Which of the following is the correct factorization of the polynomial below?
x³-18
A. (x+3)(x-6)
B. (x-3)(x+6)
C. (x+3)(x² - 4x+6)
D. The polynomial is irreducible.
SUBMIT

Answers

Answer 1

Answer: D. The polynomial is irreducible.

From the explanation below we do not get polynomial .

Step-by-step explanation:

A.(x+3)(x-6)

=  x^2-6x+3x-18

=x^2-3x-18

B.(x-3)(x+6)

 =(x^2+6x-3x-18)

  =x^2+3x-18

C.(x+3)(x^2-4x+6)

  =x^3-4x^2+6x+3x^2-12x+18

  =x^2-x^2-6x+18

D.The polynomial is irreducible


Related Questions

Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar. On a number line, point D is at -3, and point E is at 6. The point F lies on segment DE . The ratio of DF to FE is 2 : 3. Where does point F lie on the number line? Point F is at on the number line.

Answers

Using the section formula, point F lie on 3/5 in the number line.

In the given question,

On a number line, point D is at -3, and point E is at 6.

The point F lies on segment DE .

The ratio of DF to FE is 2 : 3.

We have to find where point F lie on the number line.

Since point D lies is at -3 at x axis so the point should be ( -3,0).

Point E lies is at 6 at x axis so the point should be ( 6,0).

F lies on segment DE. So let the point of F is (X, Y)

The ratio is 2:3.

Now firstly finding the value of X using section formula

X = [tex]\frac{mx_{2}+nx_{1}}{m+n}[/tex]

where [tex]x_{1}[/tex]= -3, [tex]x_{2}[/tex]= 6, m= 2 and n=3

Now putting the value

X = {2×6+(-3)3}/(2+3)

Simplifying

X = (12-9)/5

X = 3/5

Now firstly finding the value of Y using section formula

Y = [tex]\frac{my_{2}+ny_{1}}{m+n}[/tex]

where [tex]y_{1}[/tex]= 0, [tex]y_{2}[/tex]= 0, m= 2 and n=3

Now putting the value

Y = (2×0+3×0}/(2+3)

Y = 0/5

Y = 0

Hence, point F lie on 3/5 in the number line.

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kara categorized her spending for this month into four categories: rent, food, fun, and other. the amounts she spent in each category are pictured here. rent $500 food $400 fun $300 other $600 [graphs generated by this script: initpicture(-5.5,5.5,-5.5,5.5);circle([0,0],5);line([0,0],[5,0]);line([0,0],[-.868,4.924]);text([1,2],'rent','right');text([1,1],'$500','right');line([0,0],[-5,0]);text([-1,2],'food','left');text([-1,1],'$400','left');line([0,0],[2.5,-4.33]);text([1,-1],'fun','right');text([1,-2],'$300','right');text([-1,-1],'other','left');text([-1,-2],'$600','left');] what percent of her total spending did she spend on fun? answer to the nearest whole percent. %

Answers

Answer: is 16.6%

Step-by-step explanation: Use the rule of three (mathematic).

Find the x- and y-intercepts of the graph of 4x - 9y = 20. State each answer as an
integer or an improper fraction in simplest form.

Answers

What is y- intercept?The point where a graph contacts the y-axis is known as the y intercept. Any point on the y-axis has an x-coordinate of 0, as is known. Therefore, a y-x-coordinate intercept's is 0.The slope-intercept version of the equation for the line is y=mx+b. b is the line's y-intercept according to the specification of the slope-intercept form itself. You can experiment by changing x=0 to 0 to y=mx+b to check if the y-intercept changes to b. As a result, the slope-intercept form of the equation of a line's y-intercept is (0, b) or b.

