Which is a reasonable first step that can be used to solve the equation 2 (x + 6) = 3 (x minus 4) + 5?

Answer: 1.   1,906,500

 2.   840

Step-by-step explanation:

1. Given: There are 125 juniors at the high school.

Total positions = 3    [president,vice president, and secretary]

Then, Number of ways to elect a  president,vice president, and secretary( which is in order) out of  125 juniors = [tex]^{125}P_{3}=\dfrac{125!}{(125-3)!}[/tex]  [Using permutations]

[tex]=\dfrac{125!}{122!}\\\\=\dfrac{125\times124\times123\times122!!}{122!}\\\\=125\times124\times123\\\\=1906500[/tex]

Hence, Required ways =1906500

(2) Given word : "RHOMBUS"

Total letters= 7

By permutation, the umber of 4-letter arrangements = [tex]^7P_4=\dfrac{7!}{(7-4)!}=\dfrac{7!}{3!}[/tex]

[tex]=\dfrac{7\times6\times5\times4\times3!}{3!}\\\\= 7\times6\times5\times4\\\\=840[/tex]

Hence, required ways = 840

Answer:

1) The number of ways = 1906500.

2) The number of ways = 840.

1) President, vice president, and secretary are 3 different positions.

There are total 125 students.

So we can select them in [tex]125P3=\frac{125!}{\left(125-3\right)!}=1906500[/tex] ways.

2) There are total 7 different letters in RHOMBUS.

We can select 4 different letters from 7 letters in [tex]7P4=\frac{7!}{\left(7-4\right)!}=840[/tex].

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Answer:

2.793109

Step-by-step explanation:

Answer:

-8

Step-by-step explanation:

3+(−4)−8−(−1)=-8

Answer:

10

Step-by-step explanation:

When we simplify we get [tex]$$z(6xy+21x+2y+7)+30xy+105x+10y=812.$$[/tex]

Then we continue to factor to get: [tex](z+5)(6xy+21x+2y+7)&=847.[/tex]

We then see that we can factor [tex](6xy+21x+2y+7)[/tex] into [tex](z+5)(3x+1)(2y+7)&=847.[/tex]

we then do the prime factorization of 847, which i think is,  [tex]7*11*11[/tex]. we have to find the numbers that multiply to 847 and then plug them into z+5, 3x=1,2y+7.

It has to be a positive, non-negative integer, right?

We also see that 3x+1=11 so we see that x=10/3 (which wont work).

So 3x+1=7, so x=2.

So 11 has to be in another term. It has to be in 2y+7=11 so y=2

for the last term we get z+5=11 so z=6

2+2+6=10

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The value of x+y+z is 8.83.

Given equation,

[tex]6xyz+30xy+21xz+2yz+105x+10y+7z=812[/tex].

We have to calculate the value of [tex]x+y+z\\[/tex].

Here,

[tex]6xyz+30xy+21xz+2yz+105x+10y+7z=812[/tex]

Adding 35 both sides, we get

[tex]6xyz+21xz+2yz+7z+30xy+105x+10y+35=812+35\\[/tex]

Taking z common we get,

[tex]z(6xy+21x+2y+7)+30xy+105x+10y+35=847[/tex]

On further simplifying, we get

[tex](z+5)(6xy+21x+2y+7+6xy+21x+2y+7)=847[/tex]

[tex](z+5)(12xy+42x+4y+14)=847[/tex]

[tex](z+5)[6x(2y+7)+2(2y+7)]=847[/tex]

[tex](z+5)(2y+7)(6x+2)=847[/tex]

Now the prime factorization of 847 is [tex]11\times11\times7.[/tex]

So,

[tex](z+5)(2y+7)(6x+2)=11\times11\times7[/tex]

Here if [tex]z+5=11\\[/tex]

[tex]z=6[/tex]

And if [tex]2y+7=11\\[/tex]

[tex]2y=4\\y=2[/tex]

Again,

[tex]6x+2=7\\x=\frac{5}{6}[/tex]

Now,

[tex]x+y+z=\frac{5}{6} +2+6[/tex]

[tex]x+y+z=0.83+8\\x+y+z=8.83[/tex]

Hence the value of x+y+z is 8.83.

