Simplify the expression.

(6g)^3

By combining the like terms; the simplified answer in the correct way is 16x^2+6xy+6y^2

How to get answer:

- Find how many terms are in the algebraic equation. Counting I got 6 terms.

There are 2 xy's and 2 x's and 2y's

- Next combine all like terms

[tex]8x^{2} + 8x^{2} = 16x^{2}[/tex]

7xy+-xy=6xy

[tex]5y^{2} + y^{2}[/tex]=[tex]6y^{2}[/tex]

- Next Simplify

[tex]16x^{2}+6xy+6y^{2}[/tex]

A total of 812 tickets were sold for the school play. 375 adult tickets were sold.

Let's assume the number of adult tickets sold is "A" and the number of student tickets sold is "S."

We are given two pieces of information:

The total number of tickets sold is 812:

A + S = 812

There were 62 more student tickets sold than adult tickets:

S = A + 62

Now, we can set up a system of equations to represent the given information:

A + S = 812

S = A + 62

Now, we can solve the system of equations to find the values of A and S.

Substitute equation (2) into equation (1):

A + (A + 62) = 812

Combine like terms:

2A + 62 = 812

Subtract 62 from both sides:

2A = 812 - 62

2A = 750

Now, divide by 2 to solve for A:

A = 750 / 2

A = 375

So, 375 adult tickets were sold.

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Final answer:

375 adult tickets were sold.

Explanation:

Let's denote the number of adult tickets sold as x. According to the information provided, there were 62 more student tickets sold than adult tickets. So, the number of student tickets sold can be represented as x + 62.

Since a total of 812 tickets were sold, we can write the equation x + (x + 62) = 812. This equation represents the sum of adult tickets and student tickets being equal to the total tickets sold.

Solving this equation, we have 2x + 62 = 812. Subtracting 62 from both sides, we get 2x = 750. Then, dividing both sides by 2, we find that x = 375. Therefore, 375 adult tickets were sold.

Answer:

C) (x – 2)(x + 2)(x² + 4)(x⁴ + 16)

Step-by-step explanation:

The difference of squares is factored like this:

... a² - b² = (a - b)(a + b)

The given expression is the difference of squares:

... (x⁴)² - (2⁴)²

so can be factored as ...

... (x⁴ - 2⁴)(x⁴ + 2⁴) . . . . . . . 2⁴=16

Once again, the difference term is the difference of squares, so it can be factored as ...

...  x⁴ - 2⁴ = (x² -2²)(x² + 2²) . . . . . . 2²=4

And the difference in the first factor is also the difference of squares and can be factored.

... x² -2² = (x - 2)(x + 2)

Putting each factorization in its place in the whole expression, we get

... x⁸ - 256 = (x - 2)(x + 2)(x² +4)(x⁴ +16)

The answer is 293 meters because you multiply the 14650 books by how thick they are which is 0.02, and that should reveal your answer. Hope this helps!

r = [tex]\sqrt[3]{\frac{3V}{4\pi } }[/tex

given [\frac{4}{3}[/tex]πr³ = V ( multiply both sides by 3 to eliminate fraction )

4πr³ = 3V ( divide both sides by 4π )

r³ = [tex]\frac{3V}{4\pi }[/tex] ( take the cube root of both sides )

r = [tex]\sqrt[3]{\frac{3V}{4\pi } }[/tex]

104 and 105 are consecutive numbers that add up to 209. Maybe this answers your question? Let me know otherwise.

The answer to your question is,

D) 1,032

-Mabel <3

Option D. 1,032 , would be correct.

Here we can use key words to help us realize, if we are adding, subtracting, multiplying or dividing.

In this case, we know we will be dividing or multiplying because of the word ¨each¨. It might be division, but in the last sentence it asks ¨how many total¨ so we know it will be multiplication.

Therefore...

24 × 43 = 1,032

There are 1,032 total players in the league.

Answer:

C.

Step-by-step explanation:

all you do is go look and see which one is in the exact same spot

C

ΔABC and ΔGHI are congruent by SAS

AB = GI , the included angles ∠B = ∠I and BC = HI

First, divide 1200 by 4 to find out how many pounds they make per hour. The answer is 300. Then, multiply 300 by 10 to find out how many chips they would make in 10 hours. The answer is 3,000 pounds of chips.

The factory will make 3000 pounds of potato chips in 10 hours.

To find out how many pounds of potato chips will be made in 10 hours, we can set up a proportion using the given information. The rate of making potato chips is 1200 pounds in 4 hours. Let's label the unknown as 'x'. The proportion would be:

1200 pounds / 4 hours = x pounds / 10 hours.

To solve for 'x', we can cross multiply and then divide:

1200 pounds * 10 hours = 4 hours * x pounds;

Now divide both sides of the equation by 4 to isolate 'x':

x = (1200 pounds * 10 hours) / 4 hours = 3000 pounds.

Therefore, the factory will make 3000 pounds of potato chips in 10 hours.

