Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers.
Place the indicated product in the proper location on the grid.

-4x 3 y 2(7xy 4)

Answer: its the third one try that

Step-by-step explanation:

Answer:

It's C

Step-by-step explanation:

Answer:

D. y[9]=15.5410

Step-by-step explanation:

Let's find the answer by using the following observation:

Notice that the y-value differences between consecutives obstacles are:

(y-value from obstacule 2) - (y-value from obstacule 1)= 7.975 - 7.25 = 0.725

which is equal to:

(y-value from obstacule 1) / 10 = 7.25 / 10 = 0.725

So, an equation can be written as follows:

y[i+1]=y[i]+y[i]/10 let's find the other values:

y[2]=7.25+(7.25/10)= 7.975

y[3]=7.975+(7.975/10)= 8.7725

y[4]=8.7725+(8.7725/10)= 9.64975

Notice that we obtained the same y-values using the formula as the ones reported. So using the same formulas we can calculate:

y[9]=15.5410

In conclusion, the general equation is y[i+1]=y[i]+y[i]/10 with a starting point (1, 7.25) and y[9]=15.5410. So the answer is D.

Answer:

D.) f(9) = 7.25(1.1)8; f(9) = 15.541

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

We are given f(x) is height in cm while x is days old.

We are also given f(60)=210.

If you compare f(60) to f(x) you should see that x is 60 so we have the sunflower is 60 days old.  Since f(60)=210, then you have the height of the sunflower is 210 cm tall.

Answer:

B.) The height of the sunflower plant is 210 cm when it is 60 days old.

Step-by-step explanation:

Answer:

y<-3x+8

Step-by-step explanation:

We are given 3x+y<8. There is exactly one step to put this in slope-intercept form, y=mx+b form where the equal sign can be an inequality sign. Our goal is to isolate y.

To do in 3x+y<8, we will just need to subtract 3x on both sides giving us y<-3x+8.

Answer:

y<-3x + 8

Step-by-step explanation:

y=mx+b form

Answer:

[tex] x=2 \pm \sqrt{7} [/tex]

Step-by-step explanation:

Given this form ax^2+bx=k, here are my steps for completing the square while answer your question:

First step: Divide both sides by what is in front of x^2.  You want the coefficient of x^2 to be 1.  To do this for your question, divided both sides by 3.

This gives us x^2-4x  = 3.

Second step:  We are ready to begin the completing the square process at this step.  We are going to add (b/2)^2 on both sides.  For this question b=-4.

So we will be adding (-4/2)^2 on both sides.

This gives us x^2-4x+(-4/2)^2=3+(-4/2)^2.

Third step:  I like to simplified the things inside the square and I do not actually apply the square at this step.  It makes a later step easier in my opinion.

So this step gives us  x^2-4x+(-2)^2=3+(-2)^2.

Fourth step:  I'm actually going to write the left hand side as a square.  Just drag the things that are inside the squares down into ( )^2.

This is what I mean x^2-4x+(-2)^2=(x-2)^2.

So at the end of this step we have (x-2)^2=3+(-2)^2.

Fifth step: I'm going to simplify the right hand side.

This step gives us (x-2)^2=7

Sixth step:  We are ready to square root both sides.  

This gives us [tex] x-2=\pm \sqrt{7} [/tex]

Seveth step:  Get x by itself like you normally would with a linear equation.  My step here is just to add 2 on both sides.

Final answer:  [tex] x=2 \pm \sqrt{7} [/tex]

[tex]3x^2-12x=9\\x^2-4x=3\\x^2-4x+4=7\\(x-2)^2=7\\x-2=\sqrt7 \vee x-2=-\sqrt7\\x=2+\sqrt7\vee x=2-\sqrt7[/tex]

Answer:

y= 12

Step-by-step explanation:

2/3 y + 7 = 15

Subtract 7 from each side

2/3 y + 7-7 = 15-7

2/3 y = 8

Multiply each side by 3/2 to isolate y

3/2 * 2/3 y = 3/2 * 8

3/2 * 2/3 y = 3 * 4

y = 12

Option A & B are true about trapezoids and rhombuses.

What are trapezoids and Rhombuses?

A trapezoid is a polygon that has only one pair of parallel sides. These parallel sides are also called parallel bases of trapezoid. The other two sides of trapezoids are non-parallel and called legs of trapezoids.