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Answer:

I'll say x = 8

Step-by-step explanation:

because Simplifying

2x + -3 = 3x + -11

Reorder the terms:

-3 + 2x = 3x + -11

Reorder the terms:

-3 + 2x = -11 + 3x

Solving

-3 + 2x = -11 + 3x

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-3x' to each side of the equation.

-3 + 2x + -3x = -11 + 3x + -3x

Combine like terms: 2x + -3x = -1x

-3 + -1x = -11 + 3x + -3x

Combine like terms: 3x + -3x = 0

-3 + -1x = -11 + 0

-3 + -1x = -11

Add '3' to each side of the equation.

-3 + 3 + -1x = -11 + 3

Combine like terms: -3 + 3 = 0

0 + -1x = -11 + 3

-1x = -11 + 3

Combine like terms: -11 + 3 = -8

-1x = -8

Divide each side by '-1'.

x = 8

Answer:

[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{ - 4x - 14}}}}}[/tex]

Step-by-step explanation:

[tex] \sf{2x - x - (2x + 3) - 3x - 11}[/tex]

When there is a ( - ) in front of parentheses in an expression, change the sign of each term

⇒[tex] \sf{2x - x - 2x - 3 - 3x - 11}[/tex]

Collect like terms

⇒[tex] \sf{2x - x - 2x - 3x - 3 - 11}[/tex]

Since the terms having opposite signs adds up to zero, remove them from the expression

⇒[tex] \sf{ - x - 3x - 3 - 11}[/tex]

⇒[tex] \sf {- 4x - 14}[/tex]

Hope I helped!

Best regards!!

The correct answer is A. 1.5 cups

Explanation:

The total of polishing wooden furniture is equivalent to the total of olive oil plus the total of lemon juice. Additionally, in this case, the result should be given in cups. First, let's consider the values given.

50% of a cup of lemon juice + 25% of a quart with olive oil

The first quantity 50% of a cup of lemon indicates half cup of lemon was added, which is equivalent to 0.5 cups as 1 cup = 100% of a cup and 50% is the half.

Now, the second quantity is provided in quarts, which is not the same as a cup. Indeed 1 quart is equivalent to 4 cups, which represents 100%. This means 100% = 4 cups. Now, to calculate the 25% follow this procedure.

1. Write the values

4  =  100 (total  percentage)

x =    25 (percentage to be calculated

2. Solve this by using cross multiplication

x100 = 4 × 25

x100 = 100

x = 100 ÷ 100

x = 1 (cups in 25%)

This means 1 cup of olive oil was added and this plus 0.5 cup of lemon juice is equivalent to 1.5 cups of solution.

Answer:

Step-by-step explanation:

Given that

Algebra book=1  

Geometry book=1

Chemistry book= 1

English book= 1

Health book= 1

Total number of books N = (1+1+1+1+1)= 5

      Permutation is used to  determines the number of possible arrangements in a set when the order of the arrangements is crucial.

Number of arrangements = N!

Number of arrangements= 5*4*3*2*1=  120

Answer:

-9

Step-by-step explanation:

add x and y to the equation.

so now its -3(2+1)

add 2 and 1

now its -3(3)

multiply.

now its -9

Answer:

-9

Step-by-step explanation:

Hello!

It is asking us for the answer when x = -3 and y = 2 so we put in those values for x and y

-3(2 + 1)

Now follow PEMDAS

-3(3) = -9

The answer is -9

Hope this helps!

Answer:

C. Construction X because point C is the incenter of triangle LMN.

Step-by-step explanation:

The construction requires that the school must be at equal distance to cities of the triangle town. Thus, it must be located at the point of intersection of the straight path from the three cities L, M, and N.

To be able to construct the school with the specification, option C is the most suitable. Construction X describe the appropriate method because point C is the incenter of triangle town of cities L, M, and N.

