write f(x)=(x-2)(x+2)(x+1)^2 as a polynomial function​

The sequence given can be seen as:

1, 4, 16, .......

From this three terms we notice that the terms of this sequence are obtain by multiplying the previous term by 4, this means that this a geometric sequence.

We know that a geometric series is given by:

where a is the first term and r is the common ratio. In this case the common ratio is 4, then the sequence is:

This gives the total number of tiles in the nth figure, then we can rewrite as:

6 tables are required. Each prime number attender should serve 3 customers each.

The prime numbers between 1 and 100 are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.

All the numbers other than prime numbers are composite numbers.

The composite numbers from 1 to 100 are: 1, 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58, 60, 62, 63, 64, 65, 66, 68, 69, 70, 72, 74, 75, 76, 77, 78, 80, 81, 82, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95, 96, 98, 99, 100.

Now, as there are 25 primes and 75 composites in the group that visited the restaurant, we can calculate the number of tables required by dividing the number of people by the seating capacity of each table.

Each table has a seating capacity of 15, so the number of tables required will be: Number of tables = (Number of customers)/(Seating capacity of each table)Number of customers = 25 (the number of primes) + 75 (the number of composites) = 100Number of tables = 100/15 = 6 tables

Therefore, 6 tables are required.

Now, as each prime number attender has to serve an equal number of customers, we need to calculate how many customers each one should serve.

Each prime attender has to serve 75/25 = 3 customers each, as there are 75 composites and 25 primes.

Thus, each prime number attender should serve 3 customers each.

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Then, multiply this result by 100 to get the percentage. In this case, 120 is 80% of 150.

To use a double number line diagram to find what percent 120 is of 150, you need to create a diagram with two parallel lines. On the top line, mark 150 at one end and 100 at the other.

On the bottom line, mark 120 at one end and leave the other end blank. Then, draw diagonal lines connecting 120 on the bottom line to 150 on the top line and 100 on the top line to the blank end of the bottom line.

This creates two triangles. The height of the triangle with 120 is the percentage you're looking for.

To find this percentage, divide the length of the diagonal line connecting 120 and 150 by the length of the diagonal line connecting 100 and the blank end of the bottom line.

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Answer:

Caroline

Step-by-step explanation:

\(\frac{1}{5}: \frac{y}{42.5}\)

y × 5 = 1 × 42.5

5y = 42.5

5y ÷ 5 = 42.5 ÷ 5

y = 8.5

\(\frac{1}{3}: \frac{y}{26.4}\)

y × 3 = 1 × 26.4

3y = 26.4

3y ÷ 3 = 26.4 ÷ 3

y = 8.8

8.8 > 8.5

Answer:

3360 4200

Step-by-step explanation:

The value of the Integral at the lower limit from the value of the integral at the upper limit to get the length of the curve.

The length of the curve described by the function f(x) = 1 + 3x^2 + 2x^3 is to be found. The formula used to find the length of a curve is:

L = ∫(sqrt(1 + [f'(x)]^2))dx where f'(x) is the derivative of f(x)We have to first find f'(x):f(x) = 1 + 3x^2 + 2x^3f'(x) = 6x + 6x^2

The integral becomes:L = ∫(sqrt(1 + [6x + 6x^2]^2))dx = ∫(sqrt(1 + 36x^2 + 72x^3 + 36x^4))dx The integral appears to be difficult to evaluate by hand.

Therefore, we use software like Mathematica or Wolfram Alpha to solve the problem. Integrating the expression using Wolfram Alpha gives:

L = 1/54(9sqrt(10)arcsinh(3xsqrt(2/5)) + 2sqrt(5)(2x^2 + 3x)sqrt(9x^2 + 4))The limits of integration are not given. Therefore, the definite integral  be solved.

We can, however, find a general solution. We use the above formula and substitute the limits of integration.

Then, we subtract the value of the integral at the lower limit from the value of the integral at the upper limit to get the length of the curve.

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The distance from point A to point B is 2744.1 feet.

Define Trigonometric ratio

The ratios of the sides of a right triangle are called trigonometric ratios. Three common trigonometric ratios are the sine (sin), cosine (cos), and tangent (tan).

Given, horizontal distance = 1357 feet

Let h  = height of the lighthouse

tan(A) = perpendicular / base

where, perpendicular = h

base = 1357 feet

Angle is 9°

so now, put these value in trigonometric ratio

tan(9) = h / 1357

where, tan(9) = 0.1584

h = 1357 * 0.1584

h = 214.9 feet

Let d = distance from point B to the Lighthouse base

Angle is 3°

h = 214.9 feet

so, tan(3) = 214.9 / d

where, tan(3) = 0.0524

0.0524 = 214.9 / d

d = 214.9 / 0.0524

d = 4101.1 feet

Distance between point A to B = 4101.1 - 1357

                                                    = 2744.1 feet

Therefore, the distance from point A to point B is 2744.1 feet

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Answer:

75 and 246

Step-by-step explanation:1) i multiply 10 by 15 to get to get 150 since we are multiplying both sidesw of the tent i cut it in half to get my final answer of 75

2)first what i did was multiply 8 by 18 to get a answer of 96 next i multiply 10 by 15 to get 150 and lasly i add trhe two numbers up to get my final answer 246

Answer:

3.496

Step-by-step explanation:

Multiply these two by getting rid of the decimal:

 38 -decimal is moved one place here.

x092  -decimal is moved two places here.

