The polynomial f(x) is written in factored form: f(x) = (x − 3)(x + 8)(x − 11) What are the zeros of the polynomial function?
x = 3, x = 8, x = 11
x = 3, x = −8, x = 11
x = −3, x = 8, x = −11
x = −3, x = 3, x = −8, x = 8, x = −11, x = 11

Answer:

\(y=6\sqrt{3}\)

\(x=18\)

Step-by-step explanation:

\(Sin30=\frac{9}{12\sqrt{3} }\)

\(1/2=y/12\sqrt{3}\)

\(y=6\sqrt{3}\)

\(tan30=y/x\)

\(x=y/tan30=x=\frac{6\sqrt{3} }{1/\sqrt{3} }\)

\(x=18\)

------------------------

hope it helps...

have a great day!

Step-by-step explanation:

W^2 = 46.

We know that 6^2 = 36 and 7^2 = 49.

Therefore W should be between 6 and 7.

A particular solution of the differential equation y" -8y' +17y = 8e^6t is y_p = (8/5)e^(6t) obtained using the method of undetermined coefficients.

To find a particular solution of the non-homogeneous differential equation:

\(y" - 8y' + 17y = 8e^(6t)\)

using the method of undetermined coefficients, we assume that the particular solution has the form:

\(y_p = Ae^(6t)\)

where A is a constant to be determined.

We then take the first and second derivatives of y_p:

\(y'_p = 6Ae^(6t)\)

\(y"_p = 36Ae^(6t)\)

Substituting these expressions into the differential equation, we have:

\(y" - 8y' + 17y = 8e^(6t)\)

\(36Ae^(6t) - 48Ae^(6t) + 17Ae^(6t) = 8e^(6t)\)

Simplifying the left-hand side, we get:

\(5Ae^(6t) = 8e^(6t)\)

Therefore, A = 8/5.

Hence, the particular solution is:

\(y_p = (8/5)e^(6t)\)

Therefore, a particular solution of the differential equation y" -8y' +17y = 8e^6t is y_p = (8/5)e^(6t) obtained using the method of undetermined coefficients.

Learn more about undetermined coefficients

brainly.com/question/31392685

#SPJ11

Answer:

yes!

Step-by-step explanation:

a rational number is a number that you can get by a fraction, like in this case 31/2

Answer:

Yes.

Step-by-step explanation:

15.5 is a rational number, because it can be expressed as a fraction.

15 1/2

= 31/2

The value of x after the simultaneous rotation and translation of pentagon A to create pentagon B is 110°

A plane figure translation is an isometry that translates each position of the figure at a distance and in a direction indicated by the vector.

It is also regarded as a sort of transformation that involves sliding each point in a plane figure at an identical distance in a similar direction.

From the attached image, the value of x after the simultaneous rotation and translation of pentagon A to create pentagon B is 110°.

Learn more about the translation of plane figures here:

https://brainly.com/question/2467920

The slope and y-intercept of the equation y= -4/3 x-2 are -4/3 and -2 respectively.

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

In the given graph two lines are plotted.

Part A: From the graph, the two equations are intersected at (-1.5, 0) and the solution is (-1.5, 0).

Part B: Slope and y-intercept

Equations of lines from the graph are y=3/4 x+1 and y= -4/3 x-2.

For the equation y=3/4 x+1,

Compare, y=3/4 x+1 with y=mx+c, we get

Slope (m)= 3/4 and the y-intercept (c)=1

For the equation y= -4/3 x-2,

Compare, y= -4/3 x-2 with y=mx+c, we get

Slope (m)= -4/3 and the y-intercept (c)=-2

Therefore, the slope and y-intercept of the equation y= -4/3 x-2 are -4/3 and -2 respectively.

To learn more about the slope of a line visit:

https://brainly.com/question/14511992.

#SPJ9

a) Any value outside of Q1 - 1.5(IQR) and Q3 + 1.5(IQR) can be considered a potential outlier.

b) This will give us a visual representation of the distribution of income among the full-time students.

c) It is important to analyze outliers carefully to ensure that they are not artificially skewing the results of our analysis.

