Answer:
The height of the triangle is 6.5cm
Step-by-step explanation:
First of all we need to use the formula to calculate the area of a triangle:
a = area = 45.5 cm²
b = base = 14 cm
h = height
a = (b * h) / 2
we replace with the known values
45.5cm² = (14cm * h) / 2
45.5cm² * 2 = 14cm * h
91cm² / 14cm = h
6.5cm = h
The height of the triangle is 6.5cm
The first step is to draw the graph. Once we do this, we can easily see that the vertex is at (12,64), which means that the hourly profit of coffee sold is highest at 12 cups of coffee. The x-intercepts are at x = 4 and x = 20, which means that between 0 and 4 (inclusive) cups of coffee sold, and after 20 cups sold, there is no profit.
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Can’t answer the question without the data
Answer:
A) ![\frac{7}{8}a](https://tex.z-dn.net/?f=%5Cfrac%7B7%7D%7B8%7Da)
B)
Step-by-step explanation:
AB has length a and is divided by points P and Q into AP , PQ , and QB , such that AP = 2PQ = 2QB
A) Therefore, AP = 2QB
QB = AP/2
The midpoint of QB = QB/2 = (AP/2)/2 = AP/4
AP = 2PQ, Therefore PQ = AP/2
Since the length of AB = a
AB = AP + PQ + QB = a
AP + AP/2 + AP/2 = a
AP + AP = a
2AP = a
AP = a/2
The distance between point A and the midpoint of segment QB = AP + PQ + QB/2 = AP + AP/2 + AP/4 = 7/4(AP)
But AP = a/2
Therefore The distance between point A and the midpoint of segment QB = 7/4(a/2)= ![\frac{7}{8}a](https://tex.z-dn.net/?f=%5Cfrac%7B7%7D%7B8%7Da)
B)
the distance between the midpoints of segments AP and QB = AP/2 + PQ + QB/2 = AP/2 + AP/2 + AP/4 = 5/4(AP)
But AP = a/2
Therefore the distance between the midpoints of segments AP and QB = 5/4(AP) = ![\frac{5}{4} *\frac{a}{2}=\frac{5}{8}a](https://tex.z-dn.net/?f=%5Cfrac%7B5%7D%7B4%7D%20%2A%5Cfrac%7Ba%7D%7B2%7D%3D%5Cfrac%7B5%7D%7B8%7Da)