Calculation

Find the dependent variable by itself: [tex]y= \frac{4x}{9} -\frac{20}{9}[/tex]

Find the function's x-intercept: x= 5

Find the dependent variable by itself: [tex]y= \frac{4x}{9} -\frac{20}{9}[/tex]

Find the function's y-intercept: y = [tex]-\frac{20}{9}[/tex]

The chart for : 4x-9y = 20

see the attachment

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The x- and y-intercepts of the graph 4x - 9y = 20 In the simplest form, state each answer as an integer or an improper fraction. x = 20 + 9y /4

What is meant by fraction?A fraction is a portion of a whole. In arithmetic, the number is expressed as a quotient, which is the numerator divided by the denominator. In a simple fraction, both are integers.A complex fraction has a fraction in either the numerator or denominator. In a proper fraction, the top number is less than the lowest common.A fraction pretty much tells us how many parts of a whole we have. A fraction is identified by the slash that is written between the two numbers. Designers have a top number, the quaternion, and a bottom number, the denominator. For instance, 1/2 is a fraction.

Given

x, 4x - 9y = 20  

x = 20 + 9 /4 y

Steps

4x - 9y = 20

Add 9 y to both sides

4x - 9y + 9y = 20 + 9y

Simplify

4x = 20 + 9y

Divide both sides by 4

4x/4 = 20/4 + 9y/4

Simplify

x = 20 + 9y /4

Hence, The x- and y-intercepts of the graph 4x - 9y = 20 In the simplest form, state each answer as an integer or an improper fraction.

x = 20 + 9y /4

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PLEASE HELP ASAP I NEED TO GET THIS DONE!!

Answers

Answer:

B and D

Step-by-step explanation:

A is wrong because x has a negative exponent


C is wrong because x is a denominator

HELP MEEEE PLEASEEEE

Answers

Answer:

24.4 km

Step-by-step explanation:

The Pythagorean theorem states that a^2 + b^2 = c^2, where c is the hypotenuse of the triangle, and a and b are the legs. Plugging in your values, we get:

20^2 + 14^2 = c^2

Simplify: 400 + 196 = c^2

Simplify again: 596 = c^2

Square root both sides to cancel out the exponent on the right: 24.4131=c

Round: 24.4

jim and craig, working together, can mow the lawn in 5 hours. working alone, craig takes five times as long as jim. how long does it take jim to mow the lawn alone?

Answers

In  linear equation ,Shirley takes 1.66 hours to paint the deck alone.

What in mathematics is a linear equation?

A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."

Let Shirley's time = x

Let Craig's time  = 5x

(5x + x)/2 = 5

We split up the hours by 2 because we want to find out how much time individually.

6x/2 = 5

6x = 10

 x = 1.66

Shirley takes 1.66 hours to paint the deck alone.

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Answer 3,4,5,6 Thank you

Answers

B) The missing angle at the intersection point of both triangles is; x = 15°

C) The missing angle is gotten as; x = 61°

How to find the missing angles?

B) In the second image given, we can see two angles;

Now, we know that sum of angles in a triangle is 180 degrees. Thus, for the interior angles, we have;

90 + 5x - 14 + y = 180

where y is the third interior angle

Now, we know that sum of angles on a straight line is equal to 180 degrees. Thus;

y = 180 - (9x + 16)

Put 180 - (9x + 16) for y into the first equation to get;

90 + 5x - 14 + 180 - (9x + 16) = 180

180 will cancel out to get;

90 + 5x - 14 - (9x + 16) = 0

4x = 90 - 14 - 16

4x = 60

x = 60/4

x = 15°

C) The missing angle of the triangle with side of 12y + 3 is an alternate angle to get;

Missing angle = 63°

Sum of angles in a triangle is 180 degrees. Thus;

56 + 63 + 3rd angle = 180

3rd angle = 180 - (56 + 63)

3rd angle = 61°

Thus, x = 61° because they are opposite angles

Also, the two given sides are equal to each other as shown. Thus;

51 = 12y + 3

12y = 51 - 3

12y = 48

y = 48/12

y = 4

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A carpenter needs to build a box to hold his wood screws. He has a sheet of wood that measures 18 inches by 12 inches. He then cuts equal squares from each corner. (a) Write an expression for the length, width, and height for the open box. (b) Write a function for the volume (use factored form).

Answers

The expressions for the length, width, and height are 18 - 2x, 12 - 2x, and x while the volume function is V = (12 - 2x)(18 - 2x)x

(a) How to determine the expression for the length, width, and height

From the question, we have the following parameters:

Dimension of sheet = 8 inches by 12 inches

Also from the question, we understand that:

He cuts equal squares from each corner.