A rhombus is a special case of a parallelogram. In a rhombus, opposite sides are parallel and the opposite angles are equal. Moreover, all the sides of a rhombus are equal in length, and the diagonals bisect each other at right angles. The rhombus is also called a diamond or rhombus diamond.

Now determine which statement is true about trapezoid and rhombuses

We have given,

Option A: Both shapes are 2-dimensional figures.

This option is true because both trapezoid and rhombuses are a type of quadrilateral and we know quadrilaterals are 2 dimensional figures.

Option B: The first shape has the same number of angles as the second shape.

Yes,this option is true because both the shapes  are quadrilateral type  and a quadrilateral is a closed polygon containing 4 sides and 4 vertices enclosing 4 angles.

Option C: Both shapes have all sides of equal length.

No,this is not true as rhombus has all sides of equal length but trapezoid has all sides of different length.

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Answer:

  A = √29

Step-by-step explanation:

The short of it is that ...

  A² = 2² + 5² = 29

  A = √29

_____

Amplitude

If you expand the second form using the sum-of-angles formula, you get ...

  Asin(ωt +φ) = Asin(ωt)cos(φ) +Acos(ωt)sin(φ)

Comparing this to the first form, you find ...

  c₂ = 2 = Acos(φ)

  c₁ = 5 = Asin(φ)

The Pythagorean identity can be invoked to simplify the sum of squares:

  (Asin(φ))² + (Acos(φ))² = A²(sin(φ)² +cos(φ)²) = A²·1 = A²

In terms of c₁ and c₂, this is ...

  (c₁)² +(c₂)² = A²

  A = √((c₁)² +(c₂)²) . . . . . . . formula for amplitude

_____

Phase Shift

We know that tan(φ) = sin(φ)/cos(φ) = (Asin(φ))/(Acos(φ)) = 5/2, so ...

  φ = arctan(c₁/c₂) . . . . . . . formula for phase shift*

  φ = arctan(5/2) ≈ 1.19029 radians

___

* remember that c₁ is the coefficient of the cosine term, and c₂ is the coefficient of the sine term.

In this mathematics problem, to rewrite in the appropriate form, the amplitude, A, has to be first determined using the given values and the Pythagorean identity. This gives the formula as A=sqrt( + ), where A is the calculated amplitude.

To rewrite in the form, we first need to find the amplitude A. Given values and, if we use the Pythagorean identity, we can solve for A. According to the Pythagorean identity, the sum of the squares of the values equals the square of the amplitude. In mathematical terms, A=sqrt( + ). The result will give you the correct amplitude. Therefore, the given value can be rewritten in the form Acos(ωt+ϕ).

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Answer:

428.7 mm²

Step-by-step explanation:

The area (A) of the sector is calculated as

A = area of circle × fraction of circle

   = πr² × [tex]\frac{170}{360}[/tex]

   = π × 17² × [tex]\frac{17}{36}[/tex]

   = 289π × [tex]\frac{17}{36}[/tex]

   = [tex]\frac{289(17)\pi }{36}[/tex] ≈ 428.7 mm²

The area of a sector with a central angle of 170° and a radius of 17 mm is calculated using the sector area formula, resulting in approximately 428.7 mm², rounded to the nearest tenth.

To find the area of the sector, we use the formula [tex]\( \text{Area} = \frac{\text{Central Angle}}{360\°} \times \pi \times \text{Radius}^2 \)[/tex]. Substituting the given values, we get [tex]\( \text{Area} = \frac{170\°}{360\°} \times \pi \times 17^2 \)[/tex]. Simplifying, we have [tex]\( \text{Area} = \frac{17^2}{2} \times \pi \)[/tex]. Evaluating this expression, we find [tex]\( \text{Area} \approx 428.7 \)[/tex] mm². Therefore, the area of the sector, rounded to the nearest tenth, is approximately 428.7 mm². This calculation represents the portion of the circle enclosed by the given central angle and radius, providing the area of the sector.

Answer:

c

Step-by-step explanation:

5/12, 1, 1/3, 5/6. 1/3 is the smallest.

