The function f (x) = 2x - 5 is a linear function. Let g(x) represent f(x) after a horizontal translation 3 units to the right. W
1 answer:
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Answer:
.
Step-by-step explanation:
In any triangle, the sum of the lengths of any two sides should be strictly greater than the length of the third side. For example, if the length of the three sides are ,
, and
:
,
, and
.
In this question, the length of the sides are ,
, and
. The length of these sides should satisfty the following inequalities:
,
, and
.
Since , the inequality
is guarenteed to be satisfied.
Simplify to obtain the inequality
.
Similarly, simplify to obtain the inequality
.
Since needs to be a whole number, the greatest
that satisfies
would be
. Similarly, the least
that satisfies
would be
. Thus,
could be any whole number between
and
(inclusive.)
There are a total of distinct whole numbers between
and
(inclusive.) Thus, the number of possible whole number values for
would be
.
22. B) $65,000,000 per year.
23. B) Education.
Step-by-step explanation:
Step 1; To find the average rate of change in annual budget between the two given years. We divide the difference in values for the two years by the period in between the two years. In 2008, the budget was $358,708,000 while in 2010 it was $488,106,000. The period in between was 2 years i.e 2009 and 2010.
The average rate of change = =
= $64,699,000 per year.
So the average rate of change was $64,699,000 which approximately equals option B. $65,000,000.
Step 2; To find the human resources program's 2007 to 2010 ratio we divide the value in 2007 to the value in 2010. To find the other similar ratio, we divide the value in 2007 to the value in 2010 for all the other programs and determine which is closest to the human resources program.
Human resources program ratio = = 0.6841,
Agricultural / natural resources ratio = = 0.766,
Education's ratio = = 0.7196,
General government's ratio = = 0.9749,
Highways and transportation's ratio = = 0.827,
Public safety's ratio = = 0.5675.
The Human resources' program ratio is 0.6841 and the closest is Education's ratio which is 0.7196. So education is the answer.
Answer:
10 and 11
Step-by-step explanation:
Let the first integer be x.
Then the next one, since it's consecutive, must be (x+1).
The two equals 21. Thus:
Combine like terms:
Subtract 1 from both sides:
Divide both sides by 2:
So, the first integer is 10.
And the second integer is 10+1=11.