The cut-out length from the sheet would represent the height of the box

Represent this cut-out length with x

So, we have

Height = x

The width and the length are then represented as

Width = Initial width - 2x

Length = Initial length - 2x

So, we have

Width = 12 - 2x

Length = 18 - 2x

(b) Write a function for the volume

The volume of a box is the product of its dimensions

In this case, we have

Width = 12 - 2x

Length = 18 - 2x

Height = x

So, we have

Volume = Width * Length * Height

Substitute the known values in the above equation So, we have the following equation

V = (12 - 2x)(18 - 2x)x

So, the volume function is V = (12 - 2x)(18 - 2x)x

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Which statement justifies the given ordered pair as a solution to the system of equations? ​ (−1, −13) ​ {y=3x−10y=−2x−15

Answers

x = -1 and y = -13, (-1,-13) is the solution to the system of equation y = 3x - 10 and y = -2x - 15.

What is the solution to the given system of equation?

Given the system of equation in the question;

y = 3x - 10 y = -2x - 15Is (-1,-13) the correct ordered pair?

To find the solution to the system of equation, replace the occurrence of y in the second equation with y = 3x - 10  and solve for x.

y = -2x - 15

3x - 10 = -2x - 15

Add 10 to both sides

3x - 10 + 10 = -2x - 15 + 10

3x = -2x - 15 + 10

Add 2x to both sides

3x + 2x = -2x + 2x - 15 + 10

3x + 2x = - 15 + 10

Add like terms

5x = -5

x = -5/5

x = -1

Now, to solve for y, replace all occurrence of x with -1 in the first equation and solve for y.

y = 3x - 10

y = 3( -1 ) - 10

y = -3 - 10

y = -13

Therefore, the solution to the system of equation is (-1,-13).

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Write a rule for g that represents the indicated transformations of the graph of f.

f(x)=2x5−x3+x2+4; reflection in the y-axis and a vertical stretch by a factor of 3, followed by a translation 1 unit down

Answers

The rule that represents the transformation is g(x) = -6x⁵ + 3x³ + 3x² + 11

How to determine the transformation of the function?

The equation of the function is given as

f(x) = 2x⁵ - x³ + x² + 4

The sequence of transformations is given as follows:

Reflection across the y-axisVertically stretched by a factor of 3Translate down by 1 unit

When the above transformations are combined, we have:

g(x) = 3f(-x) - 1

So, we have

3f(-x) - 1 = 3[2(-x)⁵ - (-x)³ + (-x)² + 4] - 1

This gives

3f(-x) - 1 = -6x⁵ + 3x³ + 3x² + 12 - 1

Expand

3f(-x) - 1 = -6x⁵ + 3x³ + 3x² + 11

So, we have

g(x) = -6x⁵ + 3x³ + 3x² + 11

Hence, the function is g(x) = -6x⁵ + 3x³ + 3x² + 11

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32. what proportion of the 30 sampled bottles are more than 12 ounces? a. 0.20 b. 0.60 c. 0.50 d. 0.30 33. in the sample of 30 bottles, the lowest recorded fill is 11.3 ounces, however, originally this value was mistakenly entered as 1.3 ounces. suppose the error is left uncorrected and the lowest value remains 1.3 ounces. which value is most affected by the error? a. the median. b. the interquartile range. c. the mean. d. all measurements would be affected the same.

Answers

The proportion of the 30 sampled bottles are more than 12 ounces is 0.30. The value is most affected by the error will be mean.

What is mean?

The sum of all values divided by the total number of values determines the mean (also known as the arithmetic mean, which differs from the geometric mean) of a dataset. The term "average" is frequently used to describe this measure of central tendency. A data set's mean (average) is calculated by adding all of the numbers in the set, then dividing by the total number of values in the set. When a data set is ranked from least to greatest, the median is the midpoint.

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Nicole has $40 in a savings account. The account earns 5% simple interest. She wants to determine the amount in her account after 1 year if she makes no deposits or withdrawals.

Answers

Answer:

16

Step-by-step explanation:

40/5 then x the answer by 2 and you get 16 with now deposits or withdraws

maths enlargements calculations of lines in shapes help pls

Answers

The length of the line segment BD is 3 centimeters.

