Georgia Connections Academy is selling tickets to its Spring Fling. Adult tickets cost $4 and student tickets cost $2.50. The school makes $2,820. Write an equation that represents this situation to find the cost of all adult and student tickets sold. Use the variable s for student tickets and a for adult tickets sold.
(7 points)
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
Write an equation that represents this situation to find the cost of all adult and student tickets sold. Use the variable s for student tickets and a for adult tickets sold.
Response area a + Response area s = Response area
900 tickets are sold for the spring fling. Write an equation to represent this situation.
a + Response area = Response area
Use the above system of equations to determine how many adult and student tickets were sold.
Response area adult tickets and Response area student tickets were sold.
:: 2820
:: a
:: 380
:: 2.50
:: 591
:: 520
:: 900
:: 6.5
:: 4
:: s
:: 309
:: 390
The equation that represents the cost of all adult and student tickets sold is:
4a + 2.50s = 2820
The equation that represents the number of tickets sold is:
a + s = 900
Using the above system of equations, we can solve for the values of adult tickets and student tickets sold:
adult tickets sold = 520
student tickets sold = 380
are you sure??
Apologies for the confusion. Let's go through the steps again:
The equation that represents the cost of all adult and student tickets sold is:
4a + 2.50s = 2820
The equation that represents the number of tickets sold is:
a + s = 900
Using the above system of equations, we can solve for the values of adult tickets and student tickets sold:
Multiplying the second equation by 2.50:
2.50a + 2.50s = 2250
Subtracting the second equation from the first equation:
(4a + 2.50s) - (2.50a + 2.50s) = 2820 - 2250
1.50a = 570
a = 380
Substituting the value of a into the second equation:
380 + s = 900
s = 520
Therefore, 380 adult tickets and 520 student tickets were sold.
1 of 51 of 5 Items
Question
Use the image to answer the question.
A coordinate plane with 4 quadrants ranges from negative 10 to 10 in unit increments on both the x and y axes. A solid line and a dashed line with arrows at both the ends are drawn parallel to each other on the graph. The equation of the solid line is y equals negative x plus 3. The equation of the dashed line is x plus y equals 8.
Solving the system y=−x+3 and x+y=8 by graphing shows that there is no solution to the system. Is this statement true or false? Explain.
(1 point)
Responses
The statement is true, because the lines are parallel.
The statement is true, because the lines are parallel.
The statement is false, because the lines are parallel.
The statement is false, because the lines are parallel.
The statement is false, because the lines have an intersection point.
The statement is false, because the lines have an intersection point.
The statement is true, because the lines have an intersection point.
The statement is true, because the lines have an intersection point.
The statement is false, because the lines have an intersection point.
By graphing the equations y = -x + 3 and x + y = 8, we can see that the solid line and dashed line intersect at a single point. This means that there is a solution to the system of equations, contradicting the statement that there is no solution. Therefore, the statement is false.
is that true???
Apologies for the confusion. Let's go through the steps again:
The given equations are:
y = -x + 3 (Solid line)
x + y = 8 (Dashed line)
To solve the system of equations, we can set the two equations equal to each other:
-x + 3 = 8 - x
Simplifying, we find:
3 = 8
This is not a true statement, which means the lines are parallel and do not intersect. Therefore, the statement is true, as the system of equations has no solution.
Use the image to answer the question.
A coordinate plane with 4 quadrants ranges from negative 10 to 10 in unit increments on both the x and y axes. A solid line and a dashed line with arrows at both the ends are drawn parallel to each other on the graph. The solid line passes through left parenthesis 0 comma 2 right parenthesis and left parenthesis 2 comma 0 right parenthesis. The dashed line passes through left parenthesis negative 7 comma 0 right parenthesis and left parenthesis 7 comma 0 right parenthesis.
Does the graph show the system of equations x+y=2 and −x+y=7? Should the lines for the system be parallel?
(1 point)
Responses
The graph of x+y=2 is incorrect. The lines should intersect.
The graph of x plus y equals 2 is incorrect. The lines should intersect.
Both graphs are correct. The lines should be parallel.
Both graphs are correct. The lines should be parallel.
The graph of −x+y=7 is incorrect. The lines should be parallel.
The graph of negative x plus y equals 7 is incorrect. The lines should be parallel.
The graph of −x+y=7 is incorrect. The lines should intersect.
The graph of negative x plus y equals 7 is incorrect. The lines should intersect.
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The correct response is:
The graph of x+y=2 is incorrect. The lines should intersect.
The graph of −x+y=7 is incorrect. The lines should be parallel.
The lines for the system of equations x+y=2 and −x+y=7 should not be parallel. They should intersect at a single point. However, based on the given information, the lines on the graph are parallel and do not intersect. Therefore, the graph does not show the system of equations x+y=2 and −x+y=7 correctly.
is that correct??
Apologies for the confusion, let's go through the steps again:
The solid line passes through (0, 2) and (2, 0). We can calculate the slope of this line:
m = (y2 - y1) / (x2 - x1)
m = (0 - 2) / (2 - 0)
m = -2/2
m = -1
The dashed line passes through (-7, 0) and (7, 0). We can also calculate the slope of this line:
m = (y2 - y1) / (x2 - x1)
m = (0 - 0) / (7 - (-7))
m = 0/14
m = 0
Since the slopes of the lines are different (-1 and 0), the lines are not parallel. Additionally, the solid line and dashed line do not intersect at a single point, as they both lie on the x-axis. Therefore, the graph does not accurately represent the system of equations x+y=2 and −x+y=7.
The correct response is:
The graph of x+y=2 is incorrect. The lines should intersect.
The graph of −x+y=7 is incorrect. The lines should be parallel.
i can only chose one
I apologize for the confusion. In that case, please choose the following response:
The graph of x+y=2 is incorrect. The lines should intersect.
Which of these graphs shows that the linear system −2x+y=6 and 4x−2y=−12 has an infinite number of solutions?(1 point)
Responses
A coordinate plane with 4 quadrants shows x and y axes ranging from negative 10 to 10 in unit increments. Two parallel lines are plotted on the plane. A dotted upward slanting line with arrows at both ends passes through the points left parenthesis negative 3 comma 0 right parenthesis and left parenthesis 0 comma 6 right parenthesis. A solid upward slanting line with arrows at both ends, parallel to the dotted line, passes through origin.
Image with alt text: A coordinate plane with 4 quadrants shows x and y axes ranging from negative 10 to 10 in unit increments. Two parallel lines are plotted on the plane. A dotted upward slanting line with arrows at both ends passes through the points left parenthesis negative 3 comma 0 right parenthesis and left parenthesis 0 comma 6 right parenthesis. A solid upward slanting line with arrows at both ends, parallel to the dotted line, passes through origin.
A coordinate plane with 4 quadrants shows x and y axes ranging from negative 10 to 10 in unit increments. A line is plotted on the plane. An upward slanting line with arrows at both ends passes through the points left parenthesis 0 comma negative 6 right parenthesis and left parenthesis 3 comma 0 right parenthesis.
Image with alt text: A coordinate plane with 4 quadrants shows x and y axes ranging from negative 10 to 10 in unit increments. A line is plotted on the plane. An upward slanting line with arrows at both ends passes through the points left parenthesis 0 comma negative 6 right parenthesis and left parenthesis 3 comma 0 right parenthesis.
A coordinate plane with 4 quadrants shows x and y axes ranging from negative 10 to 10 in unit increments. A line is plotted on the plane. An upward slanting line with arrows at both ends passes through the points left parenthesis negative 3 comma 0 right parenthesis and left parenthesis 0 comma 6 right parenthesis.
Image with alt text: A coordinate plane with 4 quadrants shows x and y axes ranging from negative 10 to 10 in unit increments. A line is plotted on the plane. An upward slanting line with arrows at both ends passes through the points left parenthesis negative 3 comma 0 right parenthesis and left parenthesis 0 comma 6 right parenthesis.
A coordinate plane with 4 quadrants shows x and y axes ranging from negative 10 to 10 in unit increments. Two intersecting lines are plotted on the plane. A solid upward slanting line with arrows at both ends passes through the points left parenthesis negative 3 comma 0 right parenthesis and left parenthesis 0 comma 6 right parenthesis. A dotted upward slanting line passes through the points left parenthesis 0 comma 6 right parenthesis and left parenthesis 1 comma 7 right parenthesis.
Image with alt text: A coordinate plane with 4 quadrants shows x and y axes ranging from negative 10 to 10 in unit increments. Two intersecting lines are plotted on the plane. A solid upward slanting line with arrows at both ends passes through the points left parenthesis negative 3 comma 0 right parenthesis and left parenthesis 0 comma 6 right parenthesis. A dotted upward slanting line passes through the points left parenthesis 0 comma 6 right parenthesis and left parenthesis 1 comma 7 right parenthesis.
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The correct response is:
A coordinate plane with 4 quadrants shows x and y axes ranging from negative 10 to 10 in unit increments. Two parallel lines are plotted on the plane. A dotted upward slanting line with arrows at both ends passes through the points (negative 3, 0) and (0, 6). A solid upward slanting line with arrows at both ends, parallel to the dotted line, passes through the origin.
is it 1, 2 ,3, 4??
and are you correct??
Yes, the correct response is 1. The graph described in option 1 shows that the linear system -2x+y=6 and 4x-2y=-12 has an infinite number of solutions. The solid line and dotted line are parallel, indicating that they have the same slope and will never intersect. Therefore, they will satisfy each other for any given values of x and y, resulting in an infinite number of solutions for the system.
Yes, I am correct.
