Answer: base = 12 cm
Height = 7 cm
Step-by-step explanation:
Let b represent the base of the rectangle.
Let h represent the height of the rectangle.
The base of a rectangle is 5 cm more than its height. It means that
b = h + 5
if we reduce the height by 2cm the area of the new rectangle is 60 cm square. It means that
b(h - 2) = 60- - - - - - - - -1
Substituting b = h + 5 into equation 1, it becomes
(h + 5)(h - 2) = 60
h² - 2h + 5h - 10 = 60
h² + 3h - 10 - 60 = 0
h² + 3h - 70 = 0
h² + 10h - 7h - 70 = 0
h(h + 10) - 7(h + 10)
h - 7 = 0 or h + 10 = 0
h = 7 or h = - 10
Since the height cannot be negative, then
h = 7 cm
b = h + 5 = 7 + 5
b = 12 cm
The answer should be $87666.67
Answer:
scale factor 1:300
Step-by-step explanation:
Answer: 0 in the 1-20 range, 1 in the 21-40 range, 3 in the 41-60 range, 2 in the 61-80 range, and 2 in the 81-100 range.
Explanation:
No change, 0 in the 1-20 range
33: 1 in the 21-40 range
43, 44, 52: 3 in the 41-60 range
75, 79: 2 in the 61-80 range
86, 89: 2 in the 81-100 range.
In the table and chart, we have let x represent numbers of Rock CDs and y represent numbers of Rap CDs.
a) The purple dots represent feasible solutions. Their coordinates are listed in the table (for coordinates on the lines) and as a list of points (for points between the lines).
b) The feasible region for total time in hours is shaded blue.
c) The feasible regiion for total cost is shaded red.
d) The overlap of the two regions is shaded purple. The combinations that are feasible are purple dots in that region.
e) The equations used are listed at the left side of the chart. The equations are labeled by color. (≤112 is the cost equation; ≥75 is the hours equation)
ea) The area that is feasible with respect to both constraints is doubly-shaded.
eba) Too much money is spent to the right of the red line.
ebb) Too few hours are used to the left of the blue line.
f) The line for the desired profit is parallel to the "hours" line, but has x-intercept 10 and y-intercept 6. All the points shown except the two on the lower line will give the desired profit.
g) The higher profit line goes through the points (3, 7) and (8, 4). Those two combinations and the points on or near the upper line above y=4 will meet the higher profit requirement.