How to find the missing length of triangle proportional to another triangle

Herein we find two triangles proportional to each other. According to Thales's theorem, two triangles are proportional when both have congruent angles. The geometric system is represented by the following expression:

AB / AD = BC / DE = AC / AE

By direct inspection we notice that the two triangles are proportional as they have congruent angles. If we know that DE = 10 cm, BC = 8 cm and AB = 12 cm, then the side AD has the following measure:

12 cm / AD = 8 cm / 10 cm

AD = (10 cm / 8 cm) × 12 cm

AD = 15 cm

And the length of the line segment BD is:

BD = AD - AB

BD = 15 cm - 12 cm

BD = 3 cm

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A baseball is thrown from the pitcher's
mound at 40 m/s. It takes 0.46 seconds for
the ball to reach home plate. What is the
distance between the mound and home
plate?

Answers

Answer:

Step-by-step explanation:

Velocity = distance / time

In this problem, we need to calculate for distance, knowing time and velocity.

multiply time on both sides, on the right side the time will cancel out leaving time alone.

velocity * time = distance

40m/s * 0.46s = distance

distance = 18.4 meters

Hope it helped!

in the figure, h II o find the value of x and y

Answers

Answer:

y = 119

30 =x

Step-by-step explanation:

61 and y are same side interior angles and they add to 180

61+y = 180

y = 180-61

y = 119

y and 6x-61 are vertical angles and they are equal

y = 6x-61

119 = 6x-61

Add 61 to each side

119 + 61 = 6x

180 = 6x

Divide each side by 6

180/6 = x

30 =x

Answer:

y = 119°

x = 30°

Step-by-step explanation:

We know that if two lines are parallel, the co - interior angles are added up to 180°°.

Accordingly,

y + 61 = 180

y = 180 - 61

y = 119°

Also, we know that, vertically opposite angles are equal to each other.

y = 6x - 61

119 = 6x - 61

Now, we have to make x the subject.

For that, first, add 61 for both sides.

119 + 61 = 6x

180 = 6x

Now, divide both sides by 6.

30° = x

How much of a radioactive kind of zinc will be left after 2 hours if the half-life is 1 hour and
you start with 259,288 grams?
grams

Answers

Answer:

64822

Step-by-step explanation:

Half-life model:

            [tex]P=P_o* \left(\frac{1}{2}\right)^{\frac{t}{D}}[/tex]

[tex]P_o[/tex] is the initial value, D is the time taken for the quantity to reduce half-life and t is the given time period.

       [tex]\sf P_o = 259,288 \ grams\\\\D = 1 \ hour\\\\t = 2 \ hours[/tex]

            [tex]P = 259,288*(\frac{1}{2})^\frac{2}{1}\\\\P = 259,288*(\frac{1}{2})^2\\\\P = 259,288*\frac{1}{4}\\\\P = 64822[/tex]

                           

How much of a radioactive kind of bismuth will be left after 8 minutes if the half-life is 2
minutes and you start with 79,360 grams?
grams

Answers

2min-Half life 1: 79360/2=39680
4min-Half life 2: 39680/2=19840
6min-Half life 3: 19840/2=9920
8 min-Half life 4: 9920/2=4960
You will end up with 4960 grams of radioactive bismuth

"the difference of a number cubed and 10" translated expression

Answers

Answer:

[tex]x^3-10[/tex]

Step-by-step explanation:

Let the number be x.

"A number cubed" refers to x³.

"Difference" means to subtract, so the answer is [tex]x^3-10[/tex].

Ben watched 3/8 of his television show. There are still 40 minutes left. How long does the whole program last?

Answers

The show is 1 hour 4 minutes long.

What is Algebra?

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

Ben watched 3/8 of his television show.

There are still 40 minutes left.

let the show be x long.

So, 3/8x + 40 = x

x- 3/8x= 40

5x/8 = 40

x= 320/5

x= 64 minutes

x= 1 hour 4 minutes

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In triangle ABC, m angle A=45 degrees. The altitude divides side AB into two parts of 20 and 21 units. Find BC

Answers

The 20 and 21 unit leg lengths of the right triangles ΔACD and ΔBCD formed by the altitude CD indicates, by using Pythagorean theorem that the length of BC is 29 units

What is a right triangle?