3496  -move decimal three places over.

Answer: 72.36

Step-by-step explanation:

To find the total amount of salt in the bowl after Omar poured 13.2 grams, we need to add the initial amount of salt in the bowl to the amount of salt Omar added.

The initial amount of salt in the bowl was 59.16 grams.

Omar added 13.2 grams of salt to the bowl.

To find the total amount of salt in the bowl now, we add these two amounts: 59.16 + 13.2 = 72.36

Therefore, the bowl contains 72.36 grams of salt now.

Answer:

1) 7/8     8/7

2) 4.4

3) 3.7

4) 2.8

Step-by-step explanation:

Length of bottom side of Figure A: 8 cm

Length of bottom side of Figure B: 7 cm

From Figure A to Figure B, the scale factor is 7/8.

7/8

8/7

5 × 7/8 = 35/8 = 4.375

4.4

3.2 × 8/7 = 3.657...

3.7

3.2 × 7/8 = 2.8

2.8

The answer is true

15 x 32 x 2 = 2 x 15 x 32

960=960

Answer:

it is true because the answers are the same

Step-by-step explanation:

Answ

Step-by-step explanation:wirugf4

The five-number summary for this data set is 29, 32, 43.5, 50.5, and 53, and the interquartile range is 18.5.

Measures of statistical dispersion, or the spread of the data, include the interquartile range. In addition to the IQR, other names for it include the midspread, middle 50%, fourth spread, and H-spread.

To find the five-number summary and interquartile range for this data set, we first need to find the quartiles.

Step 1: Find the median (Q2)

When a data collection is sorted from least to largest, the median is the midway value. Since there are 12 values in this data set, the median is the average of the sixth and seventh values:

Median (Q2) = (41 + 46)/2 = 43.5

Step 2: Find the lower quartile (Q1)

The lower quartile is the median of the lower half of the data set. Since there are 6 values below the median, we take the median of those values:

Q1 = (32 + 32)/2 = 32

Step 3: Find the upper quartile (Q3)

The upper quartile is the median of the upper half of the data set. Since there are 6 values above the median, we take the median of those values:

Q3 = (50 + 51)/2 = 50.5

Now we have all the information we need to construct the five-number summary and interquartile range:

Minimum: 29

Lower quartile (Q1): 32

Median (Q2): 43.5

Upper quartile (Q3): 50.5

Maximum: 53

Interquartile range (IQR) = Q3 - Q1 = 50.5 - 32 = 18.5

the five-number summary for this data set is 29, 32, 43.5, 50.5, and 53, and the interquartile range is 18.5.

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Answer:

2.5 days

Step-by-step explanation:

To solve this problem, we can use the concept of work rate. The work rate is defined as the amount of work done per unit of time.

Given:

15 people working 5 hours per day can make 30 units of the product in 10 days.

From this information, we can calculate the work rate of these 15 people:

Work rate = Total units of the product / (Number of people × Number of hours × Number of days)

Work rate = 30 units / (15 people × 5 hours × 10 days)

Work rate = 0.04 units per person per hour

Now, we need to find how many days it will take for 10 people, working 10 hours per day, to make 10 units of the product.

Using the work rate formula:

Number of days = Total units of the product / (Number of people × Number of hours × Work rate)

Number of days = 10 units / (10 people × 10 hours × 0.04 units per person per hour)

Number of days = 2.5 days

Therefore, 10 people, working 10 hours per day, can make 10 units of the product in 2.5 days.

The correct answer is:

2.5 days

The Value of CD from the second equation into the first equation:2AC = AB + OC + OD⇒ 2AC = AB + AB (By substituting OC = OA and OD = OB)⇒ 2AC = 2AB⇒ AC Therefore, AC is Congruent to c .

Since AC and BD bisect each other at O, we can say that AO = OC and BO = OD.

We need to prove that AC = CD.To do this, we can use the segment addition postulate which states that if a line segment is divided into two parts, the length of the whole segment is equal to the sum of the lengths of the two parts.

Let us draw a diagram to represent the given information:From the diagram, we can see that:AO + OB = AB (By segment addition postulate)OC + OD = CD (By segment addition postulate)AO = OC (Given)BO = OD (Given)

Now, we can substitute the values of AO and OC as well as BO and OD into the equations above:AO + OB = AB ⇒ OC + OB = AB (Substituting AO = OC)OC + OD = CDNow, we can add both equations:OC + OB + OC + OD = AB + CD ⇒ 2(OC + OD) = AB + CDWe know that OC = AO and OD = BO.

