Answer:
f(x) = (x + 3) - 7
Step-by-step explanation:
the original function f(x) = x - 9 is the parent function f(x) = x shifted down 9 units
from f(x) = x - 9, we are told that the function is shifted 2 units up, this is a vertical shift. so we add 2 to -9
-9 + 2 = -7
we now have f(x) = x - 7
next we are told that the function is shifted 3 units to the left<em>. </em>this is a horizontal shift. a horizontal shift looks similar to this:
f(x) = (x ± b)
if a function is shifted to the <em>left</em>, we would use an addition sign. if it was going to the <em>right</em>, we would use a subtraction sign
the function looks like the following when we apply the above knowledge
f(x) = (x + 3) - 7 this would be our new function
Answer:
13, 15
Step-by-step explanation:
Let x represent the smaller of the two integers. Then the larger is x+2. The required relation is ...
x² = 154 +(x +2) . . . . . . the smaller squared is 154 more than the larger
x² -x = 156 . . . . . . . . . . subtract x
x² -x +1/4 = 156.25 . . . complete the square
(x -1/2) = √156.25 = 12.5 . . . . take the square root
x = 13 . . . . . add 1/2
The two integers are 13 and 15.
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<em>Check</em>
13² -15 = 169 -15 = 154 . . . as required
Answer:
The correct selections are:
B) After the donation collection period, compare the average or total amount collected from each of the two treatment groups.
C) A placebo is not being used
F) Randomly select 500 donors to receive the literature and 500 donors to receive the phone call.
Step-by-step explanation:
What this question requires from you, is to identify the correct characteristics of the study described. Let us explain why each of the selections was made.
B) After the donation collection period, compare the average or total amount collected from each of the two treatment groups: The purpose of the study is to determine the difference in the effectiveness of two methods of fundraising. Therefore at the end of the study, the average total amount raised from each group will be compared to determine which was more effective.
C) A placebo is not being used: Placebos are sham treatments used in a control group without their knowledge. The placebos do not produce any effect similar to the results anticipated the actual treatment. Here, no group is given sham treatment, there is no "control" group given placebos hence placebos are not used.
F) Randomly select 500 donors to receive the literature and 500 donors to receive the phone call: To remove any form of bias in the study, the selection of the groups is done at random, and the number of participants in each group is the same, so as to maintain uniformity during the comparison.
20 + 12x = 56
12x = 56 - 20
12x = 36
x = 36/12
x = 3
Bethany's monthly gym fee is $ 20
Bethany also pays $ 3 for a towel fee each visit
Answer:
The answer is 14.8256594724
Step-by-step explanation: