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IceJOKER [234]
2 years ago
6

how can a regular hexagon be folded to show that it has reflectional symmetry? fold the hexagon along a line from a vertex to th

e midpoint of an opposite side. fold the hexagon along a line connecting the two midpoints of adjacent sides. fold the hexagon along a line that bisects two vertex angles. fold the hexagon along a line that creates a right angle at a vertex.

Mathematics
2 answers:
Fofino [41]2 years ago
5 0
To show that a hexagon has refrectional symmetry, fold the hexagon along a line that bisects two vertex angles.
weqwewe [10]2 years ago
3 0
Folding a regular hexagon along a line that bisects two vertex angles (these angles will be opposite each other) will display reflectional symmetry. 

Another option is to fold it along a line that connects the midpoints of opposite sides.

Any shape that can be separated into two matching segments by a single line has reflectional symmetry. 

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Jonathan has a bag that has 2 red marbles and 3 blue marbles inside of it if you were to pick one marble from the bag without lo
Vika [28.1K]
There are 2 red marbles and 3 blue marbles, with a total of 5 marbles in the bag.

When Jonathan chooses a marble, we are saying that he is choosing the marble randomly.

Let's make a fraction. We want to know the chance of picking one of the 2 red marbles among all 5 marbles.

Divide 2 by 5

2/5

That's already a simplified fraction. If you want to convert this into decimal and into percentage, you would get

2/5
= 0.4
= 40%

Those are all acceptable answers.
Have an awesome day! :)
8 0
2 years ago
Emily is a songwriter who collects royalties on her songs whenever they are played in a commercial or a movie. Emily will earn $
Hitman42 [59]

Answer:

(6,2)

Step-by-step explanation:

Variable Definitions:

​x= the number of commercials

y= the number of movies

Each commercial earns Emily $50, so x commercials would earn her 50x dollars in royalties. Each movie earns Emily $150, so y movies would earn her 150y dollars in royalties. Therefore, the total royalties 50x+150y equals $600:

50x+150y=600

Since Emily's songs were played on 3 times as many commercials as movies, if we multiply 3 by the number of movies, we will get the number of commercials, meaning x equals 3y.

x=3y

Write System of Equations:

​50x+150y=600

x=3y

Solve for y in each equation:

1)  50x+150y=600

   150y=−50x+600

   y=-1/3x+4

2)  x=3y

    y=1/3x

The x variable represents the number of commercials and the yy variable represents the number of movies. Since the lines intersect at the point (6,2) we can say:

Emily's songs were played on 6 commercials and 2 movies.

​

 

4 0
2 years ago
For what values of x is x2 + 2x = 24 true?<br> –6 and –4<br> –4 and 6<br> 4 and –6<br> 6 and 4
alexgriva [62]

Answer:

Option C

x²+ 2x -24=0

x²+6x-4x-24= 0

x(x+6) -4(x+6) = 0

(x+6)(x-4) = 0

x= -6 and 4

Therefore, for x = 4 and -6 , the above given equation is true.

9 0
2 years ago
Maxis taking a cross-country road trip. Gas prices vary as the friends travel across the US from $4 dollars per gallon on the ea
Zolol [24]

Answer:

A) The amount of gas they bought on each coast;

East Coast = 35 gallons

Mid-US = 100 gallons

West Coast = 15 gallons

B) The amount of gas they bought on each coast on the return journey;

East Coast = 37 gallons

Mid-US = 116 gallons

West Coast = 21 gallons

Step-by-step explanation:

Complete Question

Maxis taking a cross-country road trip. Gas prices vary as the friends travel across the US from $4 dollars per gallon on the east coast to $3 in the mid-US, to $5 on the west coast.

(a) If they used twice as much gas in the mid-US than on either coast combined, and they spend $515 on gas to purchased 150 gallons of gas, how many gallons of gas did they buy at each price?

The answer to this question is East Coast - 35 gal, Mid-US - 100 gal, West Coast - 15 gal.

(b) On their way back they had more baggage in the car and spend $601 for 174 gallons of gas. Based on the same ratio as in Part (a), how many gallons of gas did they buy at each price? I don't know the answer to this one

Solution

Let the amount of fuel bought on the east coast = x gallons

Let the amount of fuel bought on the mid-coast = y gallons

Let the amount of fuel bought on the west coast = z gallons

a) - They used twice as much gas in the mid-US than on either coast combined

y = 2(x + z) = 2x + 2z (eqn 1)

- They spend $515 on gas to purchase 150 gallons of gas.

Total gallons purchased = x + y + z = 150

Total amount spent = 4x + 3y + 5z = 515

From eqn 1, y = 2x + 2z, inserting this value for y in the 2 other equations

x + y + z = x + 2x + 2z + z = 150

3x + 3z = 150

Divide through by 3

x + z = 50 (eqn *)

4x + 3y + 5z = 4x + 3(2x + 2z) + 5z = 515

4x + 6x + 6z + 5z = 515

10x + 11z = 515 (eqn **)

x + z = 50

10x + 11z = 515

Solving the simultaneous equation,

x = 35 gallons

z = 15 gallons

y = 2x + 2z = 2(35 + 15) = 100 gallons

B) On the return journey, the ratio between x, y and z is still the same, but the total gallons and total amount spent is now different.

They used twice as much gas in the mid-US than on either coast combined

y = 2(x + z) = 2x + 2z (eqn 1)

- They spend $601 on gas to purchase 174 gallons of gas.

Total gallons purchased = x + y + z = 174

Total amount spent = 4x + 3y + 5z = 601

From eqn 1, y = 2x + 2z, inserting this value for y in the 2 other equations

x + y + z = x + 2x + 2z + z = 174

3x + 3z = 174

Divide through by 3

x + z = 58 (eqn *)

4x + 3y + 5z = 4x + 3(2x + 2z) + 5z = 601

4x + 6x + 6z + 5z = 601

10x + 11z = 601 (eqn **)

x + z = 58

10x + 11z = 601

Solving the simultaneous equation,

x = 37 gallons

z = 21 gallons

y = 2x + 2z = 2(37 + 21) = 116 gallons

Hope this Helps!!!

5 0
2 years ago
A caterers fee is based on the number of meals she provides how much is the price per meal if the total fee is $1,088 for 64 mea
blsea [12.9K]
1,088 / 64 = 17

The caterers fee is $17 per meal
3 0
2 years ago
Read 2 more answers
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