A right triangle is a triangle that has two perpendicular sides. The altitude of a triangle is perpendicular to the base of the triangle, forming two right triangles in acute triangle.

Angle ∠A = 45°

The length of the segment the altitude CD divides AB into = 20 and 21 units

Please find attached a drawing created using MS Word based on the question parameters.

[tex]tan(\angle A) = \dfrac{CD}{AD}[/tex]

AD = 20

Therefore;

[tex]tan(45^{\circ}) = \dfrac{CD}{20}[/tex]

CD = 20 × tan(45) = 20

Pythagorean theorem applied to right triangle ΔCBD, indicates that;

[tex]\overline{BC}^2[/tex] = [tex]\overline{CD}^2[/tex] + [tex]\overline{DB}^2[/tex]

DB = 21 units, which gives;

[tex]\overline{BC}^2[/tex] = 20² + 21² = 841

BC = √(841) = 29

The length of the segment BC = 29 units

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Please help thanks, Which postulate can be used to prove the two triangles are congruent?

Answers

The postulate that can be used to prove the two triangles are congruent is the HL this is the last option

What is HL?

HL is an acronym that means Hypotenuse Leg. The Hypotenuse leg theorem is used in proving angle congruency in right angle triangle.

The theorem says that, two angles of a right angle triangle that have equal

hypotenuse andany one leg

then two triangles are congruent

The figure in the problem is a right angle triangle that is sharing same hypotenuse hence the hypotenuse is equal. and one other leg is marked to be equal

Therefore, this theorem says that the two triangle are congruent

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1) 2 more than 5 times x

2) 9 Multiply n by 6, and then divide the product by 5.

Answers

Answer:

1. 5x +2

2. 6x/5

Step-by-step explanation:

for a questionnaire survey of employees of a particular organisation to investigate a range of aspects of their job satisfaction, a researcher invites all 1000 employees to participate and aims for a sample of 200 men and 200 women. what method of sampling is this?

Answers

This is an example of stratified random sampling as the population is divided into two groups males and females and 200 samples are selected from each group.

Given that,

A researcher asks all 1000 employees to engage in a questionnaire survey to look at various areas of employee job satisfaction with the goal of selecting a sample of 200 males and 200 women.

A crucial element of the sampling method known as stratified random sampling is the division of a population into smaller subgroups known as strata

Therefore, the population is separated into two categories, males and females, and 200 samples are chosen from each group in this stratified random sampling example.

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Last year, James earned £2,100 per month.
This year, he's had a 6% increase in his monthly pay.
He worked 35 hours per week for 46 weeks in the year.
What is James' average pay per hour this year?
Give your answer to 2 dp.

Answers

James average pay per hour is $17.40

How to find James average pay per hour

information given in the problem are

Last year, James earned £2,100 per month

This year, he's had a 6% increase in his monthly pay

35 hours per week for 46 weeks in the year

The question is a percentage problem

6% increase a factor of  1.16

2100 * 1.16 = 2436

number of hours in a month

35 hours = 1 week

? hours = 4 weeks

? = 4 * 35

? = 140 hours in 4 weeks = 1 month

James average pay per hour is gotten form the calculation below

if 140 hours pays 2436 then1 hour will pay ?

140 = 2346

1  =  ?

cross multiplying

? * 140 = 2436 * 1

? = 2436 / 140

? = $17.40

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Find the distance between points P(8, 2) and Q(3, 8) to the nearest tenth.

Answers

[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ P(\stackrel{x_1}{8}~,~\stackrel{y_1}{2})\qquad Q(\stackrel{x_2}{3}~,~\stackrel{y_2}{8})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ PQ=\sqrt{(~~3 - 8~~)^2 + (~~8 - 2~~)^2} \implies PQ=\sqrt{( -5 )^2 + ( 6 )^2} \\\\\\ PQ=\sqrt{ 25 + 36 } \implies PQ=\sqrt{ 61 }\implies PQ\approx 7.8[/tex]

Bert keeps honeybees on his farm. When he first started he used a six frame beehive that held 40 pounds of honey. now he uses a 30 frame beehive. It has the same ratios of frames to honey as a smaller beehive.
How much honey does Bert’s new beehive hold?