(a) To check for outliers in the data set, we can use the box-and-whisker plot or the z-score method. However, since we do not have the exact data, we cannot use these methods. One way to identify potential outliers is to calculate the quartiles (Q1, Q2, and Q3) and the interquartile range (IQR).

(b) To draw a histogram of the data, we can use the frequency distribution table given in the question. The x-axis should represent the income ranges (e.g. $0-$100, $100-$200, etc.) and the y-axis should represent the frequency (i.e. the number of students who earned income within each range).

(c) If there are any outliers in the data set, we need to investigate them further to determine the reason for their unusual values. Possible reasons for outliers could be data entry errors, extreme values due to high- or low-income jobs, or unique situations such as unexpected windfalls or emergencies.

To learn more about frequency distribution visit;

https://brainly.com/question/14926605

#SPJ11

The correct answer is D. After the loop, the last row of matrix is 0, 0, 0, 0, 10.

This is because the code initializes a 5x5 matrix with all elements set to 0. Then, the for loop iterates over the length of the last row (which is 5), and sets the values in the last row to 10. However, the loop also has a semicolon immediately after the condition, which effectively terminates the loop before it even starts executing the loop body.

Therefore, only the initialization statement (which does nothing) and the semicolon are executed, leaving the rest of the matrix unchanged except for the last element in the last row, which is set to 10.

In computer programming, an initialization statement is a statement used to set an initial value to a variable or constant when it is declared. This is typically done to ensure that the variable or constant starts with a known and expected value, and to avoid any unpredictable behavior that may result from uninitialized data.

To know more about initialization statement, refer here:

https://brainly.com/question/13089791

#SPJ11

we must evaluate the domain points in the function

x=0

x=1

x=2

x=3

x=4

x=5

x=6

x=7

the points are

now, locate each point on the graph and join with a line

Greg's daughter will have $533 in her piggy bank in a year

The money in the piggy bank would increase everyday by the amount put in it. There are seven days in a week. If he puts $0.75 everyday apart from on Sundays when we puts $5.75, the amount that would be in the piggy bank in a week is the sum of the money deposited each day.

Total amount in a week = total amount deposited from Monday to Saturday + amount deposited on Sunday

The total amount Greg's daughter would have in a year is a function of the number of weeks in year and the total amount saved in a week

Total amount in a year = number of weeks in year x the total amount saved in a week

$10.25 x 52 = $533

In order to determine how much Greg's daughter would have in a year, first determine how much she would have in a week. Multiply this amount by the number of weeks in a year

A similar question was solved here: https://brainly.com/question/18614558?referrer=searchResults

Answer:

-112

Step-by-step explanation:

I searched your question and here is what I found:

Step-by-step explanation:

L = 4 + 3W  (from the second condition)

L2 = 66 + LW (combining the first and third condition)

L2 = 66 + L(L-4)/3

3L2 = 198 + L2 -4L

2L2 + 4L -198 = 0

(2L - 18)(L + 11) = 0; discarding the negative root for lack of practicality , L = 9

from the first equation W = (L - 4)/3 = 5/3 = 1 2/3; 1.67

Hence the length of the rectangle is 9 cm and the width is 1.67 cm

check;        

2nd condition; L = 4 + 3*1.67 = 9 (proven)

1st and 3rd condition; 92 = 66 + 9*1.67 = 81 (proven)

The length of the rectangle is 9 cm.

The width of the rectangle is 5/3 cm.

A rectangle is a two-dimensional shape where the length and width are different.

The area of a rectangle is given as:

Area = Length x width

We have,

Rectangle:

Length = 3w + 4

Width = w

Area = (3w + 4)w

Square:

Side = 3w + 4

Area = (3w + 4)²

Now,

The area of the square is 66 more than the area of the rectangle.

