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2 years ago

A group of 3 adults and 5 children pay a total of 52$ for movie tickets

Mathematics

1 answer:

Paladinen [302]2 years ago

6 0

Answer:

$9 adult
$5 child

Step-by-step explanation:

Letting "a" and "c" represent the costs of adult tickets and child tickets, the problem statement gives us two relations:

3a +5c = 52

2a +4c = 38

We can solve this system of equations using "elimination" as follows:

Dividing the first equation by 2 we get

a +2c = 19

Multiplying this by 3 and subtracting the first equation eliminates the "a" variable and tells us the price of a child ticket:

3(a +2c) -(3a +4c) = 3(19) -(52)

c = 5 . . . . . . collect terms

a +2·5 = 19 . . substitute for c in the 3rd equation above

a = 9 . . . . . . subtract 10

One adult ticket costs $9; one child ticket costs $5.

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It would be 8.1 grams

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3 years ago

Read 2 more answers

When Jill woke up, the temperature was -3 C. By noon the temperature had increased by 8 C.

AlekseyPX

-3+8.

We know that the temperature /was/ -3, so it was 3 under zero. It has /risen/ by 8, meaning we have added 8 degrees to whatever the starting temperature was.

We can find out how much the temperature is right now: it was -3, went through -2, -1, 0, 1, 2, 3, 4, and now its at 5 degrees. Thats risen by 8 degrees, right? And -3+8 is the same as 8-3 (commutative property of addition, since we basically did 8+(-3)) which equals 5, so we know that we got the correct answer. :)

3 0

3 years ago

You go out to eat with your family. The subtotal on your bill is $45.90. You must pay a 8% sales tax AND you would like to leave

Eddi Din [679]

Answer:

The answer is 57.83

Step-by-step explanation:

find 8% of 45.90 and add 18% of 45.90 and add them together.

8%*45.90=3.67

18%*45.90=8.26

Add, 45.90+8.26+3.67

The final price of your meal is 57.83

7 0

3 years ago

The sum of the interior angles of a polygon is

Crank

Answer:

D) 15

Step-by-step explanation:

The sum of the interior angles of a polygon is given by

$(n - 2) \times 180$

We have that, the sum of the interior angles of a polygon is

26 right angles. We want to find n, the number of sides.

We substitute into the formula to get:

$(n - 2) \times 180 = 26 \times 90$

Divide through by 90

$2(n - 2) = 26$

Divide through by 2

$n - 2 = 13$

$n = 13 + 2$

$n = 15$

6 0

2 years ago

What is the measure of angle 1?

tatiyna

Answer:

27 degrees

Step-by-step explanation:

The easy way is by remembering the formula (a-b)/2=c, where a is the larger angle, and b is the smallest angle. (90-36)/2=27.

The longer, more drawn out answer goes as follows. See the image to understand the notation I use:

AOE + BOD + BOA + DOE = 360
AOE + BOD = 90 + 36 = 126
BOA + DOE = 360 - AOE - BOD = 234
Since the sum of a triangle's angles is 180, ODE = (180 - DOE) / 2
Likewise, OBA = (180 - BOA) / 2
Since CDE is 180, CDO = 180 - ODE = 180 - (180 - DOE) / 2
Likewise, CBA is 180, so CBO = 180 - OBA = 180 - (180 - BOA) / 2
The interior angles of the irregular polygon CBOD add up to 360, so CBO + CDO + BOD + BCD = 360.
Substituting what we already found, 180 - (180 - BOA)/2 + 180 - (180 - DOE)/2 + 36 + BCD = 360
Cleaning it all up, we get 180 + (BOA + DOE)/2 + 36 + BCD = 360
As we found in line 3, BOA + DOE = 234, so substituting that in, 180 + 117 + 36 + BCD = 360
Finally, solving for BCD (360 - 36 - 117 - 180) we get our answer, 27

Note: The long drawn out method shown above is a way to derive the formula for the secant theorem. You do not need to use this method every time. Just remember, large angle minus small angle, all divided by 2. That is it.

5 0

2 years ago