Find the slope and y-intercept from the graph.

m=________ b=________

(m is slope)
(b is y-intercept)​

Answer:

x=7

Step-by-step explanation:

2x-5(x-3)=2(x-10)

2x-5x+15=2x-20

-3x+15=2x-20

-2x         -2x

-5x+15=-20

      -15   -15

-5x  =-35

-35/-5

x=7

Answer:This can be calculated by the following steps;

Step-by-step explanation:

x=7

Answer:

726

Step-by-step explanation:

39204/54=726

Answer:

I think it is 70.795% decrease

Hope that helps:)

I have a question for u

What is your fav?

Adrinette

LadyNoir

Marichat

Ladrien

The area of the room that is not covered by the rug is: [tex]21x^3+26x^2-24x+9[/tex]

Step-by-step explanation:

Let L be the length of the room

and

W be the width of the room

Then

L = 3x^2

W = 7x+14

Area of the bedroom:

[tex]A_r = L*W\\=3x^2(7x+14)\\=21x^3+42x^2[/tex]

Area of Rug:

Let S be the side of rug

S = 4x+3

[tex]A_{rug} =S^2\\=(4x+3)^2\\=(4x)^2+2(4x)(3)+(3)^2\\=16x^2+24x+9[/tex]

The area of the room that is not covered by the rug will be obtained by subtracting the area of the rug from the area of the room.

So,

[tex]Area\ of\ room\ not\ covered\ by\ rug =A_r - A_{rug}\\= 21x^3+42x^2-(16x^2+24x+9)\\=21x^3+42x^2-16x^2-24x-9\\=21x^3+26x^2-24x+9[/tex]

Hence,

The area of the room that is not covered by the rug is: [tex]21x^3+26x^2-24x+9[/tex]

Keywords: Rectangle, square

Learn more about area at:

#LearnwithBrainly

Explanations and Steps:

How to find the elements:

*Take every element (either one capital letter OR two letters with the first capital and second lowercase)

*Reference the periodic table to find the element name

The number of reactants:

*Reactants are on the left side, what there is before the reaction

*Each reactant is separated by the + sign

*They may be more than one element

The number of products:

*Products are on the right side, what there is after the reaction

*Each product is separated with the + sign

*They may be more than one element

Is it balanced:

Count the number of each element on both sides. It is balanced if both sides have the same number of every element.

*Write out each of the element symbols for each side

*Remember the multiply subscripts (little numbers) by coefficients (big numbers)

Answers:

6.

The elements are:

H - hydrogen

Cl - chlorine

Ca - calcium

O - oxygen

# of reactants: 2

# of products: 2

Is it balanced?

Reactants:

H 4

Cl 2

Ca 1

O 2

Products:

H 2

Cl 2

Ca 1

O 1

It's not balanced because H and O have different numbers of atoms in the reactants and products.

7.

The elements are:

K - potassium

Cl - chlorine

O - oxygen

# of reactants: 1

# of products: 2

Is it balanced?

Reactants:

K 1

Cl 1

O 3

Products:

K 1

Cl 1

O 2

It's not balanced because there are three oxygen atoms for reactants but only two oxygen atoms in the product.

8.

The elements are:

K - potassium

P - phosphorus

O - oxygen

H - hydrogen

Cl - chlorine

# of reactants: 2

# of products: 2

Is it balanced?

Reactants:

K 3

P 1

O 4

H 1

Cl 1

Products:

K 3

P 1

O 4

H 3

Cl 3

It's not balanced because H and Cl have different numbers of atoms.

9.

The elements are:

S - sulphur

O - oxygen

# of reactants: 2

# of products: 1

Is it balanced?

Reactants:

S 2

O 6

Products:

S 2

O 6

It's balanced because both sides have 2 sulphur atoms and six oxygen atoms.

10.

The elements are:

K - potassium

I - iodine

Pb - lead

N - nitrogen

O - oxygen

# of reactants: 2

# of products: 2

Is it balanced?

Reactants:

K 2

I 2

Pb 1

N 2

O 6

Products:

K 1

I 2

Pb 1

N 1

O 3

It's not balanced because K, N and O have different numbers of atoms.