Answer with Step-by-step explanation:

Mixture A-

Blue Paint - 5 cups

White Paint - 12 cups

Ratio of blue paint to white paint=5:12

Mixture B-

Blue Paint- 6 cups

White Paint- 6 cups

 Ratio of blue paint to white paint=6:6=12:12  

(on multiplying numerator and denominator by 12 i.e.6/6=12/12)

Mixture C-

Blue Paint - 4 cups

White Paint - 12 cups

 Ratio of blue paint to white paint=4:12

Mixture D-

Blue Paint - 5 cups

White Paint - 6 cups

Ratio of blue paint to white paint=5:6=10:12

(on multiplying numerator and denominator by 12 i.e.5/6=10/12)

The denominator of the ratios are same in each mixture now,to determine the lowest ratio we have to see the numerator with smallest value which is 4

Hence, Mixture C has the lowest ratio of blue paint to white paint

Answer:

A = 13.5 cm²

Step-by-step explanation:

* Lets explain how to find the area of the parallelogram

- In any parallelogram each two opposite sides are parallel

- In any parallelogram each two opposite sides are equal in length

- Each two opposite sides have height perpendicular on them

- So the parallelogram has 2 different bases and 2 different heights

- The area of the parallelogram = base × the height of this base

* Lets solve the problem

- The lengths of the two bases of the parallelogram are 4.5 cm , 5 cm

- The height of the base which length is 4.5 is 3 cm

- We will calculate the area of the parallelogram from this base

∵ The base of the parallelogram = 4.5 cm

∵ The height of this base = 3 cm

∵ Area of parallelogram = base × its height

∴ Area of parallelogram = 4.5 × 3 = 13.5 cm²

* The area of the following parallelogram is 13.5 cm²

Answer:

13.5 cm²

Step-by-step explanation:

The area (A) of a parallelogram is calculated as

A = bh ( b is the base and h the perpendicular height )

here b = 4.5 and h = 3, so

A = 4.5 × 3 = 13.5 cm²

Answer:

The correct option is C.

Step-by-step explanation:

Using the given box plots:

The data set for Asian elephant is

6, 6, 7, 7, 7, 8, 8, 8, 8, 8, 8, 9, 9, 9, 10

Divide the data set in 4 equal parts.

(6, 6, 7), 7, (7, 8, 8), 8, (8, 8, 8), 9, (9, 9, 10)

[tex]Q_1=7, Median=8, Q_3=9[/tex]

IQR of the Asian elephant is

[tex]IQR=Q_3-Q_1=9-7=2[/tex]

IQR of the Asian elephant is 2.

If the data set lies in interval [tex][Q_1-1.5(IQR),Q_3+1.5(IQR)][/tex], then the data set has no outliers.

[tex][Q_1-1.5(IQR),Q_3+1.5(IQR)]=[7-1.5(2),9+1.5(2)]=[4,12][/tex]

All the data lie in [4,12], therefore Asian elephant  has no outliers.

The data set for African elephant is

4, 6, 7, 7, 8, 8, 8, 9, 9, 9, 10, 10, 10, 10, 11, 11, 11, 11, 11, 11, 12, 12, 12, 12, 12, 12, 13, 13, 14, 14

Divide the data set in 4 equal parts.

(4, 6, 7, 7, 8, 8, 8), 9,( 9, 9, 10, 10, 10, 10, 11), (11, 11, 11, 11, 11, 12, 12), 12, (12, 12, 12, 13, 13, 14, 14)

[tex]Q_1=9, Median=11, Q_3=12[/tex]

IQR of the African elephant is

[tex]IQR=Q_3-Q_1=12-9=3[/tex]

IQR of the African elephant is 3.

[tex][Q_1-1.5(IQR),Q_3+1.5(IQR)]=[9-1.5(3),12+1.5(3)]=[4.5,16.5][/tex]

All the data lie in [4.5,16.5] except 4, therefore African elephant has lower outliers.

African have a greater IQR because there were some very short elephants.

Therefore the correct option is C.

Answer:

African Elephants have a greater IQR because there were some very short elephants (low outliers).

Step-by-step explanation:

Apex

Answer:

The confidence interval shows a range of values that includes this parameter of the population with an ascribed degree of confidence: (1) Mean; (2) Standard deviation; (3) Variance; (4) None of the above

Step-by-step explanation:

In statistics, a pair or several pairs of numbers between which it is estimated that there will be a certain unknown value with a certain probability of success is called a confidence interval.

The standard deviation, is a measure used to quantify the variation or dispersion of a set of numerical data.

The answer is: (2) standard deviation.

