left?

Answer:

The length of s is 5.3 inches to the nearest tenth of an inch

Step-by-step explanation:

In Δ RST

∵ t is the opposite side to ∠T

∵ r is the opposite side to ∠R

∵ s is the opposite side to ∠S

→ To find s let us use the cosine rule

∴ s² = t² + r² - 2 × t × r × cos∠S

∵ t = 3.7 inches, r = 1.7 inches, and m∠S = 155°

→ Substitute them in the rule above

∴ s² = (3.7)² + (1.7)² - 2 × 3.7 × 1.7 × cos(155°)

∴ s² = 13.69 + 2.89 - −11.40135196

∴ s² = 27.9813520

→ Take √ for both sides

∴ s = 5.28974025

→ Round it to the nearest tenth

∴ s = 5.3 inches

∴ The length of s is 5.3 inches to the nearest tenth of an inch

Therefore, the football team scored 4 touchdowns, 2 field goals, and 1 safety in the game.

An equation is a mathematical statement that asserts that two expressions are equal. It typically consists of variables, constants, and mathematical operations such as addition, subtraction, multiplication, division, exponentiation, and so on. An equation is often written with an equal sign (=) between the two expressions. The goal of solving an equation is to find the values of the variables that make the equation true. Equations are used extensively in mathematics, physics, engineering, and many other fields to describe relationships between different quantities.

by the question.

Let's denote the number of touchdowns scored by "T", the number of field goals scored by "F", and the number of safeties scored by "S".

From the problem, we know:

[tex]T + F + S = 8 (they scored points 8 times)\\7T + 3F + 2S = 38 (the total score was 38 points)\\T = F + S[/tex] (they scored as many touchdowns as they did field goals and safeties combined)

Substituting the third equation into the first, we get:

[tex]F + S + F + S = 8\\2F + 2S = 8\\F + S = 4[/tex]

We now have a system of three equations:

[tex]T + F + S = 8\\7T + 3F + 2S = 38\\T = F + S[/tex]

Substituting the third equation into the first two, we get:

[tex]7(F + S) + 3F + 2S = 38\\8(F + S) = 21[/tex]

Solving for F + S, we get:

[tex]F + S = 21/8[/tex]

However, we also know that F + S = 4, so there must be a mistake somewhere. Looking back at the problem, we see that the statement "they scored as many touchdowns as they did field goals and safeties combined" implies that T = F + S + 1 (since a touchdown is worth 7 points and a field goal and safety combined are worth 4 points). Substituting this into the first two equations, we get:

[tex](F + S + 1) + F + S = 8\\7(F + S + 1) + 3F + 2S = 38[/tex]

Simplifying, we get:

[tex]2F + 2S = 6\\10F + 9S = 31[/tex]

Solving for F and S, we get:

[tex]F = 2\\S = 1[/tex]

Substituting these values back into the equation T = F + S + 1, we get:

[tex]T = 4[/tex]

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Answer:

1/2

Step-by-step explanation:

7b/14b

you can cancel out the b's to get

7/14

and simplify it to

1/2.

Answer: 1/2

Step-by-step explanation:

7 + 7 = 14, so 7 is half of 14

The lengths of the segments tangent to the circle are YZ = XZ = 16.

A line that precisely crosses a circle at that point—referred to as the point of tangency—is said to be tangent to the circle. At the point of tangency, the tangent line is perpendicular to the circle's radius; as a result, the angle between the tangent line and radius is 90 degrees. Depending on where the tangency point is located, a circle can have an unlimited number of tangents. Geometrical uses for tangents to a circle include determining the lengths of line segments that are tangent to the circle.

We know that, triangle TXZ is congruent to triangle TYZ, thus YZ is congruent to XZ using CPCT.

Now,  YZ = XZ.

For the right triangle TXZ, TX = 12, and TZ = 20.

Using the Pythagoras Theorem we have:

TX² + XZ² = TZ²

Substituting the values:

12² + XZ² = 20²

XZ² = 400 - 144

XZ = 16

Now, YZ = XZ thus, YZ = 16.

Hence, the lengths of the segments tangent to the circle are YZ = XZ = 16.

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The complete question is:

The probability that you will win three rounds in a row is 1/8, or 12.5%.

The probability of winning a single round of ring toss is 50%. To calculate the probability of winning three rounds in a row, we must multiply the probability of winning each round together. So, the equation would be 0.5 x 0.5 x 0.5 which equals 0.125, or 12.5%. This means that the probability of winning three rounds in a row is 1/8, or 12.5%.