Answer:

33, 72, and 24

Step-by-step explanation:

Let's the three numbers are x, y, and z.

x + y + z = 129

z = x − 9

y = 3z

Solve the system of equations.  Using substitution:

y = 3(x − 9)

y = 3x −27

x + (3x − 27) + (x − 9) = 129

5x − 36 = 129

5x = 165

x = 33

y = 3x − 27

y = 72

z = x −9

z = 24

Answer:

68,144

The drawing will help

Answer:

The algebraic equation for the line whose slope is m = 1 and passes through point (3 , 3) is y = x

Step-by-step explanation:

The algebraic equation of a line whose slope is m and passes

through point [tex](x_{1},y_{1})[/tex] is

∵ The slope of the line is m = 1

∵ The line passes through point (3 , 3)

∴ [tex]x_{1}[/tex] = 3

∴ [tex]y_{1}[/tex] = 3

- Substitute these values in the form of the equation

∵ [tex]y-y_{1}=m(x-x_{1})[/tex]

∴ y - 3 = (1)(x - 3)

- Simplify it

∴ y - 3 = x - 3

- Add 3 to both sides

∴ y = x

The algebraic equation for the line whose slope is m = 1 and passes through point (3 , 3) is y = x

Learn more:

You can learn more about the linear equation in brainly.com/question/3965451

#LearnwithBrainly

Answer:

The first option i.e. (8 in × 10 in × 10 in) will be our choice.

Step-by-step explanation:

Each of the cartons shown here has the same volume i.e. 800 cubic inches.

Therefore, the carton having the least surface area will require the least amount of cardboard for each cubic inch of volume.

2(LW + WH + LH) is the surface area of a cuboid with dimensions L × W × H.  

Now, in the first option of cardboard with dimension 8 in × 10 in × 10 in, will have surface are = 2(8 × 10 + 10 × 10 + 8 × 10) = 520 sq, inches.

Now, in the second option of cardboard with dimension 5 in × 8 in × 20 in, will have surface are = 2(5 × 8 + 8 × 20 + 5 × 20) = 600 sq, inches.

Again, in the third option of cardboard with dimension 4 in × 10 in × 20 in, will have surface are = 2(4 × 10 + 10 × 20 + 4 × 20) = 640 sq, inches.

Finally, in the fourth option of cardboard with dimension 2 in × 10 in × 40 in, will have surface are = 2(2× 10 + 10 × 40 + 2 × 40) = 1000 sq, inches.

Hence, the first option will be our choice. (Answer)

Answer:

10 yards 2 inches

Step-by-step explanation:

To get the answer, you must subtract the amount of the smaller whale from the larger one:

Gray whale. 15 yards 5 inches

beluga whale. - 5 yards 3 inches

= 10 yards 2 inches

Answer:   53   -10      -50

Step-by-step explanation:

50 + 3 = 53     50 - 60 = -10     50 - 100 = -50

[tex]3[/tex] increased by [tex]50[/tex] is equal to [tex]53[/tex].

[tex]3[/tex] decreased by [tex]60[/tex] is equal to [tex]-57[/tex].

[tex]3[/tex] decreased by [tex]100[/tex] is equal to [tex]-97[/tex].

To increase a number [tex]a[/tex] by [tex]b[/tex] means to add [tex]a[/tex] to [tex]b[/tex]. Increase is denotes by sign [tex]+[/tex]

To decrease a number [tex]a[/tex] by [tex]b[/tex] means to subtract [tex]b[/tex] from [tex]a[/tex]. Decrease is denoted by sign [tex]-[/tex]

[tex]3[/tex] increased by [tex]50[/tex] is equal to [tex]\boldsymbol{3+50}[/tex] which is equal to [tex]53[/tex].

[tex]3[/tex] decreased by [tex]60[/tex] is equal to [tex]\boldsymbol{3-60}[/tex] which is equal to [tex]-57[/tex].

[tex]3[/tex] decreased by [tex]100[/tex] is equal to [tex]\boldsymbol{3-100}[/tex] which is equal to [tex]-97[/tex].

For more information:

https://brainly.com/question/12361020?referrer=searchResults

Answer:

We have to choose any one from option B and option C

Step-by-step explanation:

We have to perform a subtraction of two decimal numbers.

(9.43 - 4.286) = (9.430 - 4.286) = 5.144.

Hence, the answer is 5.144 which is given both options B and C.  

In case there are two options with the same value and the value is the answer, then you choose any one of them but not both.