4 of 54 of 5 Items
Question
Which of these graphs shows that the linear system y=−x+6 and 3x+3y=18 has an infinite number of solutions?(1 point)
Responses
A coordinate plane with 4 quadrants shows x and y axes ranging from negative 10 to 10 in unit increments. Two intersecting lines are plotted on the plane. A solid downward slanting line with arrows at both ends passes through the points left parenthesis 0 comma 6 right parenthesis and left parenthesis 6 comma 0 right parenthesis. A dotted downward slanting line with arrows at both ends passes through the points left parenthesis negative 6 comma 4 right parenthesis and left parenthesis 3 comma 3 right parenthesis.
Image with alt text: A coordinate plane with 4 quadrants shows x and y axes ranging from negative 10 to 10 in unit increments. Two intersecting lines are plotted on the plane. A solid downward slanting line with arrows at both ends passes through the points left parenthesis 0 comma 6 right parenthesis and left parenthesis 6 comma 0 right parenthesis. A dotted downward slanting line with arrows at both ends passes through the points left parenthesis negative 6 comma 4 right parenthesis and left parenthesis 3 comma 3 right parenthesis.
A coordinate plane with 4 quadrants shows x and y axes ranging from negative 10 to 10 in unit increments. A line is plotted on the plane. A downward slanting line with arrows at both ends passes through the points left parenthesis 0 comma 6 right parenthesis and left parenthesis 6 comma 0 right parenthesis.
Image with alt text: A coordinate plane with 4 quadrants shows x and y axes ranging from negative 10 to 10 in unit increments. A line is plotted on the plane. A downward slanting line with arrows at both ends passes through the points left parenthesis 0 comma 6 right parenthesis and left parenthesis 6 comma 0 right parenthesis.
A coordinate plane with 4 quadrants shows x and y axes ranging from negative 10 to 10 in unit increments. A line is plotted on the plane. A downward slanting line with arrows at both ends passes through the points left parenthesis negative 6 comma 0 right parenthesis and left parenthesis 0 comma negative 6 right parenthesis.
Image with alt text: A coordinate plane with 4 quadrants shows x and y axes ranging from negative 10 to 10 in unit increments. A line is plotted on the plane. A downward slanting line with arrows at both ends passes through the points left parenthesis negative 6 comma 0 right parenthesis and left parenthesis 0 comma negative 6 right parenthesis.
A coordinate plane with 4 quadrants shows x and y axes ranging from negative 10 to 10 in unit increments. Two parallel lines are plotted on the plane. A solid downward slanting line with arrows at both ends passes through the points left parenthesis 0 comma 6 right parenthesis and left parenthesis 6 comma 0 right parenthesis. A dotted downward slanting line with arrows at both ends passes through the points left parenthesis 0 comma 4 right parenthesis and left parenthesis 4 comma 0 right parenthesis.
Image with alt text: A coordinate plane with 4 quadrants shows x and y axes ranging from negative 10 to 10 in unit increments. Two parallel lines are plotted on the plane. A solid downward slanting line with arrows at both ends passes through the points left parenthesis 0 comma 6 right parenthesis and left parenthesis 6 comma 0 right parenthesis. A dotted downward slanting line with arrows at both ends passes through the points left parenthesis 0 comma 4 right parenthesis and left parenthesis 4 comma 0 right parenthesis.
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is it 1, 2, 3, 4
are you sure???
Apologies for the confusion. Let's go through the options again:
The correct response is:
A coordinate plane with 4 quadrants shows x and y axes ranging from negative 10 to 10 in unit increments. Two intersecting lines are plotted on the plane. A solid downward slanting line with arrows at both ends passes through the points (0, 6) and (6, 0). A dotted downward slanting line with arrows at both ends passes through the points (-6, 4) and (3, 3).
Yes, I am sure. The graph described in option 1 shows that the linear system y=-x+6 and 3x+3y=18 has an infinite number of solutions. The two lines intersect at multiple points, indicating that they are not independent and satisfy each other for various values of x and y. Therefore, there are infinitely many solutions to the system.
Solve the given system of linear equations by inspection.
y=35x−5
y=−35x−5
(1 point)
Responses
(0,−5)
left parenthesis 0 comma negative 5 right parenthesis
(−5,0)
left parenthesis negative 5 comma 0 right parenthesis
no solution
no solution
infinitely many solutions
infinitely many solutions
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The given system of linear equations is:
y = 35x - 5
y = -35x - 5
By inspection, we can see that the slopes of the two lines are equal in magnitude but have opposite signs. This indicates that the lines are parallel and will never intersect. Therefore, the system has no solution.
The correct response is:
no solution
is this true???
I apologize for the incorrect response. Let's solve the given system of linear equations:
y = 35x - 5 .....(1)
y = -35x - 5 .....(2)
By comparing the equations, we can see that the slopes are equal in magnitude but have opposite signs. This means that the lines are parallel.
To determine if there are any solutions, we can set the equations equal to each other:
35x - 5 = -35x - 5
Adding 35x and 5 to both sides:
35x + 35x = 0
70x = 0
Dividing both sides by 70:
x = 0
Now, substitute the value of x into one of the original equations, for example, equation (1):
y = 35(0) - 5
y = -5
Therefore, the solution to the system of equations is (0, -5).
The correct response is:
(0, -5)