Give a direct proof of the following theorem.

Premise 1: If you exercise, your health will improve.
Premise 2: If your health improves, you will be able to accomplish more.
Premise 3: If you set aside time, you can exercise.
Theorem: If you set aside time, you will be able to accomplish more.
Proof: STATEMENTS REASONS


Mathematics

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Sketch the graph of the function and find the domain and range.f(x) = (x - 2)2 - 1

A. domain: all real numbers
range: y ? -1

B. domain: all real numbers
range: y ? 2

C. domain: all real numbers
range: y ? -2
 
D. domain: all real numbers
range: y ? -1

Mathematics

Solve.Given f(x) = x2 - 18x + 68, find all values for x for which f(x) ? 0.

A. (-?, 9 - ] ? [9 + , ?)
B. (-?, -] ? [, ?)
C. [9 -  , 9 +  ]
D. (-?, 9 -  ) ? (9 + , ?)

Mathematics

Use a calculator to find the acute angle ?, to the nearest degree, that satisfies the equation.cos ? = 0.9

A. 31° B. 9° C. 26° D. 0°

Mathematics

Solve the problem.A particular substance decays in such a way that it loses half its weight each day. How much of the substance is left after 9 days if it starts out at 128 grams?

A.  g
B.  g
C. 2 g
D. 4 g

Mathematics