Answer:
first deal with g(-1)
y=4a - 3
a=4y -3 and now make y the subject again
a+3/4...now put it into f(a)
2(a +3/4) simplyifying
a+3/2 as yo final ans
Answer:
A strong positive correlation
Step-by-step explanation:
A strong correlation when the correlation coefficient is close to 1 or -1. If the correlation coefficient is close to positive 1, then it is a positive strong correlation coefficient. If the correlation coefficient is close to negative 1, then it is a negative strong correlation coefficient.
Since the function is a parabola and there are no discontinuities, the domain is all real numbers. To determine the range, the function has to be transformed into the vertex form.
The vertex form of the function is:
f(x) = -(x+1)2 +16
This means that the graph is facing downwards with the vertex at (-1,16).
So, the range is {y|y <span>≤ 16}</span>
The e vertex of the decagon will be in the top position after rotating it counterclockwise by 3 times the smallest angle of rotation.
Which vertex will be in the top position of the regular decagon?
A regular decagon has 10 sides of equal lengths with points labeled 'a' through 'j' clockwise. It is given that the point a is the top-left point. Hence, the the vertex which is in the the top position currently is 'b'.
Now, the smallest angle of rotation will be the angle between the two sides of the decagon.
In the first rotation by the smallest angle in counterclockwise direction, point 'c' will come to the top position. In the second rotation by the smallest angle in counterclockwise direction, point 'd' point will become the top most vertex. Finally, after the third similar rotation, 'e' vertex will be in the top position of the decagon. (Refer the attached diagram)
Learn more about decagon here:
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1. The first equation gives you an equivalent for y. Use that in the second equation.
.. 4x + (x+5) = 20
.. 5x + 5 = 20 . . . . collect terms
.. 5x = 15 . . . . . . . . subtract 5
.. x = 3 . . . . . . . . . . divide by 5
The first equation tells you how to find y.
.. y = x + 5
.. y = 3 + 5 = 8
The solution is (x, y) = (3, 8).
2. Add 2x to the first equation to get an expression for y.
.. y = 3 + 2x
Use this in the second equation.
.. 6x - 3(3 +2x) = 21
.. 6x - 9 - 6x = 21 . . . eliminate parentheses
.. -9 = 21 . . . . . . . . . . false. There is no solution to this set of equations.
3. Subtract 2y from the first equation to get an expression for x.
.. x = -1 - 2y
Use this in the second equation.
.. 4(-1 -2y) -4y = 20 . . . . . substitute for x
.. -4 -8y -4y = 20 . . . . . . . eliminate parentheses
.. -12y = 24 . . . . . . . . . . . . collect terms, add 4
.. y = -2 . . . . . . . . . . . . . . .divide by -12
.. x = -1 -2*(-2) . . . . . . . . . use the equation for x to find x
.. x = 3
The solution is (x, y) = (3, -2).
Word Problem
a) Let f and n represent the total dollar cost of membership in the "fee" and "no-fee" gyms. Let m represent the number of months of membership.
.. f = 150 + 35m . . . . $150 plus $35 for each month
.. n = 60m . . . . . . . . . $60 each month
b) The costs will be the same when f = n.
.. f = n
.. 150 +35m = 60m
.. 150 = 25m . . . . . . . . . subtract 35m
.. 6 = m . . . . . . . . . . . . . divide by 25
The cost of membership will be the same after 6 months.
The cost will be $60*6 = $150 +$35*6 = $360.
c) If Cathy cancels in 5 months, the no-fee gym will cost less.
.. n = 60*5 = 300
.. f = 150 +35*5 = 325
