MATHEMATICS HIGH SCHOOL

The school that Lisa goes to is selling tickets to the annual talent show. On the first day of ticket sales the school sold 4 senior citizen tickets and 5 student tickets for a total of $102. The school took in $126 on the second day by selling 7 senior citizen tickets and 5 student tickets. What is the price each of senior citizen ticket and one student ticket?

Answers

Answer 1
Answer:

The price of senior citizen ticket is 8 and price of student ticket is 14.

What is Equation?

Two or more expressions with an Equal sign is called as Equation.

Let x be the price of senior citizen ticket

y be the price of student ticket.

On the first day of ticket sales the school sold 4 senior citizen tickets and 5 student tickets for a total of $102.

4x+5y=102..(1)

The school took in $126 on the second day by selling 7 senior citizen tickets and 5 studenttickets.

7x+5y=126..(2)

Subtract equation 1 and 2

4x+5y-7x-5y=102-126

-3x=-24

Divide both sides by 3

x=8

Now let us find y

4(8)+5y=102

32+5y=102

Subtract 32 from both sides

5y=102-32

5y=70

y=14

Hence, the price of senior citizen ticket is 8 and price of student ticket is 14.

To learn more on Equation:

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Answer 2
Answer: Let:
x = cost of senior citizen ticket
y = cost of student ticket

4x + 5y = 102
7x + 5y = 126

4x + 5y = 102
4x = 102 - 5y
x = (102 - 5y)/4
x = 102/4 - 5y/4

7x + 5y = 126
7(102/4 - 5y/4) + 5y = 126
(714/4 - 35y/4) + 5y = 126
-35y/4 + 5y = 126 - 714/4

note:
-35y/4 = -8.75y
714/4 = 178.5

-8.75y + 5y = 126 - 178.5
-3.75y = -52.5
y = -52.5/-3.75
y = 14


x = 102/4 - 5y/4
x = 102/4 - 5(14)/4
x = 8

x = cost of senior citizen ticket = $8/ea
y = cost of student ticket = $14/ea

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Un topografo situado en un punto c localiza dos puntos a y b en los lados opuestos de un lago . Si el punto c esta situado a 5km de a y 8 km de b y ademas el angulo formado en el punto c es de 36 grados . Calcular el ancho del lago

Answers

The width of the lake is approximately 4.93 kilometers.

To calculate the width of the lake, you can use trigonometry. You have a triangle with one side of 5 km (from point C to point A), another side of 8 km (from point C to point B), and an included angle of 36 degrees at point C.

You can use the law of cosines to find the third side, which is the width of the lake (let's call it "x"). The law of cosines states:

c^2 = a^2 + b^2 - 2ab * cos(C)

Where:

c is the side you want to find (the width of the lake, in this case).

a is the side opposite to angle A (5 km).

b is the side opposite to angle B (8 km).

C is the included angle at point C (36 degrees).

So, plug in the values:

x^2 = 5^2 + 8^2 - 2 * 5 * 8 * cos(36 degrees)

Now, you can solve for x:

x^2 = 25 + 64 - 80 * cos(36 degrees)

x^2 = 89 - 80 * cos(36 degrees)

Now, you'll need to calculate the cosine of 36 degrees, which is approximately 0.809.

x^2 = 89 - 80 * 0.809\nx^2 = 89 - 64.72\nx^2 = 24.28

Now, take the square root of both sides to find the width of the lake:

x ≈ √24.28

x ≈ 4.93 km

So, the width of the lake is approximately 4.93 kilometers.

for such more question on triangle

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Hi mods, I do have a link in this answer but it is a link to the spanish version of brainly since this user seems to speak spanish.

Por favor, traduzca su pregunta al inglés o encuentre la versión en español de Brainly (https://brainly.com.br/ o https://brainly.lat/.)

Estoy usando el traductor de google, lo siento por el mal español

ver diagrama adjunto abajo (el asombrosamente dibujado)

podemos formar un triangulo

Usa la ley de los cosenos del segundo apego.

Queremos encontrar el valor de c que representa el ancho del lago

En este problema, a=5, b=8, y C=36°

c^2=a^2+b^2-2abcos(C)

c=√(a^2+b^2-2abcos(C))

c=√(5^2+8^2-2(5)(8)cos(36^o))

c=√(25+64-80cos(36^o))

c=√(89-80cos(36^o))

c≈4.92734 km


el ancho del lago es de aproximadamente 4.93km

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Answers

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Answers

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Answers

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PLEASE HELP I WILL GIVE EXTRA POINTS AND BRAINALIST to the first person

Answers

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Answers

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