Answer:

  POLYNOMIAL is a 10-letter word

Step-by-step explanation:

A polynomial is such an expression.

Virtually any kind of algebraic expression is made by adding or subtracting terms, grouping them, applying functions to them, or dividing them. (A term is already a product; increasing the number factors doesn't change that.)

A polynomial is a special kind of sum-of-terms expression involving terms that are non-negative integer powers of a variable.

Answer:

  A ≈ 32°

Step-by-step explanation:

You are given two sides and the angle between them, so the law of cosines applies. The measure of side b can be found to be ...

  b² = a² + c² -2ac·cos(B)

  b² = 2² +3² -2·2·3·cos(95°) ≈ 14.0459

  b ≈ 3.74778

Then the law of sines can help you find angle A, the angle opposite the shortest side.

  sin(A)/a = sin(B)/b

  A = arcsin(a/b·sin(B)) = arcsin(2/3.74778·sin(95°)) ≈ 32.11°

  A ≈ 32°

The smallest angle is about 32°.

Answer:

Fixed cost is the weekly cost of the rent payment for the factory i.e. $2,250

Variable cost can be computed as :

Variable cost = Total wages paid + Cost of raw material

Variable cost = (20 workers × 40hrs/week × $15) + ($10/unit × $500 units)

Variable cost = $17,000

∴ The Total Cost is given as:

Total Cost = Fixed Cost + Variable Cost

Total Cost = $2,250 + $17,000 = $19,250

∴ Total variable cost is $17,000; total fixed cost is $2,250; total cost is $19,250

Option (a.) is correct

Answer:

1/11

Step-by-step explanation:

if you solve for the expression, you get .0909090909

if you divide 1 by 11, you get the same answer of .0909090909

Answer:

The minimum number of lenses that Mira must purchase is= 12 packs=600 lenses

Step-by-step explanation:

You know that one Telescope is made for:

2 lenses (they are purchased by packs of 50 (only 25 works for Telescopes)

1 tube (they are purchased by packs of 10)

1 eyepiece (they are purchased by packs of 30)

Then the minimum number of lenses Mira must purchase to make a set of telescopes with no leftover components other than the unusable lenses, should be a whole number that is divisible by 30 and 10.

You can calculate how many packs Mira Needs to purchased in order to find that number.

You Know that 2 lenses are needed for 1 Telescope and that they are purchased by packs of 50 where only 25 works for Telescopes

Then you can express that how:

Number of telescopes Mira can make from Lenses= (50/4)* Number of packages of lenses

Then If Mira purchases:

1 pack of lenses, she can make 12.5 telescopes (it's no divisible by 30 and 10)

2 packs of lenses, she can make 25 telescopes(it's no divisible by 30 and 10)

3 packs of lenses, she can make 37,5 telescopes(it's no divisible by 30 and 10)

4 packs of lenses, she can make 50 telescopes(it's no divisible by 30 and 10)

5 packs of lenses, she can make 62,5 telescopes(it's no divisible by 30 and 10)

6 packs of lenses, she can make 75 telescopes(it's no divisible by 30 and 10)

7 packs of lenses, she can make 87,5 telescopes(it's no divisible by 30 and 10)

8 packs of lenses, she can make 100 telescopes(it's no divisible by 30 and 10)

9 packs of lenses, she can make 112,5 telescopes(it's no divisible by 30 and 10)

10 packs of lenses, she can make 125 telescopes(it's no divisible by 30 and 10)

11 packs of lenses, she can make 137,5 telescopes(it's no divisible by 30 and 10)

12 packs of lenses, she can make 150 telescopes(it's a whole number and is divisible by 30 and 10)

Then she needs to purchase 600 lenses, 5 packs of eyepieces and 15 packs of tubes in order to make 150 Telescopes.

Answer: it's only refracting

E2020

Answer:

> 1

Step-by-step explanation:

A scale factor greater than 1 will produce an enlargement

A scale factor less than 1 will produce a reduction

Since the image is larger than the pre- image the scale factor > 1

Step-by-step explanation:

[tex]\text{A conjugate of}\ a+b\ \text{is}\ a-b.\\\\1)\ \sqrt8-\sqrt9\to\sqrt8+\sqrt9\\\\2)\ 2x^2+\sqrt3\to2x^2-\sqrt3\\\\3)\ a-\sqrt{a-1}\to a+\sqrt{a-1}\\\\4)\ \sqrt{x}+2\sqrt{b}\to\sqrt{x}-2\sqrt{b}[/tex]

Answer:

  3

Step-by-step explanation:

Segment BC corresponds to segment DF. The length of BC is the distance between coordinates (0, 2) and (3, 2). These points are on the same horizontal line (y=2), so the distance between them is the difference of their x-coordinates: 3 - 0 = 3.