Answer:

A

Step-by-step explanation:

Construction Y because point E is the circumcenter of Triangle LMN

Answer:

circumference= 40.82 cm

Step-by-step explanation:

formula circumference= 2 x pi x radius ( 2 x 3.14x 6.5)

3) shaded region =  area circle - area rectangle = 132.665 cm - 60 cm^2= 72.665 cm^2

4) 1 foot = 30.48 cm,  6 feet = 182.88 cm  = radius 182.88 cm  area circle =  pi x square radius  = 3.14 x  182.88 ^2  ---------->  3.14 x 33445.0944  =105017.5964 cm^2  

if 5.49 = 70%   , 100% = x     so 5.49 x 100 divided 70 = X  so X = 7.844      then 5.49 is the 70 % of 7.844

if 6.99 is 36% of something,  6.99   =      36%

                                                     X    =    100%    

                                               so 6.99 x 100 = X (equis) x 36%

6.99 x 100 / 36 = X, so X = 19.416   .    6.99 is the 36% of 19.416

Answer:

6x9=54

Step-by-step explanation:

6 folders with 9 photos in each = 54 photos all together.

Answer:

48 square units

Step-by-step explanation:

Let the length of the rectangle be x units.

By Pythagoras theorem:

[tex]x = \sqrt{ {10}^{2} - {6}^{2} } \\ x = \sqrt{ 100 - 36 } \\ x = \sqrt{64} \\ x = 8 \: units \\ [/tex]

Length of rectangle = 8 units

Area of rectangle

= Length * width

= 8 * 6

= 48 square units

Answer:

The correct option is c) $17.50/case.

Step-by-step explanation:

Note: The data in the question are merged. The data are therefore sorted and the whole question is represented before answering the question. Please, see the attached pdf file for the sorted data and the represented question.

The explanation of the answer is now given as follows:

Marginal cost refers to the cost incurred in order to produce one more unit of a product.

Therefore, marginal cost is the change in the total cost that is caused by a one-unit increase in the quantity of a commodity that is produced.

From the table in the question, the marginal cost at q = 108 can be calculated as follows:

Change in total quantity at 180 cases = 108 - Number of cases immediately before 108 = 180 - 104 = 4

Change in total cost at 180 cases = Total cost at 108 cases - Total cost immediately before 108 cases = 1990 - 1920 = 70

Marginal cost at 108 cases = Change in total cost at 180 cases / Change in total quantity at 180 cases = 70 / 4 = 17.50 per case

Therefore, the correct option is c) $17.50/case.

Answer:

[tex]w=-8[/tex]

Step-by-step explanation:

So we have the equation:

[tex]-6=2(w+5)[/tex]

First, distribute the right side:

[tex]-6=2(w)+2(5)\\-6=2w+10[/tex]

Subtract 10 from both sides. The right cancels:

[tex](-6)-10=(2w+10)-10\\-16=2w[/tex]

Divide both sides by 2. The right cancels:

[tex](-16)/2=(2w)/2\\-8=w[/tex]

Flip:

[tex]w=-8[/tex]

Thus, the value of w is -8.

Answer:

-8 = w

Step-by-step explanation:

-6= 2(w + 5)

Divide each side by 2

-6/2= 2/2(w + 5)

-3 = w+5

Subtract 5 from each side

-3-5 = w+5-5

-8 = w

Answer:

A) 41 degrees

Step-by-step explanation:

A) SohCahToa

20 = hyp.

15 = adj.

therefore, use Cos (Cah).

cos x = 15/20

x= cos^-1 (15/20)

x= 41 degrees

The required values are shown below.

A right-angled triangle is a triangle, that has one of its interior angles equal to 90 degrees or any angle is a right angle.

Since, All the triangle are right angle triangle.

Use right angle properties,

(a)

To find the value of θ,

Use cos θ = base/hypotenuse = 15 / 20 = 3/4

cos θ  = 3/4

θ  = cos⁻¹ (3/4)

θ  = 41.41

The value of θ  is 41.41°.

(b)

Use sin θ  = 3/10 =

θ   = 17.45

The value of θ is 17.45.