Here in our case, we have to choose any one from option B and option C and we will be rewarded full marks. (Answer)

Answer:

y=8/13, 10/13=x

Step-by-step explanation:

-2y = x-2, so 2y = -x+2. y = -1/2x+1, and we plug this in -4x+3y to get

-4x-1.5x+3=x-2

-5.5x+3=x-2,

-6.5x=-5

13x=10

x=10/13.

for y we plug the x in to get -40/13=-5y

40/13=5y

y=8/13

Answer:

x = -2/7

y = 8/7

Step-by-step explanation:

1) Since the equations at the end are both equivalent to -2y:

-4x + 3y = -2y

x - 2 = -2y

2) We want to get y by itself:

-4x + 3y = -2y --> -4x = y

x - 2 = -2y --> -x/2 + 1 = y

3) Since both are equal to y, we can solve for x; set the equations equal to each other, then combine like terms via adding/subtracting/dividing/multiplying (in accordance to PEMDAS):

(-2) (-4x) = (-x/2 + 1) (-2)

8x = x - 2

(8x) -x = (x - 2) -x

7x = -2

(7x) / 7 = (-2) / 7

x = -2/7

4) Now that we know what x equals, substitute x with -2/7 in one of the initial equations:

x - 2 = -2y

-2/7 - 2 = -2y

5) Then, combine like terms via adding/subtracting/dividing/multiplying (in accordance to PEMDAS); then, simplify to get what y equals:

(-2/7 - 2) (-7) = (-2y) (-7)

2 + 14 = 14y

16 = 14y

(16) / 14 = (14y) / 14

16/14 = y

6) Simplify (reduce):

8/7 = y

7) Your final answer is:

x = -2/7, y = 8/7

Answer:

11 Test Packets

Step-by-step explanation:

151-30=121/11=11

The teacher purchased 11 packets of tests for the math competition.

The question is about calculating the number of test packets Andrew's teacher purchased for the math competition. We know that there was a basic enrollment fee of $30, and each packet of 10 tests cost an additional $11. The total cost was $151. To find out how many test packets the teacher purchased, the first step is to subtract the enrollment fee from the total amount spent. Therefore, $151 - $30 = $121 was spent on test packets.

Then, we divide this amount by the cost of each test packet. So $121/$11 gives us 11. Hence, the teacher purchased 11 packets of tests for Andrew's math competition.

https://brainly.com/question/31160285

#SPJ3

Answer:

  y = 18

Step-by-step explanation:

Direct variation means y varies by the same factor x does. Here, x has changed by a factor of -6, so the new value of y is ...

  y = (-6)(-3) = 18

If y varies directly with x, and y = -3 when x = 1, the value of y when x = -6 is found using the formula y = kx. The value of y when x = -6 is 18.

In mathematics, if y varies directly with x, it means y = kx for some constant k. To find k, we substitute the given values of x and y into the equation, so -3 = k(1) gives k = -3.

Now that we have the value of k, we can find the value of y when x = -6. Substituting these values into our equation y = kx, we get y = -3*(-6), which simplifies to y = 18.

So when x = -6 and y varies directly with x, the value of y is 18.

https://brainly.com/question/34355670

#SPJ2

Answer:

[tex]\large\boxed{\dfrac{65y^3+15y^2-25y}{5y}=13y^2+3y-5}[/tex]

Step-by-step explanation:

[tex]\dfrac{65y^3+15y^2-25y}{5y}=\dfrac{65y^3}{5y}+\dfrac{15y^2}{5y}-\dfrac{25y}{5y}\\\\=13y^2+3y-5[/tex]

Answer:

19 dimes and 9 nickels

Step-by-step explanation:

Model the situation using two equations, then solve the system.

let n be number of nickels and d be number of dimes.

n + d = 28     <= This equation is about the number of coins.

0.05n + 0.10d =  2.35   <=This equation is about the worth in dollars.

Rearrange n + d = 28.

n = 28 - d

Now we can substitute this equation into the other one.

Sub n =28-d at the "d" variable for the equation 0.05n + 0.10d =  2.35

0.05n + 0.10d =  2.35

Now there is only one variable.

0.05(28 - d) + 0.10d =  2.35   <=distribute this

0.05(28 - d) + 0.10d =  2.35

1.4 - 0.05d + 0.10d = 2.35   <=combine like terms

1.4 + 0.05d = 2.35    <= begin to isolate d

0.05d = 2.35 - 1.4

0.05d = 0.95

d = 0.95/0.05

d = 19

Now that we know d=19, we can substitute it into any equation.

Choose the equation n + d = 28 because the numbers are easier.

n + d = 28

n + 19 = 28    <=isolate n

n = 28 - 19

n = 9

Since n=9 and d=19, Kay has 9 nickels and 19 dimes.

