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Dima020 [189]
2 years ago
9

Three good friends are in the same algebra class. Their scores on a recent test are three consecutive even integers whose sum is

270
Mathematics
1 answer:
klio [65]2 years ago
6 0

Let the lowest score be x.

<u>The 3 consecutive even scores are:</u>

1st score = x

2nd score = x + 2

3rd score = x + 4

-

<u>Sum of their score is 270:</u>

x + (x + 2) + (x + 4) = 270

-

<u>Solve x:</u>

x + (x + 2) + (x + 4) = 270

x + x + 2 + x + 4 = 270

3x + 6 = 270

3x = 264

x = 88

-

<u>Find their scores:</u>

1st score = x = 88

2nd score = x + 2 = 88 + 2 = 90

3rd score = x + 4 = 88 + 4 = 92

-

Answer: The scores are 88, 90 and 92

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Answer:

See Below.

Step-by-step explanation:

We are given the graph of <em>y</em> = f'(x) and we want to determine the characteristics of f(x).

Part A)

<em>f</em> is increasing whenever <em>f'</em> is positive and decreasing whenever <em>f'</em> is negative.

Hence, <em>f</em> is increasing for the interval:

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Part B)

<em>f</em> has a relative maximum at <em>x</em> = <em>c</em> if <em>f'</em> turns from positive to negative at <em>c</em> and a relative minimum if <em>f'</em> turns from negative to positive to negative at <em>c</em>.

<em>f'</em> turns from positive to negative at <em>x</em> = -2 and <em>x</em> = 1.

And <em>f'</em> turns from negative to positive at <em>x</em> = -1 and <em>x</em> = 3.

Hence, <em>f</em> has relative maximums at <em>x</em> = -2 and <em>x</em> = 1, and relative minimums at <em>x</em> = -1 and <em>x</em> = 3.

Part C)

<em>f</em> is concave up whenever <em>f''</em> is positive and concave down whenever <em>f''</em> is negative.

In other words, <em>f</em> is concave up whenever <em>f'</em> is increasing and concave down whenever <em>f'</em> is decreasing.

Hence, <em>f</em> is concave up for the interval (rounded to the nearest tenths):

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And concave down for the interval:

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Part D)

Points of inflections are where the concavity changes: that is, <em>f''</em> changes from either positive to negative or negative to positive.

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<em>f'</em> has extrema at (approximately) <em>x</em> = -1.5, 0, and 2.2.

Hence, <em>f</em> has inflection points at <em>x</em> = -1.5, 0, and 2.2.

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Answer:

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From the diagram in the question above,

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