Let x be the width of the cardboard (which means the length of the cardboard is x+88), then the dimensions of the box are:
Length = [(x + 88) - 2(33)]
Width = x - 2(33)
Heighth = 33
Volume = length · width · heighth
144,144 = [(x + 88) - 2(33)] · [x - 2(33)] · 33
144,144 = (x+22)(x-66)(33)
4368 = (x+22)(x-66)
4368 = x² - 44x - 1452
0 = x² - 44x - 5820
use the quadratic formula to calculate that x = 101
Answer: cardboard width = 101, cardboard length = 189
Answer:
1/4 or 0.25
Step-by-step explanation:
I did this on a graphic calculator so i can't really explain, but I hope this helps! :)
You want to get familiar with what the slope-intercept form equation means. even though the discussion board covers some of this... slope-intercept is y = mx + b, and in it, x and y are a point on your graph (x, y), m is the slope, and b is your y-intercept. in word problems, any constant will typically be b.
but, really, to answer this word problem, you don't have to think so hard about y = mx + b. just read the problem and bring your information together:
"the venue will cost $1500 to rent for an evening"
"$25 per person"
so they only gave you two bits of information, and you just have to decide where they fit. if the venue costs $1500 for an evening, that's a fixed cost--the 1500 isn't going to go up or down depending on the number of people at the charity event. it stays. you're paying 1500 regardless, even if 2 people show up. because the discussion board states that b should represent your starting amount, you're automatically $1500 in the hole, because you have to spend that much to get the venue. you will, however, write it as a positive integer, because the question wants you to calculate the total cost, by my understanding--you're adding the cost of the people with the cost of the venue.
$25 is not a fixed amount. if it's $25 per person, then if 2 people come, it costs $50, if 3 people arrive, it costs $75. this cost is dependent upon the number of people, which you can call "x"
with that information, write any other equation you would for a word problem:
y = 25x + 1500
that's your equation, and it just so happens that this equation is in y = mx + b format. the x-value represents the number of people who show up for the charity; the y-value represents the overall cost.
and you need three solutions for this equation--which, luckily, is a quick and easy process!! choose an x-value and solve for y.
y = 25x + 1500
when x = 1...
y = 25(1) + 1500
y = 25 + 1500
y = 1525
ordered pair: (1, 1525)
when x = 2...
y = 25(2) + 1500
y = 50 + 1500
y = 1550
ordered pair: (2, 1550)
when x = 3...
y = 25(3) + 1500
y = 75 + 1500
y = 1575
ordered pair: (3, 1575)
i hope that helped!!
Slope = (y2 - y1)/(x2 - x1) = (10 - 70)/(5 - (-15)) = -60/(5 + 15) = -60/20 = -3