This means,

(3w + 4)² =  (3w + 4)w + 66

9w² + 16 + 24w = 3w² + 4w + 66

9w² - 3w² + 24w - 4w + 16 - 66 = 0

6w² + 20w - 50 = 0

2 (3w² + 10w - 25) = 0

3w² + 10w - 25 = 0

3w² + (15 - 5)w - 25 = 0

3w² + 15w - 5w - 25 = 0

3w(w + 5) - 5(w + 5) = 0

(3w - 5)(w + 5) = 0

w + 5 = 0 and 3w - 5 = 0

w + 5 = 0

w = -5 (rejected since its negative)

3w - 5 = 0

3w = 5

w = 5/3

Now,

Length.

= 3w + 4
= 3 x 5/3 + 4

= 5 + 4

= 9

Width = 5/3

Thus,

The length and width of the rectangle are 9 and 5/3.

Learn more about rectangles here:

https://brainly.com/question/15019502

#SPJ2

Step-by-step explanation:

80+70+2×+×=180

=150+2×+×=180

=150+3×=×180

180-150=3×

30=3×

/3=/3

×=10

Answer:

11, 17, 29, 65

Step-by-step explanation:

Rrplace x with values on the x colon

Answer:

Column 1 (When x = 1): y = 11

Colum 2(When x = 2): y = 17

Column 3(When x = 4): y = 29

Colum 4(When x= 10): y = 65

Step-by-step explanation:

When x = 1; y = 6(1) + 5

              => y = 6 + 5

             => y = 11

When x = 2; y = 6(2) + 5

               => y = 12 + 5

              => y = 17

When x = 4;  y =  6(4) + 5

                => y = 24 + 5

                => y = 29

When x = 10; y = 6(10) + 5

                => y = 60 + 5

                => y = 65

Hope this helps!

Total stockholders’ equity 7,800,000

Statement of stockholders’ equity for CC for the year ended December 31, 2012:Particulars Amount ($)
Common Stock 100,000

Additional Paid-in Capital 4,100,000
Retained Earnings (Opening Balance) 3,000,000
Add: Net Income for the year ended December 31, 2012 800,000
Total retained earnings 3,800,000

Less: Cash Dividend Declared on July 1 and paid on July 31 (200,000)
Retained earnings (Closing balance) 3,600,000
Total stockholders’ equity 7,800,000

Explanation:The given information is as follows:Common Stock on January 1, 2012 = $100,000Additional Paid-in Capital on January 1, 2012 = $4,100,000

Retained Earnings on January 1, 2012 = $3,000,000Net Income for the year ended December 31, 2012 = $800,000Cash Dividend Declared on July 1 and paid on July 31 = $200,000

To prepare the statement of stockholders’ equity for the year ended December 31, 2012, we will begin by preparing the opening balances of each of the equity accounts. We will then add the net income to the retained earnings account.

The closing balance for retained earnings is then computed by subtracting the cash dividend declared and paid from the total retained earnings. Finally, the total stockholders' equity is calculated by adding the balances of all the equity accounts.

Calculations:Opening balance of common stock = $100,000

Opening balance of additional paid-in capital = $4,100,000

Opening balance of retained earnings = $3,000,000

Net Income for the year ended December 31, 2012 = $800,000

Retained earnings (Opening Balance) = $3,000,000

Add: Net Income for the year ended December 31, 2012 = $800,000

Total retained earnings = $3,800,000Less: Cash Dividend Declared on July 1 and paid on July 31 = $200,000Retained earnings (Closing balance) = $3,600,000

Total stockholders’ equity = Common Stock + Additional Paid-in Capital + Retained Earnings (Closing balance) = $100,000 + $4,100,000 + $3,600,000 = $7,800,000

Therefore, the statement of stockholders’ equity for CC for the year ended December 31, 2012, is as follows:Particulars Amount ($)
Common Stock 100,000
Additional Paid-in Capital 4,100,000

Retained Earnings (Opening Balance) 3,000,000
Add: Net Income for the year ended December 31, 2012 800,000
Total retained earnings 3,800,000

Less: Cash Dividend Declared on July 1 and paid on July 31 (200,000)
Retained earnings (Closing balance) 3,600,000
To learn more about : equity

https://brainly.com/question/27821130

#SPJ8

Answer:

