Find the vertex, focus, and directrix of the parabola. Graph the equation.(x + 3)2 = -8(y + 3)

A. vertex: (3, 3)
focus: (1, 3)
directrix: x = 5

B. vertex: (-3, -3)
focus: (-5, -3)
directrix: x = -1

C. vertex: (3, 3)
focus: (3, 1)
directrix: y = 5

D. vertex: (-3, -3)
focus: (-3, -5)
directrix: y = -1


Answer: D

Mathematics

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Assume that the given mutual fund investment earns monthly returns that are reinvested and subsequently earn at the same rate. Find the beginning value of the investment, first monthly return, or effective annual rate of return as indicated. Find the first monthly return.

A. $2764.87 B. $595.18 C. $2705.35 D. $59.52

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Productivity and yield of cultivated crops are often reduced by insect pests. The following graph shows the relationship between the yield of a certain crop, f(x), as a function of the density of aphids x. (Aphids are small insects that suck plant juices.) Here, f(x) is measured in kilograms/ 4,000 square meters, and x is measured in hundreds of aphids/bean stem. By computing the slopes of the respective tangent lines, estimate the rate of change of the crop yield with respect to the density of aphids when that density is 200 aphids/bean stem and when it is 800 aphids/bean stem.

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A. - 0.5 when it is 200 aphids/bean stem,- 1.333 when it is 800 aphids/bean stem
B. 00.5 when it is 200 aphids/bean stem,01.333 when it is 800 aphids/bean stem
C. 02 when it is 200 aphids/bean stem,00.75 when it is 800 aphids/bean stem
D. - 2 when it is 200 aphids/bean stem,- 0.75 when it is 800 aphids/bean stem

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Solve the problem.Samuel consumed 2174 calories of food on Monday, 2335 calories on Tuesday, and 1856 calories on Wednesday. In order for Samuel's average calorie intake to equal a daily average of 2000 calories, how many calories of food must he consume on Thursday?

A. 2091 calories B. 2122 calories C. 1752 calories D. 1635 calories

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Solve the equation.(ex)x ? e21 = e10x

A. {7} B. {3} C. {-3, -7} D. {3, 7}

Mathematics