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I do not know what diagram that you are talking about, but it might be the one that I am thinking, so if this is the questions on your page, then let me know.

A - Vertex angles

B - 5 is congruent to 4

C - 5 and 4 are alternate interior angles, or Z angles

P and R are parrallel.

Hope I helped.

As per given information: m∠5 = 40° and m∠2 = 140°. It then uses the theorems that supplementary angles are congruent and that if two same-side interior angles are congruent, then the lines are parallel, to conclude that a || b.

The proof begins with the givens: m∠5 = 40° and m∠2 = 140°. From this, we can conclude that ∠5 and ∠2 are supplementary angles (since their measures add up to 180°).

We also know that ∠5 and ∠2 are same-side interior angles (since they are both on the same side of the transversal and inside the two lines).

Now, we can use the following theorems to complete the proof:

Theorem 1: Supplementary angles are congruent.

Theorem 2: If two same-side interior angles are congruent, then the lines are parallel.

Proof:

Given: m∠5 = 40° and m∠2 = 140°

∠5 and ∠2 are supplementary angles. (Theorem 1)

∠5 and ∠2 are same-side interior angles.

If two same-side interior angles are congruent, then the lines are parallel. (Theorem 2)

Therefore, a || b.

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Let's assume

It started in 2000

so, t=0 in 2000

[tex]P_0=6.4million[/tex]

we can use formula

[tex]P(t)=P_0 e^{rt}[/tex]

we can plug value

[tex]P(t)=6.4 e^{rt}[/tex]

In 2005, the same survey was made and the total amount of gamma ray bursts was 7.3 million

so, at t=2005-2000=5

P(t)=7.3 million

we can plug value and then we can solve for r

[tex]7.3=6.4 e^{r*5}[/tex]

[tex]r=0.02632[/tex]

now, we can plug back

[tex]P(t)=6.4 e^{0.02632t}[/tex]

now, we have

P(t)=1 billion =1000 million

so, we can set it and then we can solve for t

[tex]1000=6.4 e^{0.02632t}[/tex]

[tex]t=191.924[/tex]

approximately

[tex]t=192[/tex]

Year is 2000+192

year is 2192................Answer

I'm pretty sure 4/10=40/100

Here is the equation:

[tex]\frac{3}{10} = \frac{30}{100} \rightarrow \frac{4}{10}  =\frac{x}{100}[/tex]

To find the missing number, you have to cross multiply. Here's the equation:

[tex]\frac{4}{10} = \frac{x}{100} \\ \\ 100 \times 4 = 10x[/tex]

Multiply:

[tex]100 \times 4 = 400 \\ 400 = 10x[/tex]

To leave the variable x alone, you need to divide both sides by 10

[tex]\frac{400}{10} = \frac{10x}{10}[/tex]

Divide:

[tex]400 \div 10 = 40 \\ x = 40[/tex]

Your answer is 40

If you have any questions, feel free to ask in the comments! :)

Answer:

The answer is probably 4.

Step-by-step explanation:

Answer:

Option C.

Step-by-step explanation:

The given table represents a linear function.

If a linear is graphed by a line and the line passes through two points (x, y) and (x', y'), slope of the line is calculated by the formula

Slope = [tex]\frac{y-y'}{x-x'}[/tex]

Since line passes through two points (-2, -2) and (-1, 1)

Therefore, slope = [tex]\frac{1+2}{-1+2}[/tex]

                            = [tex]\frac{3}{1}[/tex]

                            = 3

Slope of the line will be 3.

Option C. is the answer.

Answer:

3 3/5

Step-by-step explanation:

The domain is how far the graph stretches horizontally (on the x-axis).

Domain:  ( -∞ , ∞ )  or  -∞ < x < ∞

The range is how long the graph stretched vertically (on the y-axis).

Range:  ( -∞ , 2 ]  or  -∞ < y ≤ 2

The zeros are where the graph intersects with the x-axis. In other words, the x-values when y=0.

Zeros:  x = -1  and  x = 3

Games*80% = 4

g*.8 = 4

g = 4/.8

games = 5

5 games played

Answer:

5

Step-by-step explanation:

It's A. if a = b, then a^2 = b^2

The object of any equation with a variable (whether it is on one side or both) is to isolate the variable.  We do this by moving all of the x's to one side of the equation and everything else to the other side.

For example:

3x - 5 = 2x + 1

-2x         -2x    

 x  - 5 =         1

    +5           +5

x         =         6

Now, there are 3 different types of solutions:

1) x = ____  there is one solution

2) 0 = 0   or some other TRUE statement  there are infinite solutions because every value for x is a solution

3) 0 = 1   or some other FALSE statement  there are no solutions because no value for x will provide a solution

HOPE THIS HELPED!

K= = 5r -s

subtract s from both sides

K + s = 5r

divide 5 from both sides

r = K + s / 5

I would say the answer would be B. or C.

not sure which but i hope i helped narrow it down..

