Answer:
see below
Step-by-step explanation:
It works well to think about what these compound inequalities mean. One way to do that is to graph them, or to imagine what the graph of them looks like.
Since the result is a single inequality (x < 2), the compound will be "and" with x < 2 being more restrictive, or will be "or" with x < 2 being the least restrictive of completely overlapping inequalities.
Of the choices offered, C is the one of interest.
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<em>Comment on other choices</em>
A has all real numbers as solutions except in the range 2 ≤ x ≤ 3.
B has no solutions
C simplifies to x < 2 . . . . the one we want
D simplifies to x < 4
Answer:
(x + 3)² + (y - 1)² = 80
Step-by-step explanation:
Circle equation: (x - h)² + (y - k)² = r²
We are given <em>h</em> and <em>k</em>, so we just plug that in:
(x + 3)² + (y - 1)² = r²
To find <em>r</em>, we need to use distance formula: between the center of the circle and the point on the circle. We should get √80 as <em>r</em>. We plug that in to get our answer:
(x + 3)² + (y - 1)² = 80
We are asked to perform the long division on the following expression.
Let us perform the long division.
So, we have
Quotient: q(x) = 19x^2 - 24x + 30
Remainder: r(x) = -32
Divisor: b(x) = x + 1
Therefore, the equivalent expression is
The 3rd option is the correct answer.
Answer: 4950
Step-by-step explanation:
The number of possible combinations of n things taken r at a time is given by :-
Total nonnegative integers less than 100 ={0,1,2,... ,99} = 100
So, the number of combinations of choosing 2 out of them =
So, the number of ways to choose a set of two nonnegative integers less than 100 = 4950