:
Step-by-step explanation:
2x^2-3x-5=y
(2x-5)(x+1)=y
(2x-5)(x+1)=0
2x-5=0
2x=5
x=2.5
x+1=0
x=-1
you have an even degree (2) and a positive coefficient (2)
therefore as x---> -∞, f(x)----> +∞
also, as x----> +∞, f(x)----> +∞
also notice that this is a parabola that opens upwards so both "ends" approach positive infinity
plot the x-intercepts, find the vertex using h=-b/2a and substituting this value into the equation to find k and make a table of values to graph the parabola unless you only want a rough sketch of the graph-you know the x-intercepts and you found the vertex using h=-b/2a
<h2><u>Answer:</u></h2>
x=(nπ/2)±15
x=(2nπ+90)/3
x=90-2nπ
<h2><u>Steps:</u></h2>
cos3x+sin2x-sin6x+cos5x=0
(cos3x+cos5x)+(sin2x-sin6x)=0
equation(1)
<u>Use formula:</u>
<u>So in equation (1),if c=3x ,d=5x,C=2x,D=6x</u>
》2cos{(c+d)/2}.cos{(c-d)/2}+2cos{(C+D)/2}.sin{(C-D)/2}=0
》2cos{(3x+5x)/2}.cos{(3x-5x)/2}+2cos{(2x+6x)/2}.sin{(2x-6x)/2}=0
》2cos(4x).cos(-x)+2cos(4x).sin(-2x)=0
》2cos(4x)[cos(-x)+sin(-2x)]=0
》2cos(4x)[cos(x)-sin(2x)]=0
<u>1)</u><u> </u><u>Either:</u>
2cos(4x)=0
cos(4x)=0/2
cos(4x)=0
cos(4x)=cos(90)
General solution for such case is:X=2n±a
So,
4x=2nπ±90
x=(2nπ±90)/4
x=(nπ/2)±15
<u>2) Or:</u>
cos(x)-sin(2x)=0
cos(x)=sin(2x)
General solution for such case is:X=2n±a
So,
x=2nπ±(90-2x)
x=2nπ±90±2x
x±2x=2nπ±90
<u>Take +ve sign,</u>
x+2x=2nπ+90
3x=2nπ+90
x=(2nπ+90)/3
<u>Take -ve sign,</u>
x-2x=2nπ-90
-x=2nπ-90
x=(2nπ-90)/(-1)
x=90-2nπ
Answer:
43/30
Step-by-step explanation:
Chad should buy 6 2-pound bag of peanuts.
Without having any left over, multiply 5/6 by 6 to get 5.
Answer:
58
Step-by-step explanation:
We are given the arithmetic sequence:-
-12,-7,-2,3,...
First, find the common difference which we can obtain by:-
Check:-
-7-(-12) = -7+12 = 5
-2+7 = 5
3+2 = 5
Therefore, our common difference is 5.
<u>G</u><u>e</u><u>n</u><u>e</u><u>r</u><u>a</u><u>l</u><u> </u><u>A</u><u>r</u><u>i</u><u>t</u><u>h</u><u>m</u><u>e</u><u>t</u><u>i</u><u>c</u><u> </u><u>T</u><u>e</u><u>r</u><u>m</u>
Since we want to find the 15th term, substitute a1 = -12, n = 15 and d = 5.