4.6

Step-by-step explanation:

4.639    if bold underlined numeral is ≥ 5 round '6' up to 7  o/w  leave alone

= 4.6    rounded

Answer:

see explanation

Step-by-step explanation:

Using the trigonometric identities

sin²x + cos²x = 1 ⇒ 1 - sin²x = cos²x

cot x = \(\frac{cosx}{sinx}\)

Consider the left side

\(\frac{(1-sin0)(1+sin0)}{sin^20}\) ← expand numerator using FOIL

= \(\frac{1-sin^20}{sin^20}\)

= \(\frac{cos^20}{sin^20}\)

= cot²Θ = right side

Answer:

4

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

When we divide fractions, we are essentially multiplying by the reciprocal of the fraction.

2/3 ÷ 1/6

= 2/3 × 6

= 12/3

= 4

Answer:

a) 10 y = x

b) 8.5 min

Step-by-step explanation:

a) x - axis = distance

y - axis = time

the line passing through points (10,1) (20,2) (30,3).......

line equation is y - y1 = m (x - x1)

m = (y2 -y1) / (x2 - x1)

= (2 - 1) / (20 - 10)

m = 1/10

y - 1 = 1/10 * (x - 10)

10(y - 1) = x - 10

10y - 10 = x - 10

10y = x

here x represents distance

y represents time

b) for distance of 85 inches

time =

10 * time = 85

time = 8.5 min

The total length of wire needed to make this shape is 72 cm.

Let's assume each equilateral triangle has side length 'a'. Since all triangles are equilateral, they have the same side length.

The perimeter of the outside of the shape is given as 24 cm, which means the sum of all the sides of the triangles equals 24 cm.

Since the shape consists of six equilateral triangles, we can express the perimeter as:

6a = 24

a = 24 / 6

a = 4 cm

Perimeter of one equilateral triangle = 3 * a

Perimeter of one equilateral triangle = 3 * 4

Perimeter of one equilateral triangle = 12 cm

Total length of wire needed = Perimeter of one equilateral triangle * Number of triangles

Total length of wire needed = 12 cm * 6

Total length of wire needed = 72 cm

Learn more about total length here:

https://brainly.com/question/30471207

#SPJ11

For R200 Linda gets about 24 liters of petrol, Costing R8.33 per liter.

A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.

Given, Linda paid R200 to put in his car when the price of petrol was R8.33 per liter.

Therefore, The number of liters of petrol Linda gets can be obtained by dividing the total amount by the price of one liter of petrol which is,

= (200/8.33) liters.

= Approximately 24 liters of petrol.

learn more about the unitary method here :

https://brainly.com/question/28276953

#SPJ1

Answer: A

Step-by-step explanation: Anything at the bottom of the chart is the X-axis and the M is a reflection so the M is supposed to be upside down

get it?? i hope i explained it well

The solution is, the circumference of the circle with radius 14in. is  87.96 inch.

A perimeter is a closed path that encompasses, surrounds, or outlines either a two dimensional shape or a one-dimensional length. The perimeter of a circle or an ellipse is called its circumference. Calculating the perimeter has several practical applications.

Perimeter refers to the total outside length of an object,

here, we have,

the radius = r = 14 inch.

we know,

circumference = 2*pi* r

so, calculating we get,

circumference = 87.96 inch.

Hence, The solution is, the circumference of the circle with radius 14in. is  87.96 inch.

Learn more about perimeter here:

brainly.com/question/397857

#SPJ1

Answer: 1,000

Step-by-step explanation:

38.63 x4= 154

Answer:

2.32

Step-by-step explanation:

multiply 57.84 x 4 = 231.36

divide 231.36 / 100 = 2.31 but if you estimate then its 2.32

An ice cream shop has 10 flavors and one can choose 4 different flavors. The question asks for the total number of possible flavor combinations.Therefore, we need to find the number of ways in which 4 flavors can be chosen from 10 flavors.

In such cases where order does not matter and repetitions are not allowed, we can use the formula for combinations which is as follows:C(n, r) = n! / (r! (n - r)!)Where n is the total number of items, r is the number of items being chosen at a time and ! represents the factorial function.