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Answer:

x = 33

Step-by-step explanation:

You can find the greatest common factor of the triangle side lengths on the right. It is 9. Both triangles are scaled versions of 3-4-5 triangles. Divide any side from the left triangle by its respective side length from 3-4-5, in this case 44/4 or 55/5. We can see that the scalar for this triangle is 11. This means the 3- the shortest side length. Is actually 3 x 11 = 33.

Therefore x = 33.

Answer:

Side length of equilateral triangle is = 29 units

In geometry, an equilateral triangle is a triangle that has all its sides equal in length.

3 given lengths are

3x+8 , 5x - 6 , 2x +15

so,

[tex] \rm \: 3x + 8 = 5x - 6 = 2x + 15[/tex]

consider 2 sides,

[tex] \rm \implies 3x + 8 = 2x + 15[/tex]

[tex] \rm \implies 3x - 2x = 15 - 8[/tex]

[tex] \rm \implies x= 7[/tex]

so,

[tex] \rm \: 3x + 8 = 3 \times 7 + 8 = 29[/tex]

As equilateral triangle

3x+8 = 5x - 6 = 2x +15 = 29

The sides of a triangle are straight lines that are joined by the three vertices of the triangle.

so,

Side,length of equilateral triangle is 29 units

Number of Sides = 3

Number of angles = 3

Each interior angle = 60

Each exterior angle = 120

Perimeter = 3 times of side-length

Area = √3/ 4 x (side)2

Height = √3 (side)/2

Here,

AC ≅ AB

→ 5x -6 = 3x+8

→ 5x - 3x = 8+6

→ 2x = 14

→ x = 14/2

→ x = 7

Now Putting the value of x

AC = 5x - 6

= 5(7) -6

= 35 -6

= 29

AB = 3x + 8

= 3(7) +8

= 21 + 8

= 29

BC = 2x + 15

=2(7)+15

= 14 + 15

= 29

Thus,

Area of triangle

[tex] \sf \: \frac{1}{2}bh [/tex]

Area of equilateral triangle

[tex] \sf \: \frac{ \sqrt{3} }{4} {a}^{2} [/tex]

Area of Isosceles Triangle

[tex] \sf \: \frac{b}{4} \sqrt{ {4a}^{2} - {b}^{2} } [/tex]

Answer:

$1.60

Step-by-step explanation:

This is a very simple question

First start off with 1.2/0.75

1.2 divided by 0.75 = 1.6

Add a zero on to 1.6 and you have your answer of

$1.60

If Ta is multiplication by a matrix, The four possible geometric objects are 0 the origin, Plane through the origin, a line through the origin and R³.

Row reduction results in a line across the origin if the rank of the augmented matrix is 2, which indicates that there is one free variable and that the values of the other two variables depend on the free variable. Therefore a line across the origin is the kernel of TA.

If TA is multiplication by a matrix with Three columns, Then The kernel. of TA is one of four possible geometric objects.

A has three clumps.

So, A is of size : n x 3

and kernel vectors are of size 3 x 1

So dim kernel [tex]\alpha[/tex] = 3.

case 1: dimension (dim) = 3

A 3 dimensional surface.

Case 2: dim = 2.

A. 2 dimensional surface is a plane.

Case 3 dim = 1

AI dimensional surface is a line.

case u! dim = 0

A point.

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The cost of operating the dryer for a month is $6.

An electric clothes dryer has a power rating of 4000W. Assume that a family does five loads of laundry each week for 4 weeks. Further assume that each load takes one hour. A. Find the energy used in both J and kWh.

1J = 1W.s

Energy used = Power x time= 4000W x (5 x 4) x 1h= 80000Wh= 80 kWh

Thus, the energy used in kWh is 80 kWh.1kWh = 1000Wh

1kWh = 3.6 x 10^6 J

Thus, the energy used in J is 80 x 3.6 x 10^6 = 288 x 10^6 J.B. If the cost of electricity is $.075/kWh, find the cost of operating the dryer for a month (4 weeks).

The energy used by the dryer for a month is 80 kWh.

Cost of operating the dryer for a month = Energy used x Cost per kWh= 80 kWh x $0.075/kWh= $6

Therefore, the cost of operating the dryer for a month is $6.

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By answering the presented question, we may conclude that Because equation both of these answers are real values, the solution to the equation x2 - 9 = 0 is that it has two real solutions.

