Determine whether the first literal expression is equal to the second literal expression.b - a, a - (-b)
A. Yes
B. No
Answer: B
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Solve the problem.The growth rate of a certain tree (in feet) is given by y = 
+ e-t2/2 , where t is time in years. Estimate the total growth of the tree through the end of the second year by using Simpson's rule. Use 2 subintervals. Round your answer to the nearest hundredth.
A. 2.34 ft B. 3.41 ft C. 5.11 ft D. 3.68 ft
A rancher wishes to fence a rectangular area of 500 sq. ft. He wants to use only whole-number dimensions.What dimensions will require the least amount of fencing? [Remember the area of a rectangle is A = l X w and the perimeter is P = 2(l + w).]
What will be an ideal response?
Decide whether or not the points are the vertices of a right triangle.Consider the three points A = (7, 7), B = (9, 11), C = (11, 10). Determine whether the triangle ABC is a right triangle. Explain your reasoning.
A. The side lengths of triangle ABC are d(A, B) = 3
, d(A, C) = 5, d(B, C) = 
.
[d(A, B)]2 + [d(B, C)]2 = (3
)2 + (
)2 = 18 + 5 = 23
[d(A, C)]2 = 52 = 25
Since [d(A, C)]2 ? [d(A, B)]2 + [d(B, C)]2, triangle ABC is not a right triangle.
B. The side lengths of triangle ABC are d(A, B) = 2
, d(A, C) = 5, d(B, C) = 
.
[d(A, B)]2 + [d(B, C)]2 = (2
)2 + (
)2 = 20 + 5 = 25
[d(A, C)]2 = 52 = 25
Since [d(A, C)]2 = [d(A, B)]2 + [d(B, C)]2, triangle ABC is a right triangle.
C. The side lengths of triangle ABC are d(A, B) = 2
, d(A, C) = 2
, d(B, C) = 2.
[d(A, B)]2 + [d(B, C)]2 = (2
)2 + 22 = 20 + 4 = 24
[d(A, C)]2 = (2
)2 = 24
Since [d(A, C)]2 = [d(A, B)]2 + [d(B, C)]2, triangle ABC is a right triangle.
D. The side lengths of triangle ABC are d(A, B) = 2
, d(A, C) = 5, d(B, C) = 2.
[d(A, B)]2 + [d(B, C)]2 = (2
)2 + 22 = 20 + 4 = 24
[d(A, C)]2 = 52 = 25
Since [d(A, C)]2 ? [d(A, B)]2 + [d(B, C)]2, triangle ABC is not a right triangle.
Solve.The effective yield from a grove of miniature pear trees is described by the equation E = x(700 - x), where x is the number of pear trees per acre. What is the maximum effective yield? How many pear trees per acre should be planted to achieve the maximum yield?
A. Maximum yield = 30,625 number of trees per acre planted = 175 B. Maximum yield = 122,500 number of trees per acre planted = 350 C. Maximum yield = 122,500 number of trees per acre planted = 175 D. Maximum yield = 122,500 number of trees per acre planted = 700