Hey! How are you? My name is Maria, 19 years old. Yesterday broke up with a guy, looking for casual sex.

Write me here and I will give you my phone number - *pofsex.com*

My nickname - Lovely

Answer:

height is 21cm and the base is 14cm

Step-by-step explanation:

Take a look at the equation for the area of a triangle [tex]A = \frac{bh}{2}[/tex]

Write "height of a triangle is 7 cm greater than the base" as an equation:

h = b + 7

Substitute h and the area of the triangle, 147 into the equation for area.

[tex]A = \frac{bh}{2}[/tex]

[tex]147 = \frac{b(b+7)}{2}[/tex] distribute over brackets

[tex]147 = \frac{b²+7b)}{2}[/tex]  get rid of fractions

[tex]147*2 = b²+7b[/tex]

[tex]294 = b²+7b[/tex]

Rearrange to standard for for quadratic equations

0 = b²+7b - 294

standard form is 0 = ax² + bx + c

In this base, the x variable is replaced by "b".

Use the quadratic formula to solve for b. Substitute the other three values.

[tex]x = \frac{-b ±\sqrt{b^{2}-4ac} }{2a}[/tex]

[tex]x = \frac{-(7) ±\sqrt{7^{2}-4(1)(-294)} }{2(1)}[/tex] Simplify

[tex]x = \frac{-7 ±\sqrt{1225} }{2}[/tex]

[tex]x = \frac{-7 ±35 }{2}[/tex]

Split the equation at ±

[tex]x = \frac{-7 +35 }{2}[/tex]

[tex]x = \frac{28}{2}[/tex]

[tex]x = 14[/tex]  <=base

[tex]x = \frac{-7 -35 }{2}[/tex]

[tex]x = \frac{-42}{2}[/tex]

[tex]x = -21[/tex]  <=We know this number is not possible, so its inadmissible.

The base is 14 cm.

Substitute base = 14 in h = b + 7

h = b + 7

h = 14 + 7

h = 21

The height is 21cm.

Therefore, the height is 21cm and the base is 14cm.

Answer:

53/3

Step-by-step explanation:

1 5/6=11/6

3 1/6=19/6

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

11/6+5(19/6)=11/6+95/6=106/6

simplify

53/3

Answer:

The slope is 1

Step-by-step explanation:

Answer:2 hrs

Step-by-step explanation:

x+2x+3x=12

6x=12

x=2

Answer:

Length of the garden = 69.28 meters.

Step-by-step explanation:

See the attached diagram.

Let CD is the pole with a height of 30 m and the elevation of the top of the pole from the endpoints of the length A and B are 60° and 30° respectively.

So, ∠ DAC = 60° and ∠ DBC = 30°  

Now, Δ ACD is a right triangle and [tex]\tan 60 = \frac{CD}{AC}[/tex]

⇒ [tex]AC = \frac{CD}{\tan 60} = \frac{30}{\tan 60} = 17.32[/tex] meters.

Now, from Δ BCD which is a right triangle, [tex]\tan 30 = \frac{CD}{CB}[/tex]

⇒ [tex]CB = \frac{30}{\tan 30} = 51.96[/tex] meters.

Hence, AB = AC + CB = 17.32 + 51.96 = 69.28 meters. (Answer)

Answer:

The length of the rectangle garden is 20 [tex]\sqrt{3}[/tex] i.e 34.64 meters .

Step-by-step explanation:

Given as :

The height of the pole = H = 30 m

The two angles of elevation as 60° and 30°

Let The length of the rectangle garden = L m

Now, From figure

The measure from pole ground to first elevation 60° = x m

The measure from pole ground to second elevation 30° = (L + x ) m

Now, from triangle BOC

Tan Ф = [tex]\dfrac{\textrm perpendicular}{\textrm base}[/tex]

I.e Tan 60° = [tex]\dfrac{\textrm 30}{\textrm x}[/tex]

Or, [tex]\sqrt{3}[/tex] = [tex]\dfrac{\textrm 30}{\textrm x}[/tex]

or, x = [tex]\frac{30}{\sqrt{3} }[/tex]

I.e x = 10[tex]\sqrt{3}[/tex] meter      ...1

Again From triangle BAC

Tan Ф = [tex]\dfrac{\textrm perpendicular}{\textrm base}[/tex]

I.e Tan 30° = [tex]\dfrac{\textrm 30}{\textrm L + x}[/tex]