An equation in mathematics is a statement that states the equality of two expressions. An equation is made up of two sides that are separated by an algebraic equation (=). For example, the argument "2x + 3 = 9" asserts that the phrase "2x + 3" equals the number "9". The purpose of equation solving is to determine the value or values of the variable(s) that will allow the equation to be true. Equations can be simple or complicated, regular or nonlinear, and include one or more elements. In the equation [tex]"x^2 + 2x - 3 = 0,"[/tex]for example, the variable x is raised to the second power. Lines are utilised in many different areas of mathematics, such as algebra, calculus, and geometry.

(x-3)(x+3) = 0 is a rewrite of the equation [tex]x^2 - 9 = 0.[/tex] This suggests that the equation's solutions are x = 3 and x = -3.

Because both of these answers are real values, the solution to the equation x² - 9 = 0 is that it has two real solutions.

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the weight of the pumpkin is 22 times the weight of an apple.

To find out how many times the weight of an apple is contained in the weight of a pumpkin, we need to divide the weight of the pumpkin by the weight of the apple.

First, we need to convert the mixed number 5 1/2 into a fraction. We can do this by multiplying the whole number by the denominator of the fraction, and then adding the numerator. So:

5 1/2 = (5 x 2 + 1)/2 = 11/2        

Now we can set up the division:

11/2 ÷ 1/4

To divide fractions, we need to flip the second fraction and then multiply. So:

11/2 ÷ 1/4 = 11/2 x 4/1 = 44/2

Simplifying the fraction, we get:

44/2 = 22

Therefore, the weight of the pumpkin is 22 times the weight of an apple.

In other words, the pumpkin weighs 22 times as much as the apple.

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Answer:

it's the third one trust me

Answer:

m = 1/7

Step-by-step explanation:

3m(n + 3p) = n + p

1st step: Replace the known  letters

3m(4 + 3 X 8) = n + p

2nd step: Solve inside the parathenstics

3m(28) = n + p

3rd step: simplify both sides of the equation

84m = 4 + 8 (combine like terms)

84m = 12

4th step: divide both sides by 84

m = 1/7

The measure of the angle through which the minute hand of a standard 12-hour clock rotates from the time Monique looked at the clock at the beginning of class to the time she looked at it again at the end of class is 6t degrees, where t is the time elapsed in minutes.

The number of times the figure rotates around for a central point throughout the course of a full 360-degree rotation is referred to as the order of rotation in mathematics. Since it takes 4 of these revolutions to accomplish a full 360-degree rotation, a figure that swings 90 degrees and then returns to its original location has an order of rotation of 4. The idea of rotational symmetry—the characteristic of an image that remains constant during a rotation of a specific angle—and the order of rotation are closely related. The number of rotations a figure with symmetrical can undergo and yet maintain its original appearance is known as the order of rotation.

In the given question,

A normal 12-hour clock's minute hand completes one full rotation every 60 minutes. This implies it rotates 360 degrees in 60 minutes, or at a rate of 6 degrees per minute.

Now, locate the location of the minute hand at the start of class. When Monique looked at the clock at the start of class, the minute hand would be pointing directly at the number 12. As a result, the minute hand begins at 0 degrees.

Then, at the conclusion of class, find the location of the minute hand. If Monique glanced at the clock again at the conclusion of class, she would notice that the minute hand had moved t minutes from its initial position. As a result, the minute hand would be at:

6 degrees per minute × t minutes = 6t degrees

Now, we can find the angle through which the minute hand rotates by taking the difference between the starting and ending positions of the minute hand:

Ending position - Starting position = 6t degrees - 0 degrees = 6t degrees

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The complete question is: What is the measure of the angle through which the minute hand of a standard 12-hour clock rotates from the time Monique looked at the clock at the beginning of class to the time she looked at it again at the end of class?

Therefore, the probability that on the next page, the author will make at most two word processing errors is 0.99207367.

To find the probability of making word processing errors, we must use Poisson Distribution.

What is Poisson Distribution?

A Poisson distribution is a probability distribution that estimates the number of occurrences of an event in a fixed time or space interval.

It is used to model a situation where events occur randomly and independently over a fixed period or area.

The Poisson distribution's primary assumptions are that events are rare, random, and that one event does not affect another event's outcome. The Poisson distribution is useful in predicting the number of occurrences of a specific event in a given time or space interval. This distribution is useful in several fields, including finance, insurance, and public health.Now let's solve the given problem,

The probability that there are no word processing errors is given by[tex]:P (X = 0) = e^ -μμ = 200/500 = 0.4[/tex] (average number of errors per page = 2/5)P (X = 0) = e^ -0.4 = 0.67032005Now, the probability that there are 2 or fewer errors is given by:[tex]P (X ≤ 2) = ΣP (X = i) i = 0 to 2P (X ≤ 2) = P (X = 0) + P (X = 1) + P (X = 2)P (X ≤ 2) = 0.67032005 + 0.26812802 + 0.0536256P (X ≤ 2) = 0.99207367[/tex]

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The surface area of the cube is 486 cm².