Answer:

DF = 3

Step-by-step explanation:

If ABC is equivalent to EDF, then DF is equivalent to BC, which form the following ordered pairs:

D = (0,2)

F = (3,2)

It can be seen that both pairs have the same value of "y" or second value, that is 2.

As a rule, when the points are located on the y-axis (of the ordinates) or on a line parallel to this axis, the distance between the points corresponds to the absolute value of the difference of their ordinates.

So,

DF = D(x) + F(x) = 0 + 3 = 3

If we apply the equation of the distance between two points we get the same result,

[tex]DF=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}   }=\sqrt{(3-0)^{2}+(2-2)^{2}   }=\sqrt{(3)^{2}+(0)^{2}   }=\sqrt{9+0   }=\sqrt{9}=3[/tex]

Hope this helps!

Answer:

GCF of 36x^3 and 48x^4 is 12x³....

Step-by-step explanation:

To find the GCF of 36x3 and 48x4 we have to perform prime factorization of both the terms:

Prime Factorization of 36x³ = 2*2*3*3*3*x*x*x

Prime factorization of 48x^4 = 2*2*2*2*3*x*x*x*x

Thus the common factors are 2*2*3*x*x*x

Therefore GCF of 36x^3 and 48x^4 is 12x³....

Answer:

it is 12x^3

Step-by-step explanation:

Answer:

The inverse is g(x)=-x+5.

Both f and g have domain and range all real numbers.

In interval notation that is [tex](-\infty,\infty)[/tex]

Step-by-step explanation:

f(x)=-x+5 is a linear function.

Since isn't f(x)=constant then it is diagonal so this means the range is all real numbers.

For any linear function, the domain will be all real numbers.  

So to find the inverse of y=-x+5, you interchange x and y and resolve for y.

y=-x+5

(interchange)

x=-y+5

(solve for y)

Subtract 5 on both sides:

x-5=-y

Multiplying both sides by -1:

-x+5=y

So the inverse is g(x)=-x+5. To find find the domain and range of the inverse function given you already did it for the original function, the sets are swapped.  The sets were the same here because they were both all real numbers.

Answer:

Domain of this function become R

Step-by-step explanation:

Answer:

264 transistors.

Step-by-step explanation:

By proportion the total number made if  16 are faulty is (35/2) * 16

=  280.

The number of good ones is 280 - 16

= 264 transistors.

Answer:

264 good ones

Step-by-step explanation:

2 in 35 are faulty = in a batch of 35, 2 will be faulty = there are 33 good for every 2 faulty ones there are

16 faulty have been made - to figure out how many batches there have been do 16/2=8

8 batches of 35, 8 × 35 = 280 total

280 total - 16 faulty = 264 good

OR do 8 batches × 33 good per batch = 264 good

at least thats how i interpreted it!

Answer:

A parameter is a numerical measurement describing data from a population. A statistic is a numerical measurement describing data from a sample

Step-by-step explanation:

In statistics we have to deal with populations and samples to carry out our studies. A population is a large group under consideration and the elements or members of the population have some common features or attributes. For example, all the school going kids in a certain town will be considered a population. Sample on the other hand is a subset(a part) of the population. For example, all school going kids in the town aged 5-6 years will be considered a sample.

The term Parameter and Statistic are very similar as they represent some numeric description. Parameter represents the data of the entire population, while statistic represents that data of a sample. An easy way to remember this is to match the initials i.e. Parameter for Population and Statistic for Sample.

Considering this, we can say the correct answer is:

A parameter is a numerical measurement describing data from a population. A statistic is a numerical measurement describing data from a sample

A parameter is a numerical value describing a characteristic of a population whilst a statistic is a numerical value describing a characteristic of a sample. A population is any whole set, while a sample is a subset of the population.

The primary difference between a parameter and a statistic lies in the data they refer to. A parameter is a numerical measurement that describes a characteristic of a population. A population is the whole set of items or individuals that we are interested in. On the other hand, a statistic is a numerical measurement that describes a characteristic of a sample, where a sample is a subset of the population.

