A keen obseravation is to write \(y=3^x\) and \(y^2=9^x\).
After some simplifying and expainding, we get 2 negative and 2 positive soluions and y=0.
The two positive solutions are y=\(\sqrt{3}\) and y=\(1\), thus the corresponding values of x are 0 and 1/2.
Notice that if we factor out \(2^{2017}\) from each term on the left side, we have:
\(2^{2017}(2^3-2^2-2^1+1)=2^{2017}(3)\)
Thus, the value of \(k\) is three(3).
Use the angle bisector theorem to find BY and YA. Y is the point of intersection between AB and CM.
After you get the values of BY, CY, and AY, use the intersecting chords theorem(Power of A Point) to find the value of YM.
Sorry for not being clear. Basically, you would want to test all the values around zero,
Hint: Before trying to use the rational root theorem, try to test some values of x and find a pattern in their behavior.
Test values from -4 to 4 and see how the polynomial reacts. If one of the values makes the equation equal to zero, you can synthetic division to continue on with the process.
4/6=6/7+x
28+4x=42
4x=14
x=14/4=7/2 units.
This also ties in for quadratic, cubics, and other higher degree polynomials.
Your equation is f(x)=2x^2-4x which is a parabola.
The axis of symmetry is -b / 2a, when -(-4)/2(2)=4/4=1. x=1 is the line of symmetry.
The vertex is 2(1)^2-4(1)=2-4=-2
(1,-2)-Vertex.
Compund Interest Formula: P(1+ r/n)^nt
P=Principal
r=interest rate, as a decimal.
n= number of times applied of a time period.
t=time in years
90000=P(1+0.03/2)^(2)(12)
Aproximately, P=62958.95......
2x^2+2y^2+10x-6y-18=0
2x^2+10x+2y^2-6y=18
2(x^2+5x)+2(y^2-3y)=18
(x^2+5x)+(y^2-3y)=9
(x^2+5x+6.25)+(y^2-3y+2.25)=9+6.25+2.25
(x+2.5)^2+(y-1.5)^2=17.5
17.5pi?
Use systems of equations to solve for each of the variables.
6a+4r=13.50
5a+7r=16.75
30a+20r=67.50
30a+42r=100.50
22r=33
r(orange)=$1.50
a(apple)=$1.25
(a): The probability is 9 C 5 / 2^9 = 126 / 512 = 63 / 256....
(b): C(9,0)+C(9,1)=1+9=10.
512-10=502
502/512=251/256.
n, n+2, n+4, n+6 are the given numbers.
4n+12=56
4n=44
n=11
Thus, the four consecutive odd integers are 11, 13, 15, 17.
Let w be the width of the room and that means the length is 7 plus the width.
w=w l=w+7
The perimeter is 34 meters, and that means 2(w)+2(w+7)=34, 2w+2w+14=34, 4w=20, w= five(5) meters.
Thus, the length of the room is 5+7=twelve(12) meters for option (D).
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