Therefore, we can write:2(AO + BO) = AB + CDSince AO = OC and BO = OD, we can write:2(OA + OD) = AB + CDNow, substituting AO = OC and BO = OD, we can write:2AC = AB + CD

Finally, we can substitute the value of CD from the second equation into the first equation:2AC = AB + OC + OD⇒ 2AC = AB + AB (By substituting OC = OA and OD = OB)⇒ 2AC = 2AB⇒ AC

Therefore, AC is congruent to c .

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Answer:

x = 19

Step-by-step explanation:

the question tells you that the angle CBD is 90°.

so, that means that angle DBE and angle CBE add up to 90.

using this, you can make the following equation:

2x - 1 + 5x - 42 = 90

2x + 5x + -43 = 90

7x - 43 = 90

add 43 to both sides

7x = 90 + 43

7x = 133

x = 133/7

x = 19

ANSWER:

STEP-BY-STEP EXPLANATION:

Answer:

Step-by-step explanation:

As seen in earlier sections, the process of completing the square is a useful tool in finding noninteger values of quadratic equations, especially intercepts. When a quadratic equation of the

form f (x) = ax2

+ bx + c is put through the process of completing the square it yields an

equation of the form f (x) = a(x – h)2

+ k . The conversion of the equation to this form will

yield critical information about the equation’s characteristics before you begin to graph it.

1.) The value of h is the distance left (if negative) or right (if positive) the graph

translates from the standard position.

2.) The value of k is the distance up (if positive) or down (if negative) the graph

translates from the standard position.

3.) The values of h and k, when put together as an ordered pair, give the vertex i.e.

(h, k).

4.) The equation x = h is the formula for the axis of symmetry.

The following example demonstrates how to find the following critical information of the

equation:

a.) vertex

b.) axis of symmetry

c.) y intercept (if any)

d.) x intercepts (if any)

Example 1: Find the vertex, axis of symmetry, x-intercept(s), and y-intercept and gr

each sunflower is $2.25. please mark brainliest and have a great day.

Answer:

Step-by-step explanation:

f(x) = 3x^2 + 6x + 3

a of s: -6/6 = -1

3(-1)^2 + 6(-1) + 3

3 - 6 + 3

-3 + 3 = 0

(-1,0)

answer is A. the first one

The equilibrium price and quantity in the milk market are $37.5 and $15.75

When you combine the supply and demand curves, there is a point where they intersect; this point is called the market equilibrium. The price at this intersection is the equilibrium price, and the quantity is the equilibrium quantity.

Given that, the equations for that the supply and demand for milk:

Supply of Milk: Q = 0.50P - 3

Demand for Milk: Q = 27 - 0.30P

We need to find the equilibrium price and quantity in the milk market.

Market equilibrium is struck when:

Market Demand = Market supply

Therefore,

Market equilibrium =

0.50P - 3 = 27 - 0.30P

0.50P + 0.30P = 30

0.80P = 30

P = 37.5

Equilibrium price = 37.5

Put P = 37.5 in equation 0.50P - 3,

0.50(37.5)-3 = 15.75

Equilibrium quantity = 15.75

Hence, the equilibrium price and quantity in the milk market are $37.5 and $15.75

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Answer:

x = -75

Step-by-step explanation:

\(\frac{3}{5} x=-45\\\\3x=-225\\x=-75\)

Answer:

-75

Step-by-step explanation:

Have a nice day:)

Answer:

The surface is 181.5 square yards.

Step-by-step explanation:

A = 6a² =

6 · 5.5²

181.5

The solution set of\(fog(x)= gof(x)\) is the set of all real numbers, denoted as \({x|x∈R}\)

An equation is a mathematical expression that uses symbols, such as numbers and variables, to represent a relationship between two or more values or quantities. Equations are used to describe physical laws, solve problems and to make predictions. Equations are fundamental to all areas of mathematics and science, and their use is essential for understanding and exploring the natural world.

This equation can be written as \(x^2 = 2^x,\) which is a transcendental equation with no exact solution. However, we can use numerical methods to find approximate solutions. For example, using Newton's method, an approximate solution is\(x ≈ 2.281.\)

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The measure of angle CDE ( ∠CDE) is 55°. The correct option is the first option  55°

From the question, we are to determine the measure of angle CDE.

From one of the circle theorems, we have that

"The measure of the angle formed by two tangents that intersect at a point outside a circle is equal to one-half the positive difference of the measures of the intercepted arcs"

Thus,

m ∠CDE = 1/2(measure of arc CBE - measure of arc CE)

From the given information,

Measure of arc CE = 125°

Then,

Measure of arc CBE = 360° - 125°

Measure of arc CBE = 235°

Therefore,

m ∠CDE = 1/2(235° - 125°)

m ∠CDE = 1/2(110°)

m ∠CDE = 55°

Hence, the measure of ∠CDE is 55°

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Answer:

Guys this answer is wrong

Step-by-step explanation:
when you are coming from the center point of the circle it mirrors the arc wich is 125 degrees
But when we are trying to figure out the angle which is CDE its always half of the arc of the circle
So you would do 125/2
wich gives you 62.5
therefore your answer is 62.5
No hate to the other guy but plsssss make sure you read the question before answering

Answer:

D

Step-by-step explanation:

this would simplify, in slope-intercept form, as y= 15x - 66