Answers:
- Domain is (-4, 3]
- Range is (-5, 5]
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Explanation:
The domain is the set of allowed x input values, aka the set of all allowed x coordinates of the points. We see that . It might help to draw vertical lines through the endpoints until you reach the x axis. Note the open hole at x = -4 to indicate we do not include this as part of the domain (hence the lack of "or equal to" for the first inequality sign).
The interval then can be condensed into the shorthand form (-4, 3] which is the domain in interval notation.
It says: x is between -4 and 3. It can't equal -4 but it can equal 3.
So the use of parenthesis versus square brackets tells the reader which endpoint is included or not.
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The range describes all possible y outputs. We see that y = 5 is the largest it gets and y = -5 is the lower bound. It might help to draw horizontal lines through the endpoints until you reach the y axis. The open hole means -5 is not part of the range.
The range as a compound inequality is . This condenses into the shorthand of (-5, 5] which is the range in interval notation.
Verbally, the range is the set of y values such that y is between -5 and 5. It can't equal -5 but it can equal 5.
We are given that there
will be (1/2) a litre after the first pouring, so considering two successive
pourings (n and (n+1)) with 1/2 litre in each before the nth pouring occurs:
1/2 × (1/n) = 1/(2n)
1/2 - 1/(2n) = (n-1)/2n
1/2 + 1/(2n) = (n+1)/2n
(n-1)/2n and (n+1)/2n in
each urn after the nth pouring
Then now consider the
(n+1)th pouring
(n+1)/2n × 1/(n+1) =
1/(2n)
(n+1)/(2n) - 1/(2n) =
n/(2n) = 1/2
Therefore this means that after
an odd number of pouring, there will be 1/2 a litre in each urn
Since 1997 is an odd
number, then there will be 1/2 a litre of water in each urn.
Answer:
<span>1/2</span>
Divide 400 by 10 and you will get 40. It's not hard
Answer:
Step-by-step explanation:
just apply to the power of 2 to every term
-4 times -4 is 16
x^2 to power of 2 is 2 times 2 so x^4
y^2 is y^2
a^3 to power of 2 is 3 x 2 = 6 so a^6
16x^4y^2a^6
Answer:
x ≤ 2
Step-by-step explanation:
Most of the properties of equality also apply to inequalities. The exception is multiplication (or division) by a negative number. An equation can be multiplied or divided by any number you like (except division by 0) and it will remain true. <em>An inequality must have the relation symbol reversed when multiplying or dividing by a negative number</em>.
Here, we don't run into that issue, because we can solve this by dividing both sides by the coefficient of x, which is +3.
(3x)/3 ≤ 6/3
x ≤ 2 . . . . . . . simplify