Does the line through (3, 7) and (-2, -5) intersect with the line through (4, 8) and (10, -2)?(1 point) use on of the options below Yes…these lines are not parallel Yes…these lines are not parallel No…these lines are parallel No…these lines are parallel Yes…these lines are perpendicular Yes…these lines are perpendicular No…these lines are perpendicular No…these lines are perpendicular You cannot tell without a graph You cannot tell without a graph Yes…these lines are parallel Yes…these lines are parallel
Yes...these lines are not parallel.
To determine if the lines intersect or are parallel, we can calculate the slope of each line.
The slope between the points (3, 7) and (-2, -5) can be calculated using the formula:
slope = (change in y) / (change in x)
slope = (-5 - 7) / (-2 - 3)
slope = -12 / -5
slope = 12/5
Similarly, the slope between the points (4, 8) and (10, -2) can be calculated using the same formula:
slope = (-2 - 8) / (10 - 4)
slope = -10 / 6
slope = -5/3
Since the slopes of the two lines are not equal, the lines are not parallel.
Therefore, the lines do intersect. The correct answer is: Yes...these lines are not parallel.
To determine whether the lines intersect or are parallel, we can use the slope-intercept form of the equation of a line, which is given by:
y = mx + b
Where:
m = slope of the line
b = y-intercept of the line
1. Calculate the slope (m1) of the line passing through (3, 7) and (-2, -5):
m1 = (y2 - y1) / (x2 - x1)
= (-5 - 7) / (-2 - 3)
= (-12) / (-5)
= 12/5
2. Calculate the slope (m2) of the line passing through (4, 8) and (10, -2):
m2 = (y2 - y1) / (x2 - x1)
= (-2 - 8) / (10 - 4)
= (-10) / 6
= -5/3
Now, if the slopes of two lines are equal, the lines are parallel. If the slopes are negative reciprocals of each other, the lines are perpendicular. Otherwise, the lines intersect.
Comparing the slopes m1 = 12/5 and m2 = -5/3, we can see that they are neither equal nor negative reciprocals of each other. Therefore, the lines are not parallel and not perpendicular. Hence the correct option is:
Yes…these lines are not parallel.
An amusement park that you are excited to try is $28 per visit. You have the option to purchase a monthly membership for $90 and then pay $15 for each visit. (4 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. You have plans to attend 3 times this summer. Which option is best? You think you will visit probably about 8 times this summer. Which option is best? You have budgeted $150 for visiting the park this summer. Which option is best? How many visits would be approximately the break even point where both options would cost about the same?
To determine which option is best, we will compare the total cost of each option for different scenarios:
1. You plan to attend 3 times this summer:
Option 1: 3 visits x $28/visit = $84
Option 2: $90 membership + 3 visits x $15/visit = $135
In this case, Option 1 is the best choice because it has the lowest total cost.
2. You think you will visit approximately 8 times this summer:
Option 1: 8 visits x $28/visit = $224
Option 2: $90 membership + 8 visits x $15/visit = $210
In this case, Option 2 is the best choice because it has the lowest total cost.
3. You have budgeted $150 for visiting the park this summer:
Option 1: $150 budget / $28/visit = 5.36 (approximately 5) visits
Option 2: $90 membership + 5 visits x $15/visit = $165
In this case, Option 2 is the best choice because it fits within your budget and has the lowest total cost.
To find the break-even point where both options would cost about the same, we can set up the equation:
$90 + $15 * x = $28 * x
$90 = $28 * x - $15 * x
$90 = $13 * x
Solving for x:
x = $90 / $13
x ≈ 6.923
Therefore, the break-even point is approximately 6.923 visits.
Which method of solving a system of linear equation do you prefer to use? Why do you find this particular method easier than the other two?
As an AI language model, I don't have personal preferences. However, I can provide information on different methods of solving a system of linear equations.
There are three common methods for solving a system of linear equations: graphing, substitution, and elimination. Each method has its advantages and may be preferred depending on the specific situation.
1. Graphing: This method involves graphing both equations on a coordinate plane and finding the point of intersection. Graphing can provide a visual representation of the solution and can be helpful when the system has two easily graphable equations. However, graphing can be time-consuming and less accurate when dealing with complex or non-linear equations.
2. Substitution: This method involves solving one equation for one variable and substituting that expression into the other equation. It can be particularly useful when dealing with equations where one variable is isolated or easily isolated. Substitution can be more straightforward for systems with only a few variables, but it can be more tedious and involve complex algebraic manipulations for larger systems.
3. Elimination: This method involves manipulating the equations to eliminate one variable, then using the resulting equation to solve for the remaining variable(s). Elimination is often preferred when dealing with systems of linear equations in which coefficients can be easily manipulated to cancel out a variable. It can be more efficient when working with systems that involve multiple equations and variables.
The choice of method depends on the specific situation, personal preference, and familiarity with each method. It's important to consider the given equations, the complexity of the system, and the desired accuracy or efficiency when deciding which method to use.