I really appreciate all the work the people on this site put in this, seriously, all of you are heroes and I can't thank you enough for how much you helped me. Thanks in advance once again if you can help me because I absolutely suck at linear equations and especially graphs <3 Also I'm not English so my grammar might be a tad off I apologize for that
1a. A family wants to buy carpet for their stairs and they ask two companies for the price. p is in the following formulas the price and t is the amount of stairsteps.
Company 1 uses p=25t
Company 2 uses p=140+15t
The stairs of the family consists of 14 stairsteps. Which of the two companies would be the cheapest option?
1b. Their neighbours also want to carpet their stairs. They have a few more stairsteps than the other family. Which option would be cheaper?
2a. There are two equatations: b=4a+8 and b=-2a+30
What would be the graphs of both equations in the same coordinate system. Use for a the values 0 to 10.
2b. How do you solve the inequality of -2a+30>12 ? And how do you find this answer in the graph?
2c. What would be the coordinates of the break-even point? (Keep the fractions in the answer please so I can understand it better :"))
2d. For which value of a would the formula b=4a+8 give higher results than b=-2a+30 ?
3. Calculate the points of intersection of the following two pairs of equations.
y=5x+6 en y=9x-32
y=-0,5x+1,5 en y=-4(x-3)
1 (a) Note that if we set the equations equal we have
25t = 140 + 15t subtract 15t from both sides
10t = 140 divide both sides by 10
t = 14 equalizes the cost
So....for the first family, either option is the same
But...since the slope of the first function - 25 - is greater than the other function - 15 ...this option will be more expensive after 14 steps.....so for the second family, the second option is better than the first
2....For this one....I'm using x for a and y for b
So we have
y = 4x + 8
y = -2x +30
Here's the graph : https://www.desmos.com/calculator/25etgvd1ja
-2x + 30 > 12 subtract 30 from both sides
-2x > -18 divide both sides by -2 and reverse the inequality sign
x < 9
Here's the graphical solution : https://www.desmos.com/calculator/wqeiyuxd89
2c.....break even point.....set the functions equal and solve for x
4x + 8 = -2x + 30 add 2x to both sides, subtract 8 from both sides
6x = 22 divide both sides by 6
x = 22/6 = 11/3
And y = 4(11/3) + 8
y = 44/3 + 24/3
y = 68/3
Here's the graph with the break-even point : https://www.desmos.com/calculator/iwcgpjjzqf
2d......we want to solve this
4x + 8 > -2x + 30
6x > 22
x > 22/6
x > 11/3