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!!
Answer:
32.5 feet
Step-by-step explanation:
This situation forms a right triangle. We are given the distance from the base of the tower (long leg of the triangle) and are asked to find the height (short leg of the triangle).
With this information, we can use the tan ratio, opposite over adjacent, to find the height of the tower.
tan 18 = 
Multiply each side by 100:
(100) tan 18 = x
Simplify and round to the nearest tenth:
32.49 = x
32.5 = x
So, the height of the tower is approximately 32.5 feet
Triangle ABC and triangle DCE are congruent, so line DE = line AB
Use the cosine rule to find angle ACB
Angle ACB = 48.1°
What is the number down their?