Or, [tex]\frac{1}{\sqrt{3} }[/tex] = [tex]\dfrac{\textrm 30}{\textrm L + x}[/tex]

Or, L + x = 30 × [tex]\sqrt{3}[/tex]   ....2

Put the value of x from  1 into 2

i.e L + 10[tex]\sqrt{3}[/tex] meter   = 30 × [tex]\sqrt{3}[/tex]

or, L = 30 [tex]\sqrt{3}[/tex] - 10 [tex]\sqrt{3}[/tex]  

Or, L = 20 [tex]\sqrt{3}[/tex] = 34.64 meters

I.e length of garden is 20 [tex]\sqrt{3}[/tex]

Hence The length of the rectangle garden is 20 [tex]\sqrt{3}[/tex] i.e 34.64 meters . answer

Answer:

[tex]g(x)=1.5^{x}-4[/tex]

Step-by-step explanation:

Given:

The parent function is given as:

[tex]f(x)=1.5^{x}[/tex]

Let us consider a point on [tex]f(x)\ and\ g(x)[/tex] and compare their transformation.

The easiest point to consider is the y-intercept. At the y-intercept, the value of 'x' is 0.

The y-intercept of the function [tex]f(x)[/tex] is for [tex]x=0[/tex]. So,

[tex]f(0)=1.5^{0}=1[/tex]

The y-intercept of [tex]f(x)[/tex] is the point (0, 1).

Now, as per question, the transformed function [tex]g(x)[/tex] passes through the point (0, -3). Therefore,

The function [tex]g(x)[/tex] in the graph has the y-intercept equal to -3  as at y-intercept, the 'x' value is 0.

Therefore, the y-intercept of [tex]g(x)[/tex] is the point (0,-3).

Now, consider the transformation for the points (0, 1) and (0, -3).

[tex](0,1)\rightarrow (0,-3)[/tex]

Here, the 'x' value remains the same but the 'y' values decreases by 4 units. So, the rule will be:

[tex](x,y)\rightarrow (x,y-4)[/tex]

As per translation rules, if C units is added to 'y' value, then the graph moves up if 'C' is positive and moves down if 'C' is negative.

Also, the equation is of the form: [tex]g(x)=f(x)+C[/tex]

Here, [tex]C=-4[/tex].

Therefore, the graph shifts down by 4 units.

The equation of the function [tex]g(x)[/tex] is given as:

[tex]g(x)=f(x)+C=1.5^{x}-4[/tex]

Answer:

D

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

Answer:

Set C

Step-by-step explanation:

12/4=3

24/4=6, not 4

this shows it is not proportional

Answer:

The measure of angle G is [tex]53\°[/tex]

Step-by-step explanation:

Let

F ----> the measure of interior angle F of the triangle FGH

G ---> the measure of interior angle G of the triangle FGH

H ---> the measure of interior angle H of the triangle FGH

we know that

The sum of the interior angles in a triangle must be equal to 180 degrees

so

[tex]F+G+H=180\°[/tex] ----> equation A

[tex]G=2F-5[/tex] ----> equation B

[tex]H=4F-18[/tex] ----> equation C

Solve the system of equations by substitution

substitute equation B and equation C in equation A

[tex]F\°+(2F-5)\°+(4F-18)\°=180\°[/tex]

Solve for F

[tex]7F-23=180[/tex]

[tex]7F=180+23[/tex]

[tex]F=29\°[/tex]

Find the measure of angle G

[tex]G=2F-5[/tex]

substitute the value of F

[tex]G=2(29)-5=53\°[/tex]

The measure of angle G in triangle FGH is [tex]\( 53^\circ \).[/tex]

1. Define Variables:

  - Let the measure of angle F be [tex]\( x \).[/tex]

  - The measure of angle G is given as "five less than twice the measure of angle F," so [tex]\( G = 2x - 5 \)[/tex].

  - The measure of angle H is given as "eighteen less than four times the measure of angle F," so [tex]\( H = 4x - 18 \).[/tex]

2. Use the Triangle Angle Sum Property:

  - The sum of the angles in a triangle is always [tex]\( 180^\circ \)[/tex]. Therefore:

  [tex]\[ F + G + H = 180^\circ \][/tex]

3. Substitute the Expressions:

  - Substitute F = x , G = 2x - 5 , and  H = 4x - 18  into the equation:

  x + (2x - 5) + (4x - 18) = 180

4. Combine Like Terms:

  x + 2x - 5 + 4x - 18 = 180

  7x - 23 = 180

5. Solve for x :

  - Add 23 to both sides of the equation:

  7x = 203

  - Divide by 7:

  x = 29

6. Calculate the Measure of Angle G:

  - Use the expression G = 2x - 5 :

  G = 2(29) - 5 = 58 - 5 = 53°

7. Verify the Measures:

  - Calculate F  and H  using x = 29 :

  F = 29°

  H = 4(29) - 18 = 116 - 18 = 98°

  - Check the sum:

  F + G + H = 29 + 53 + 98 = 180°

  The sum is correct, confirming the calculations.

