Does the line through (3, 7) and (-2, -5) intersect with the line through (4, 8) and (10, -2)?(1 point)
Responses
You cannot tell without a graph
You cannot tell without a graph
Yes…these lines are perpendicular
Yes…these lines are perpendicular
Yes…these lines are parallel
Yes…these lines are parallel
Yes…these lines are not parallel
Yes…these lines are not parallel
No…these lines are parallel
No…these lines are parallel
No…these lines are perpendicular
You cannot tell without a graph
n 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?
You have plans to attend 3 times this summer. Which option is best?
Monthly membership option:
Cost of membership = $90
Cost per visit = $15
Total cost for 3 visits = $90 + ($15 × 3) = $90 + $45 = $135
Single visit option:
Cost per visit = $28
Total cost for 3 visits = $28 × 3 = $84
Therefore, the single visit option is best.
You think you will visit probably about 8 times this summer. Which option is best?
Monthly membership option:
Cost of membership = $90
Cost per visit = $15
Total cost for 8 visits = $90 + ($15 × 8) = $90 + $120 = $210
Single visit option:
Cost per visit = $28
Total cost for 8 visits = $28 × 8 = $224
Therefore, the monthly membership option is best.
You have budgeted $150 for visiting the park this summer. Which option is best?
Monthly membership option:
Cost of membership = $90
Cost per visit = $15
Maximum number of visits within budget = (Budget - Cost of membership) / Cost per visit = ($150 - $90) / $15 = $60 / $15 = 4 visits
Single visit option:
Cost per visit = $28
Maximum number of visits within budget = Budget / Cost per visit = $150 / $28 ≈ 5.36 visits (rounded down to 5 visits)
Therefore, the monthly membership option is best.
How many visits would be approximately the break-even point where both options would cost about the same?
Monthly membership option:
Cost of membership = $90
Cost per visit = $15
Single visit option:
Cost per visit = $28
To find the break-even point, we need to determine the number of visits when the total cost for the monthly membership option is equal to the total cost for the single visit option.
Let's represent the number of visits as "x".
Total cost for monthly membership option = Cost of membership + (Cost per visit × x) = $90 + ($15 × x)
Total cost for single visit option = Cost per visit × x = $28 × x
We can set up the following equation to find the break-even point:
$90 + ($15 × x) = $28 × x
Simplifying the equation:
$90 = $28x - $15x
$90 = $13x
x ≈ 6.92
Therefore, at approximately 7 visits, both options would cost about the same.
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?
(2 points)
Answer both questions in ur own words
As an AI language model, I don't have preferences or personal experiences. 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.
Graphing involves plotting the equations on a coordinate plane to visually determine the intersection point or points where the equations meet. This method can be helpful for gaining a graphical understanding of the solution but may not be as precise or efficient when dealing with complex equations or large systems.
Substitution involves solving one equation for one variable and then substituting that expression into the other equation(s). By substituting the expression, you can solve for the remaining variable(s). This method can be straightforward and useful when dealing with equations that are already conveniently solved for a variable, but it may require several steps and become more complex for systems with many variables.
Elimination involves adding or subtracting the equations to eliminate one variable and then proceed to solve for the remaining variable(s). This method can be efficient for systems with multiple variables and equations, as it systematically eliminates variables and simplifies the system. However, it may involve rearranging equations and manipulating coefficients.
The preference for a particular method may depend on individual preferences, the complexity of the system, the availability of graphing tools or technology, and the desired level of precision. Some may find graphing helpful for visualizing the solution, while others may prefer the algebraic methods of substitution or elimination for their systematic approach and potential for efficient computation.
Overall, the choice of method may vary depending on the specific system of equations and the solver's comfort level and familiarity with the different approaches. It can be beneficial to understand and be proficient in all three methods to have the flexibility to choose the most appropriate method for each situation.
You cannot tell without a graph.
To determine if the line through (3, 7) and (-2, -5) intersects with the line through (4, 8) and (10, -2), we can use the slope-intercept form of a linear equation.
First, let's find the slope of the line through (3, 7) and (-2, -5). The slope formula is given by:
m = (y2 - y1) / (x2 - x1)
Using the coordinates, the slope becomes:
m1 = (-5 - 7) / (-2 - 3) = (-12) / (-5) = 12/5
Next, let's find the slope of the line through (4, 8) and (10, -2). The slope formula is the same:
m = (y2 - y1) / (x2 - x1)
Using the coordinates, the slope becomes:
m2 = (-2 - 8) / (10 - 4) = (-10) / 6 = -5/3
If the two lines are parallel, their slopes should be equal. Since m1 = 12/5 and m2 = -5/3, the slopes are not equal, therefore the lines are not parallel.
If the two lines are perpendicular, their slopes should be negative reciprocals of each other. In other words, the product of their slopes should be -1. Let's check:
m1 * m2 = (12/5) * (-5/3) = -12/3 = -4
Since the product of their slopes is not -1, the lines are not perpendicular either.
Thus, the correct answer is: No... these lines are not parallel and not perpendicular.