Using this formula we can find the total number of possible flavor combinations. Substituting the values in the above formula, we get:C(10, 4) = 10! / (4! (10 - 4)!)C(10, 4) = (10 * 9 * 8 * 7) / (4 * 3 * 2 * 1)C(10, 4) = 210Hence, there are 210 possible flavor combinations when one can choose 4 different flavors

.Explanation:The formula to be used for this type of question is combination. Combination is the method of selecting objects from a set, typically without replacement (without putting the same item back into the set) and where order does not matter. The formula for combination is given by C(n,r)=n!/(r!(n-r)!).

For more questions on: combinations

https://brainly.com/question/29595163

#SPJ8                  

There can be 6,636 committees formed with at least 2 freshmen from the group of freshmen and sophomores.

What is debate team?

A debate team is a group of individuals who participate in organized debates, engaging in structured discussions and arguments on a specific topic or proposition. The team typically consists of multiple members who work collaboratively to prepare arguments, research evidence, develop persuasive strategies, and engage in public speaking. Debate teams often compete against other teams in formal debate competitions, where they present their arguments, counter-arguments, and rebuttals to persuade judges and audiences of their position's validity. The purpose of a debate team is to enhance critical thinking, public speaking skills, and the ability to construct well-reasoned arguments in a persuasive manner.

To determine the number of committees that can be formed with at least 2 freshmen, we need to consider different cases.

Case 1: Selecting 2 freshmen and 3 sophomores.

The number of ways to choose 2 freshmen from a group of 8 is given by the combination formula: C(8, 2) = 28.

Similarly, the number of ways to choose 3 sophomores from a group of 10 is given by: C(10, 3) = 120.

The total number of committees for this case is 28 * 120 = 3,360.

Case 2: Selecting 3 freshmen and 2 sophomores.

The number of ways to choose 3 freshmen from a group of 8 is: C(8, 3) = 56.

The number of ways to choose 2 sophomores from a group of 10 is: C(10, 2) = 45.

The total number of committees for this case is 56 * 45 = 2,520.

Case 3: Selecting 4 freshmen and 1 sophomore.

The number of ways to choose 4 freshmen from a group of 8 is: C(8, 4) = 70.

The number of ways to choose 1 sophomore from a group of 10 is: C(10, 1) = 10.

The total number of committees for this case is 70 * 10 = 700.

Case 4: Selecting 5 freshmen and 0 sophomores.

The number of ways to choose 5 freshmen from a group of 8 is: C(8, 5) = 56.

There are no sophomores left to choose from.

The total number of committees for this case is 56.

To find the total number of committees, we sum up the number of committees from each case:

3,360 + 2,520 + 700 + 56 = 6,636

Therefore, there can be 6,636 committees formed with at least 2 freshmen from the group of freshmen and sophomores.

To know more about debate team visit:

https://brainly.com/question/1022252

#SPJ4

(a) Vertex: (6, 3)

(b) Maximum value: 3

(c) Axis of symmetry: x = 6

(d) Range of the function g: (-∞, 3]

(e) The function g is increasing on the interval (-∞, +∞).

Given function g(t) = - (1/12)x² + x

(a) Using the formula t = -b/2a, where a = -1/12 and b = 1.

Substituting these values, we get:

t = -1 / 2(-1/12) = 6

Therefore, the vertex of the function is (6, 3).

(b) Substitute the x = 6 into the function to get the maximum value:

g(6) = - (1/12)(6)² + 6 = 3

Therefore, the maximum value of the function is 3.

(c)  The axis of symmetry is the line x = 6.

(d) The range of the function g is all real numbers less than or equal to the maximum value of the function, which is 3.

Therefore, the range of the function g is (-∞, 3].

(e) Since the coefficient is positive, the function is increasing on the interval (-∞, ∞).

Since the vertex is at (6, 3) and the y-intercept is at (0, 0), the function is decreasing on the interval.

Learn more about the functions here:

brainly.com/question/12431044

#SPJ4