What is surface area?

Surface area refers to the total area of all the faces or surfaces of a three-dimensional object. It is the sum of the areas of each face of the object.²

The formula for surface area varies depending on the shape of the object. For example, the surface area of a cube can be found by adding up the areas of all six faces, where each face has the same area given by the formula A = s², where s is the length of an edge. Therefore, the surface area of a cube with edge length s is 6s².

Calculation steps:

A cube has 6 square faces, all with the same area.

Since the edge length of the cube is 9 centimeters, each face has an area of:

A = (edge length)² = 9² = 81  cm²

Therefore, the total surface area of the cube is:

6A = 6(81) = 486  cm²

Hence, the surface area of the cube is 486 cm² .

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After answering the provided question, we can conclude that As a result, triangle the side GH measurement is approximately 16 units.

A triangle is a closed, double-symmetrical object made up of three line segments called sides that intersect at three points called vertices. Triangles can be distinguished by their sides and angles. Triangles can be equilateral (equal factions), isosceles, or scalene based on their sides. Triangles are classified as acute (all angles less than 90 degrees), okay (one angle equal to 90 degrees), or orbicular (all angles greater than 90 degrees) (all angles greater than 90 degrees). The province of a triangle can be calculated using the formula A = (1/2)bh, where an is the neighbourhood, b is the triangle's base, and h is its height.

Due to the similarity of triangles CDE and FGH, their corresponding sides are proportional. That is to say:

CE/GH = CD/FH = DE/FG

Given that DE = 8 and CD = 10, we can use the third ratio to calculate FH:

10/FH = 10/16

When we multiply by two, we get:

FH = 16/10 * 10 = 16

As a result, the side GH measurement is approximately 16 units.

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Answer: 2/11

Step-by-step explanation:

The experimental probability that the next batter will get a hit is 2/11.

What is probability?

Probability is a way of calculating how likely something is to happen. It is difficult to provide a complete prediction for many events. Using it, we can only forecast the probability, or likelihood, of an event occurring. The probability might be between 0 and 1, where 0 denotes an impossibility and 1 denotes a certainty.

Based on the given condition, the probability that the next batter will get a hit is

=> 4/22

=> 2/11

Hence the experimental probability that the next batter will get a hit is 2/11.

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27.42 feet.


Assuming the limb forms a right angle with the trunk of the tree, we can use trigonometry to find the length of the limb.

The opposite side of the triangle is the height of the limb, the adjacent side is the height of the tree, and the angle between them is 62 degrees.

Using the tangent function, we have:

tan(62°) = opposite / adjacent

Solving for the opposite side (height of the limb), we get:

opposite = tan(62°) x adjacent

opposite = tan(62°) x 14.9

opposite ≈ 27.42

Therefore, the longest limb is approximately 27.42 feet tall.

Answer:

what do need help with ,?

The unit rate among these for the better values is: 0.25

What further instances of unit rates can you give?

These are a few illustrations of unit rates :The distance travelled in one hour is measured in miles per hour (mph); the price of an item is measured in pounds; and the price of an electrical kilowatt-hour is measured in kWh.

- Price per gallon - the price of a liquid per gallon.

The quantity of calories in one serving of food is known as the "calories per serving."

Now , divide the price by the weight to obtain the unit rate.

The unit rate for the first choice is:

2.50 / 10 = 0.25

The unit rate for the second choice is:

3.65 / 14 = 0.26

Due to its lower unit rate, the first choice is therefore more advantageous.

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If tan ⁡θ = - 1, a possible value of θ is C. 135 degrees.

If tanθ = -1, we are looking for an angle where the ratio of the opposite side to the adjacent side is -1. This occurs in the second and fourth quadrants, where either the opposite side is positive and the adjacent side is negative or vice versa.

In the second quadrant, the angle would be (180 - 45)° = 135° or (3π/4) radians.

In the fourth quadrant, the angle would be (360 - 45)° = 315° or (7π/4) radians. Both of these angles have a tangent of -1.

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The full question is:

If tan⁡ θ = - 1, a possible value of θ is:

Step-by-step explanation:

Volume of Pyramid = 1/3  (base area ) * height

                    21         = 1/3  (   s x s) *  3

                     21  =    s^2

                       s = side length = sqrt (21 )