Answer:

Its B

Step-by-step explanation:

Answer:

Corresponding angle theorem, vertical angle theorem, and the transitive property of congruence.

Step-by-step explanation:

Considering a set of parallel lines cut by a transversal. (Refer the attached image).

Now that lines J and K are parallel, then by "corresponding angle theorem"

[tex]\angle 1=\angle 5[/tex]

By "vertical angle theorem"

[tex]\angle 5 = \angle 7[/tex]

Using, "transitive property of congruence"

[tex]\angle 1 = \angle 7[/tex]

And that is our required proof. In this whole proof we have used "corresponding angle theorem", "vertical angle theorem", and the "transitive property of congruence".

Angles between a transversal line and parallel lines are congruent based on vertical angle theorem, corresponding angles and transitive property.

I will use the attached figure to explain the congruence of the angles.

Corresponding Angles Theorem

From the attached figure, the following angles are congruent based on corresponding angle theorem

[tex]\angle 2 = \angle 6[/tex]            

[tex]\angle 1 = \angle 5[/tex]

[tex]\angle 4 = \angle 8[/tex]

[tex]\angle 3 = \angle 7[/tex]

Vertical Angle Theorem

From the attached figure, the following angles are congruent based on vertical angle theorems

[tex]\angle 2 = \angle 3[/tex]            

[tex]\angle 1 = \angle 4[/tex]

[tex]\angle 5 = \angle 8[/tex]

[tex]\angle 6 = \angle 7[/tex]

Transitive Property

From the attached figure, the following angles are congruent based on transitive property

[tex]\angle 1 = \angle 7[/tex]

[tex]\angle 4 = \angle 6[/tex]

[tex]\angle 5 = \angle 3[/tex]            

[tex]\angle 2 = \angle 8[/tex]

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I believe 0.75/ 8=0.09375 so 0.09375 is the answer i hope i helped

The percent increase to earned money will be 9.375%.

What is Percentage?

A relative value indicating hundredth part of any quantity is called percentage.

Given that;

An employee was hired at a wage of $8 per hour.

After a raise, the employee earned $8.75 per hour.

Now, The increase percent will be calculate as;

Increase percent in money = Increase money/Actual money x 100

                                          = (8.75 - 8.00) / 8 x 100

                                          = (0.75/8) x 100

                                          = 75/8

                                          = 9.375

Thus, The percent increase to earned money will be 9.375%.

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5/15 because there are 5 blue marbles and 15 marbles all together.

Solution :

Given a soda can has a diameter of 6 cm.

As we know,  the circumference of circle with radius r is , [tex]C=2\pi r[/tex].

And diameter of  the circle [tex]D = 2r[/tex]

So, the circumference of the circle with diameter D is ,  [tex]C=\pi D[/tex]

Put D= 6

[tex]\Rightarrow C=6 \pi\\\\Using\: \pi=3.14\\\Rightarrow C=6\times3.14\\\\\Rightarrow C=18.84[/tex]

Hence, the circumference of the can is 18.84 cm. (option C)

$504 + $580= $1084 is how much the bus company got in all.

Answer:

$1,084

Step-by-step explanation:

Multiply 36 by $14 and you get 504.

Then multiply 20 by $29 an you will get 580.

In order to figure out how much money they collected in total, you should add your two answers together, which will then be 1,084. The bus company collected $1,084

5(1.50)+5(2.50)+2n

or

7.5+12.5+2n

20+2n= Cost

The algebraic expression for the cost of Ms. Thomas's order is:

$2n + $20

Ms. Thomas ordered 5 pencil packs, n notebooks, and 5 sets of markers. We are asked to write an algebraic expression that represents the cost of Ms. Thomas's order. The cost of each item is given as follows:

Pencil pack: $1.50

Notebook: $2

Markers: $2.50

To write an algebraic expression for the cost of Ms. Thomas's order, we need to multiply the cost of each item by the number of items ordered, and then add the products together.

The cost of 5 pencil packs is 5 x $1.50 = $7.50.

The cost of n notebooks is n x $2 = $2n.

The cost of 5 sets of markers is 5 x $2.50 = $12.50.

Therefore, the algebraic expression for the cost of Ms. Thomas's order is:

$7.50 + $2n + $12.50

Simplifying this expression, we get:

$2n + $20

Therefore, the algebraic expression for the cost of Ms. Thomas's order is $2n + $20

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Answer:

3 inches/hour

Step-by-step explanation:

During one winter snow storm in Denver Colorado Jesse noted that 16 inches of snow fell in [tex]5\frac{1}{3}[/tex] hours = [tex]\frac{16}{3}[/tex] hours

the snow fell in [tex]\frac{16}{3}[/tex] hours = 16 inches

snow fell in 1 hour = [tex]\frac{16}{\frac{16}{3}}[/tex]

                              = [tex]\frac{16\times 3}{16}[/tex]

                              = [tex]\frac{48}{16}[/tex]

                              = 3 inches

The rate of snowfall would be 3 inches/hour.