(c)

Use Pythagorean theorem,

x² + x² = 5²

2x² = 25

x² = 25/2

x = 5/√2

(d)

sin30 = x / 8

1/2 = x/8

x = 4

cos 30 = y / 8

√3 / 2 = y/8

y = 4√3

The values of x and y are 4 and 4√3 respectively.

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Answer:

54

Step-by-step explanation:

angle A+angle B+Angle C =180 degree [ angle sum property of a triangle]

36 +90 + angle B =180 degree

126 +angle B =180 degree

angle B= 180-126

54 degree

Ans

Answer:

Area = 3097.96[tex]m^{2}[/tex]

Perimeter = 270.96m

Step-by-step explanation:

Step 1: State the shapes making up the indoor sports exhibiti[tex]\pi[/tex]on

2 rectangles

1 semi circle

Step 2: Find the area and perimeter of the shapes

ARectangle1 = lw = (10)(40) = 400m^2

PRectangel1 = 2l + w = 2(10) + 40 = 60m

ARectangle2 = lw = (33)(68) = 2244m^2

PRectangel2 = l + w = 33 + 68 = 101m

ASemiCicle = [tex]\frac{\pi r^{2}}{2} =\frac{\pi 17^{2} }{2} =\frac{289\pi }{2}=144.5\pi=453.96m^{2}[/tex]

PSemiCircle = [tex]2\pi r=2\pi(17)=35\pi =109.96m[/tex]

Step 3: Add up the areas and perimeters

Area = 400 + 2244 + 453.96

Area = 3097.96[tex]m^{2}[/tex]

Perimeter = 60 + 101 + 109.96

Perimeter = 270.96m

Therefore the area of the indoor sports exhibition is 3097.96[tex]m^{2}[/tex] and the perimeter is 270.96 m

Answer:

-15.1

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]-x+(-8) \\\\x = 7.1[/tex]

Substitute 7.1 for x in the given equation

[tex]-(7.1 )+(-8)[/tex]

Remove parentheses (a)=a

[tex]=-7.1-8[/tex]

Subtract the numbers: -7.1-8=-15.1

[tex]-15.1[/tex]

Answer:

49 children

Step-by-step explanation:

Adult : Child = 2 : 7

Adult = 14

2 = 14

So, 1 = 14/2 = 1 = 7 in the ratio.

So, 7 x 7 = 49 children are there.

Answer:

49

Step-by-step explanation:

Let's set up a proportion!

2         14

--         --

7          x

Now, we cross multiply

14 times 7 = 98

2 times x = 2x

98 = 2x

98 divided by 2 equals 49

Answer:

  A  The amount of money the school charges for all n tickets

Step-by-step explanation:

The number 6 in the term 6n is the "marginal" profit, the additional profit earned from the sale of 1 more ticket. Then 6n represents the revenue from the sale of all n tickets.

Answer:

Kayla's reasoning is not correct.

Step-by-step explanation:

The locker problem is as follows:

Imagine you are at a school that has student lockers. There are 200 lockers, all shut and unlocked, and 200 students. Suppose the first student goes along the row and opens every locker. The second student then goes along and shuts every other locker beginning with number 2. The third student changes the state of every third locker beginning with number 3. (If the locker is open the student shuts it, and if the locker is closed the student opens it). The fourth student changes the state of every fourth locker beginning with number 4. Imagine that this continues until the 200 students have followed the pattern with the 200 lockers. At the end, which lockers will be open and which will be closed? Why?

Solution:

So from the information we know that the first student goes along the row and opens every locker.

Then the second student shuts every other locker, i.e. locker numbers 2, 4, 6, 8, 10, ..., 196, 198 and 200.

Then the third students changes the state of every third locker, i.e. he/she closes an open locker and opens a closed locker.

So the open lockers are: 1, 5, 6, 12,...

Then the fourth students changes the state of every fourth locker.

So the open lockers are: 1, 4, 5, 6, 8,....

So, on we will observe that the open lockers have a perfect square number such as, 1, 4, 9, 16,....