Answers

If now he uses a 30 frame beehive. It has the same ratios of frames to honey as a smaller beehive. The amount of  honey that Bert’s new beehive hold is 200.

How to find the number of honey?

Given data:

Number of frame beehive = 6

Pound of honey = 40

Current Frame beehive = 30

First step is to formulate an equation and then use the formulated equation to find  the number of honey

40 × 30 ÷ 6

Hence,

40 × 5

= 200 honey

Therefore the number of honey is 200.

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A satellite dish has the shape of a parabola when viewed from the side. the dish is 48 inches wide and 36 inches deep. how far is the receiver from the bottom of the dish if the receiver is placed at the focus?

Answers

If the receiver is placed at the focus, it is 4 inches from the bottom of the dish. The result is obtained by using the equation of parabola with the vertex is at (0,0).

What is the equation of a parabola?

With the vertex at (0,0), the equation of a parabola can be expressed as

x² = 4ay

Where

x = half of the diameter of parabola a = the y-axis of the focus of parabolay = the depth of parabola

Given

Diameter of the dish = 48 inchesy = 36 inches

How far is the receiver from the bottom of the dish if it is placed at the focus?

Suppose that the vertex is at (0,0).

x = 1/2 × diameter

x = 1/2 × 48

x = 24

Now, we got two points (-24, 36) and (24,36). See the picture in the attachment!

By using the x and y value, the value of a is

x² = 4ay

24² = 4a(36)

576 = 144a

a = 576/144

a = 4 inches

Hence, the receiver is placed at 4 inches from the bottom of the dish.

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dave is making a rectangular garden bed. after assembling it, he finds that the bed has a width of three-fourths of a foot and a length of nine and one-third feet. what is the area of the garden in square feet

Answers

The area of the garden is 7 square feet.

Define area.

The area a rectangle occupies is the space it takes up inside the limitations of its four sides. The dimensions of a rectangle determine its area. In essence, the area of a rectangle is equal to the sum of its length and breadth. An example of a quadrilateral with equal and parallel opposite sides is a rectangle. It is a polygon with four sides and four angles that are each 90 degrees. A rectangle is a shape with only two dimensions. A rectangle's area (A) is calculated by multiplying its length ('a') by its breadth ('b'). Area of Rectangle is therefore equal to (a× b) square units.

Given,

Width = 3/4

Length = 9 + 1/3

Length = 28/3

Area:

Length × Width

3/4 × 28/3

84/12

7

The area of the garden is 7 square feet.

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correct answer gets brainliest!

Answers

Answer:

x = 14

Step-by-step explanation:

the inscribed angle JKL is half the measure of its intercepted arc, that is

83 = [tex]\frac{1}{2}[/tex] arc JL = [tex]\frac{1}{2}[/tex](9x + 40) ← multiply both sides by 2 to clear the fraction

166 = 9x + 40 ( subtract 40 from both sides )

126 = 9x ( divide both sides by 9 )

14 = x

help asap, ill give

Answers

The greatest number of bags Caesar can make is 16 bags. Each of these bags will have 5 boxes of pasta and 8 jars of sauce.

If Caesar made fewer bags, he would have boxes of pasta and jars of sauce remaining.

He could use 8 bags but this is not the greatest number he could use.

What is the number of pasta and sauce in each bag?

Boxes of pasta = 32Jars of sauce = 48

Find the greatest common factor of 32 and 48

32 = 1, 2, 4, 8, 16, 3248 = 1, 2, 3, 4, 6, 8, 12, 16, 24 and 48.

The greatest common factor of 32 and 48 is 16

So, the greatest number of bags Caesar can make is 16 bags

Number of pasta in each bag = 32/16

= 5 boxes of pasta per bag

Number of sauce in each bag = 48/16

= 8 jars of sauce per bag

If Caesar made fewer bags, he would have boxes of pasta and jars of sauce remaining.

He could use 8 bags but this is not the greatest number he could use.

Therefore, Caesar can use the greatest common factor to determine the highest number of bags he could use.

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