For example, if we were to measure the average height of all adult men in a certain city (the population), the resulting value would be a parameter. If we were to take a sample group of 100 men from that city and measure their average height, the resulting value would be a statistic.

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Ari will think that there is not enough ice cream for the amount of caramel.

3:5 and 6:8 are not equivalent

But let's prove that;

We know that 3 x 2 is 6, so let's multiply 3 x 2 and 5 x 2, when we do so, we get 6:10.

6:10 is greater than 6:8, so there is obviously less ice cream for the amount of caramel.

Step-by-step explanation:

the e standard form of parabola with vertex (h,k) is

y=a(x-h)²+k

here (h,k)=(-3,6)

so the answer to your question is

y=-3(x-(-3))²+6

y=-3(x+3)²+6

Answer:

Option D is correct.

Step-by-step explanation:

The vertex is (-3,6)

We will check which equation satisfies the given vertex.

A) y = -3(x-3)^2 - 6

if x = -3 then value of y should be 6

Checking:

y = -3(-3-3)^2 - 6

y = -3(-6)^2 - 6

y = -3(36) -6

y = -114

if x= -3, y ≠ 6

B) y = -3(x+3)^2 - 6

if x = -3 then value of y should be 6

Checking:

y = -3(-3+3)^2 - 6

y = -3(0)-6

y = -6

if x= -3, y ≠ 6

C) y = -3(x-3)^2 + 6

if x = -3 then value of y should be 6

Checking:

y = -3(-3-3)^2 + 6

y = -3(-6)^2 + 6

y = -3(36) + 6

y = -102

if x= -3, y ≠ 6

D) y = -3(x+3)^2 + 6

if x = -3 then value of y should be 6

Checking:

y = -3(-3+3)^2 + 6

y = -3(0)^2 + 6

y = 6

So, if x= -3, y =6 so, if the vertex of parabola is at (-3,6) the equation will be

y = -3(x+3)^2 + 6

So. Option D is correct.

Answer:

  remaining zeros: negative i comma 5 minus i

Step-by-step explanation:

The remaining two zeros are the conjugates of the two zeros given. That brings the total number to 4 zeros, consistent with the number of zeros expected for a 4th-degree polynomial.

The conjugate of a complex number has the same real part and the opposite imaginary part.

Answer:

-i, 5-i

Step-by-step explanation:

Given that a function f(x) has only real coefficients and also of degree 4.

Since any polynomial with real roots have imaginary roots only with conjugate pairs, we can find other two roots easily

Degree of polynomial = 4

No of roots = 4

GIven roots are i, 5+i

Conjugate of the given roots are -i, 5-i

Hence remaining zeroes of f are -i, 5-i

Answer:

It would take Tom 8 hours alone

Step-by-step explanation:

We are looking at this basic equation:

Tom + Shirley = 8 hours

Tom takes x hours to cut the grass; this means that 1/x of the job gets done in 1 hour

It takes Shirley 3 times as long as Tom, so it takes her 3x hours to cut the grass; this means that 1/3x of the job gets done in 1 hour

If the total number of hours it takes them to do the job is 6 hours; this means that 1/6  of the job gets done in 1 hour

Looking back at the original basic equation, we will fill in our info:

[tex]\frac{1}{x}+\frac{1}{3x}=\frac{1}{6}[/tex]

We can solve for x by first finding the LCD and eliminating the denominators.  The LCD is 6x, since all the denominators go into 6x evenly.

We will multiply the rational equation through by the LCD:

[tex]6x[\frac{1}{x}+\frac{1}{3x}=\frac{1}{6}][/tex]

Dividing each denominator into the LCD gives us:

6 + 2 = x so

x = 8

This means that it takes Tom 8 hours to do the job alone.  It would take Shirley 24 hours alone.  Ugh.

The time it would take Tom to mow the lawn alone is 3 hours

From the information given;

Let Tom's working hours be x.

Let Shirley's working hours be y.

We have  that;

Shirley and Tom work 6 hours together, this is expressed as;

x + y = 6

Given that Shirley work 3 hours alone, we have;

y = 3

Substitute the value of y as 3 in the equation

x + 3 = 6

x = 6 - 3

x = 3

Thus, the time it would take Tom  to mow the lawn alone is 3 hours

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