Consider that the pattern is as follows:

Student 1 opens the locker, Student 2 closes it, Student 3 opens it, person 4 Student and so on.

This is because the square numbers always have an odd number of factors, which leads them to be open at the end.

Take any locker number, 40, for example. Its state (open or closed) is changed for every student whose number in line is a factor of the locker number.

Student      Locker 40 status

     1                    Open

     2                   Close

     4                   Open

     5                   Close

     8                   Open

     10                  Close

    20                  Open

    40                  Close

Like all other lockers numbered with non-square numbers, it ends up closed after all the students have gone through the line because it has an even number of factors.

Consider the locker number 16:

Student      Locker 16 status

     1                    Open

     2                   Close

     4                   Open

     8                   Close

     16                  Open

Thus, we can conclude that all the doors with square numbers on them will remain open because all square numbers have an odd number of factors and the doors with non-square numbers on them will remain close because they have even number of factors.

There will be a total of 14 lockers open.

1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169 and 196

So, if there are 10 lockers open in the first 100 lockers there must be only 4 other lockers opened in the next 100.

Answer:

The original price was 36.40

Step-by-step explanation:

p = original price of cake

using the coupon

p - 15% off = 30.94

p - .15 p = 30.94

Combine like terms

.85p = 30.94

divide each side by .85

p = 30.94/.85

p =36.40

The original price was 36.40

Answer:

-12

Step-by-step explanation:

-15+x+y=

-15+(-3)+6

-15-3+6

-15+3

-12

The ratio of blue paints to yellow paint is a mixture of 2 : 3.

Suppose that we've got two quantities with measurements as 'a' and 'b'

Then, their ratio(ratio of a to b) a:b

or

[tex]\dfrac{a}{b}[/tex]

The Total cans of blue paint = 14

Total cans of yellow paint = 20

Day 1:

Yellow paint = 6 cans

Blue paint = 4 cans

The ratio of blue paints to yellow paint

= 2 : 3

Day 2:

Yellow paint = 9 cans

Blue paint = 6 cans

The ratio of blue paints to yellow paint

2 : 3

Day 3:

Cans of yellow remaining after 2 days

Yellow paint = Total cans of yellow paint - day 1 cans of yellow paint - day 2 cans of yellow paint

= 20 - 6 - 9

= 20 - 15

= 5 cans

Cans of blue remaining after 2 days

Blue paint = Total cans of blue paint - day 1 cans of blue paint - day 2 cans of blue paint

= 14 - 4 - 6

= 14 - 10

= 4 cans

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Answer:

the correct answer is 1/2.

How i came to this answer was adding all of the number of medals together for all of the years, coming up to a total of 22. When asking about probability of any given set or amount of things, you always take the selected values and take them out of the whole amount. Years 2009 and 2012 have a whole selected value of 11 (4+7). Therefore you're "taking" 11 from 22, coming up with the fraction 11/22 seeing as that is not a answer choice the next step is to simply the fraction to 1/2.

Answer:

C    Mark me as brainliest!!!

Step-by-step explanation:

Answer:

x0 is the answer I just did that question and got it right

Answer:  Answer is in the steps

Step-by-step explanation:

If we given the angle measure in variables then we will sum them up equal 180 and solve for x to determine the angle measure.

9x + x  +x+4 = 180  

   11x + 4 =  180

            -4   -4

11x = 176

x=16  

In this  case we can find the angle measures by using the expressions.

x = 16  degrees

x+4 =  20 degrees

9x =  144 degrees  

you can write yd^2 or [tex]yd^{ \ 2}[/tex] to indicate "square yards"

=========================================================

Work Shown:

The triangle has a base of 3+3+2 = 8, and a height of 7

A = area of triangle

A = 0.5*base*height

A = 0.5*8*7

A = 28

The rectangle has a length and width of 3 and 2

B = area of rectangle

B = length*width

B = 3*2

B = 6

The shaded area is the difference of the two areas

C = area of shaded region

C = A - B

C = 28 - 6

C = 22