Thus, the measure of angle G in triangle FGH is [tex]\( 53^\circ \).[/tex]

Answer:

The answer is given below.

Step-by-step explanation:

Alternate exterior angles: I is a pair of angles on the outer side of the each of two parallel lines but on opposite side of the transversal.

Vertically opposite angles: They are angles opposite each other when two lines intersect each other or cross each other.

Corresponding angles:  The angles which occupy the same relative position at each intersection where a transversal intersect the two parallel lines.

Same side interior angles: These are the angles between the parallel lines with the transversal.

Alternate interior angles: These are those angles that are alternate to each other and lie inside the parallel lines forming in Z shape.

Linear pair angles: It is a pair of adjacent angles formed by two intersecting lines

[tex]\angle 1\ and\ \angle 6:\ \textrm{alternate exterior angles}\\\angle 1\ and\ \angle 3:\ \textrm{Vertical opposite angles}\\\angle 3\ and\ \angle 6:\ \textrm{corresponding angles}\\\angle 4\ and\ \angle 8:\ \textrm{same side interior angles}\\\angle 4\ and\ \angle 5:\ \textrm{alternate interior angles}\\\angle 5\ and\ \angle 6:\ \textrm{linear pair angles}[/tex]

Answer:

A

Step-by-step explanation:

A

Answer:

you mean

[tex] - 7.2[/tex]

?

if so, then,

[tex] - 7.2 = - \frac{72}{10} [/tex]

[tex] - \frac{36}{5} [/tex]

...

Check the picture below.

Answer:

5

Step-by-step explanation:

100 books, half of them are fiction. So 50 of them are fiction. There are 50 books remaining. 10% of them are animal books. What is 10% of 50?

Convert 10% to a decimal: .10

Multiply .10 by 50

.10×50=5

5 books are animal books.

The classroom library contains 5 animal books.

The percentage is defined as a ratio expressed as a fraction of 100.

Arithmetic operations can also be specified by adding, subtracting, dividing, and multiplying built-in functions.

The operator that performs the arithmetic operations is called arithmetic operators.

* Multiplication operation: Multiplies values on either side of the operator

For example 4*2 = 8

/ Division operation: Divides left-hand operand by right-hand operand

For example 4/2 = 2

Given that the classroom library has 100 books.

And half of the books are fiction.

There are 50 books remaining and a tenth is about animals

So 10% of them are animal books.

To calculate 10% of 50 :

⇒ 10% of 50

⇒ 10%(50)

Convert 10% to a decimal,

⇒ 0.10×(50)

Multiply 0.10 by 50

⇒ 5

Hence, the classroom library contains 5 animal books.

Learn more about Arithmetic operations here:

brainly.com/question/25834626

#SPJ2

Billy ate 1/6, Bob ate 1/4, and Buck ate 5/12 of the candies. To find the number of candies left, subtract the total fraction eaten from the total.

To find out how many candies were left, we need to subtract the candies that Billy, Bob, and Buck ate from the total number of candies in the bowl.

Billy ate 2/12 of the candies, which is equivalent to 1/6 of the candies because 2/12 can be simplified to 1/6.

Bob ate 3/12 of the candies, which is equivalent to 1/4 of the candies because 3/12 can be simplified to 1/4.

Buck ate 5/12 of the candies.

To find the total fraction of candies eaten, we add the fractions: 1/6 + 1/4 + 5/12. The common denominator for these fractions is 12.

Converting all the fractions to have a denominator of 12, we have: 2/12 + 3/12 + 5/12 = 10/12 = 5/6.

So, the three boys ate 5/6 of the candies.

To find the number of candies left, we subtract 5/6 from the total number of candies in the bowl:

120 - (5/6 * 120) = 120 - (5/6 * 120/1) = 120 - (5 * 120/6) = 120 - 100 = 20.

Therefore, there are 20 candies left in the bowl.