Given:
Expression is

To prove:
If r is any rational number, then
is rational.
Step-by-step explanation:
Property 1: Every integer is a rational number. It is Theorem 4.3.1.
Property 2: The sum of any two rational numbers is rational. It is Theorem 4.3.2.
Property 3: The product of any two rational numbers is rational. It is Exercise 15 in Section 4.3.
Let r be any rational number.
We have,

It can be written as

Now,
3, -2 and 4 are rational numbers by property 1.
is rational by Property 3.
are rational by Property 3.
is rational by property 2.
So,
is rational.
Hence proved.
Answer:
D
Step-by-step explanation:
To obtain f(g(x)) substitute x = g(x) into f(x), that is
f(10 - 5x)
= (10 - 5x)² + 5 ← expand (10 - 5x)²
= 100 - 50x - 50x + 25x² + 5 ← collect like terms
= 25x² - 100x + 105 → D
Answer:
36ft³
Step-by-step explanation:
Bottom rectangular prism: 2x2x6=24
Top rectangular prism: 2x2x3=12
24+12=36ft³
Answer:
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