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Travka [436]
3 years ago
6

At a regional soccer​ tournament, tickets for two adults and seven students cost ​$42. Tickets for three adults and eleven stude

nts cost ​$65. Determine the price of an adult ticket and the price of a student ticket.
Mathematics
1 answer:
tatiyna3 years ago
7 0

The cost of adult ticket is $7 and child ticket is $4.

Step-by-step explanation:

Let,

Price of one adult ticket = x

Price of one child ticket = y

According to given statement;

2x+7y=42    Eqn 1

3x+11y=65   Eqn 2

Multiplying Eqn 1 by 3

3(2x+7y=42)\\6x+21y=126\ \ \ Eqn\ 3

Multiplying Eqn 2 by 2

2(3x+11y=65)\\6x+22y=130\ \ \ Eqn\ 4

Subtracting Eqn 3 from Eqn 4

(6x+22y)-(6x+21y)=130-126\\6x+22y-6x-21y=4\\y=4

Putting y=4 in Eqn 1

2x+7(4)=42\\2x+28=42\\2x=42-28\\2x=14\\

Dividing both sides by 2

\frac{2x}{2}=\frac{14}{2}\\x=7

The cost of adult ticket is $7 and child ticket is $4.

Keywords: linear equation, elimination method

Learn more about elimination method at:

  • brainly.com/question/10538663
  • brainly.com/question/10557275

#LearnwithBrainly

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In triangle NOP, Np is extended through Point P to Point Q, m < NOP =(x+17) degrees, m< PNO =(2x-4) degrees, and m< OPQ
Zigmanuir [339]
To find the measure of angle OPQ, we have two equations...
y+5x-17=180 because angles OPN and OPQ are supplementary...
AND
x+17+2x-4+y=180 because the total degrees of a triangle must add up to 180.
The equations...
5x+y=197
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solce the system of equations...
x=15
y=122
Since we wanted to solve for y, 122 is the answer.
The measure of angle OPQ is 122.

Sorry this took forever. The website is hard to use because I'm used to using the app:)

Best of wishes!

6 0
3 years ago
Quadrilateral ABCD is inscribed in a circle with angle measures m∠A = (11x − 8)°, m∠B = (3x2 + 1)°, m∠C = (15x + 32)°, and m∠D =
dimulka [17.4K]

Answer:

No for all of the 4 values

Step-by-step explanation:

The sum of the internal angles of a quadrilateral is always 360°, so we have that:

m∠A + m∠B + m∠C + m∠D = 360

11x - 8 + 3x2 + 1 + 15x + 32 + 2x2 - 1 = 360

5x2 + 26x - 320 = 0

Solving the quadratic function using Bhaskara's formula, we have:

Delta = 26^2 + 4*5*320 = 7076

sqrt(Delta) = 84.12

x1 = (-26 + 84.12)/10 = 5.81

x2 = (-26 - 84.12)/10 = -11.01 (this value will generate negative angles, so it is not valid).

Now, finding the angles, we have:

m∠A = 11*5.81 - 8 = 55.91°

m∠B = 3*(5.81)^2 + 1 = 102.27­°

m∠C = 15*5.81 + 32 = 119.15°

m∠D = 2*(5.81)^2 - 1 = 66.51°

As all these values are different from the values shown, the answer is No for all of them.

8 0
3 years ago
#3 AB and AD are tangent to the circle centered at point C. Find the value of x. *
dezoksy [38]

Answer:

x=4

Step-by-step explanation:

tangent lines from the same point to a circle are congruent in length, so we can say that

5x+8 = 8x-4

5x -5x +8 = 8x - 5x -4

8 = 3x - 4

8+4 = 3x -4 + 4

3x = 12

3x/3 = 12/3

x=4

8 0
3 years ago
One number is 8 more than the other. When the larger is divided by the smaller, the quotient is 7/5
Wewaii [24]

Answer:

<h3>          The numbers are 20 and 28</h3>

Step-by-step explanation:

x  - the other number  (the smaller one)

x+8  - 8 more than the other number (the larger number)

 

\dfrac{x+8}x=\dfrac75\\\\(x+8)\cdot5=x\cdot7\\\\5x+40=7x\\^{\quad-40\qquad-40}\\{}\quad5x = 7x-40\\^{\quad-7x\quad-7x}\\-2x=-40\\^{\div(-2)\quad\div(-2)}\\{}\ \ x=20\\\\x+8=28

6 0
3 years ago
On a coordinate plane, 2 quadrilaterals are shown. Quadrilateral Q R S T has points (negative 1, 0), (5, 0), (3.5, negative 6) a
andreyandreev [35.5K]

Based on the calculations, the scale factor for this dilation is equal to 1/3.

<h3>How to determine the scale factor for this dilation?</h3>

First of all, we would use the distance formula to find the length of side QR and Q'R' as follows:

Distance = √[(x₂ - x₁)² - (y₂ - y₁)²]

Substituting the given points into the formula, we have;

Distance QR = √[(5 - (-1))² + (0 - 0)²]

Distance QR = √[(5 + 1)² + (0)²]

Distance QR = √[6² + 0]

Distance QR = √36

Distance QR = 6 units.

For side Q'R', we have:

Distance Q'R' = √[(1 - (-1))² + (2 - 2)²]

Distance Q'R' = √[(1 + 1)² + (0)²]

Distance Q'R' = √[2² + 0]

Distance Q'R' = √4

Distance Q'R' = 2 units.

Now, the scale factor for this dilation is given by:

Scale factor = Q'R'/QR

Scale factor = 2/6

Scale factor = 1/3.

Read more on scale factor here: brainly.com/question/17079307

#SPJ1

8 0
1 year ago
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