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polet [3.4K]
3 years ago
10

The greatest integer that satisfies the inequality 1.6−(3−2y)<5

Mathematics
1 answer:
Cerrena [4.2K]3 years ago
6 0

Solve the inequality 1.6-(3-2y)<5.

1. Rewrite this inequality without brackets:

1.6-3+2y<5.

2. Separate terms with y and without y in different sides of inequality:

2y<5-1.6+3,

2y<6.4.

3. Divide this inequality by 2:

y<3.2

4. The greatest integer that satisfies this inequality is 3.

Answer: 3.

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(r o g)(2) = 4

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Step-by-step explanation:

Given

g(x) = x^2 + 5

r(x) = \sqrt{x + 7}

Solving (a): (r o q)(2)

In function:

(r o g)(x) = r(g(x))

So, first we calculate g(2)

g(x) = x^2 + 5

g(2) = 2^2 + 5

g(2) = 4 + 5

g(2) = 9

Next, we calculate r(g(2))

Substitute 9 for g(2)in r(g(2))

r(q(2)) = r(9)

This gives:

r(x) = \sqrt{x + 7}

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r(9) = \sqrt{16}{

r(9) = 4

Hence:

(r o g)(2) = 4

Solving (b): (q o r)(2)

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r(x) = \sqrt{x + 7}

r(2) = \sqrt{2 + 7}

r(2) = \sqrt{9}

r(2) = 3

Next, we calculate g(r(2))

Substitute 3 for r(2)in g(r(2))

g(r(2)) = g(3)

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g(3) = 14

Hence:

(q o r)(2) = 14

8 0
2 years ago
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