Ok so assume that if you have
xy=0 then x and y=0
-1/4(x^2-4x+3)>0
multiply both sides by -4 to clear fraction (-4/-4=1)
flip sign
x^2-4x+3<0
factor
(x-3)(x-1)<0
we know that (+) times (-)=(-) and
(-) times (-)=(+) so we don't want them to be both negative, we want different sign
we cannnot have 3 since it would be (0)(2)<0 which is false
we cannot have 1 either since (-2)(0)<0 is also false
lets see if the solution is in betwen 3 and 1 or outside of 3 and 1
ltry 2
2^3-4(2)+3<0
8-8+3<0
3<0
false
therefor it is outside ie
x>3 and x<1
Answer:
f(7) = 1.08
Step-by-step explanation:
Given that:
f(5) = 12
A geometric sequence that is defined recursively by the formula
.....[1 ] where, n is an integer and n> 0.
Substitute n = 6 in [1] we have;
![f(6) = 0.3 \cdot f(5)](https://tex.z-dn.net/?f=f%286%29%20%3D%200.3%20%5Ccdot%20f%285%29)
Using f(5) = 12 we have;
![f(6) = 0.3 \cdot 12](https://tex.z-dn.net/?f=f%286%29%20%3D%200.3%20%5Ccdot%2012)
⇒![f(6) =3.6](https://tex.z-dn.net/?f=f%286%29%20%3D3.6)
We have to find f(7).
Substitute n = 7 in [1] we have;
![f(7) = 0.3 \cdot f(6)](https://tex.z-dn.net/?f=f%287%29%20%3D%200.3%20%5Ccdot%20f%286%29)
Substitute the given values f(6) = 3.6 we have;
![f(7) = 0.3 \cdot 3.6](https://tex.z-dn.net/?f=f%287%29%20%3D%200.3%20%5Ccdot%203.6)
Simplify:
f(7) = 1.08
Therefore, the value of f(7)to the nearest hundredth is, 1.08
Answer:
<h2>
by SAS. </h2><h2>
Yes </h2>
Step-by-step explanation:
∠HIG and ∠JIK are vertical angles, so:
m∠HIG = m∠JIK
![\dfrac{GI}{IJ}=\dfrac{7.5}3=2.5\\\\\dfrac{HI}{IK}=\dfrac{2.5}1=2.5](https://tex.z-dn.net/?f=%5Cdfrac%7BGI%7D%7BIJ%7D%3D%5Cdfrac%7B7.5%7D3%3D2.5%5C%5C%5C%5C%5Cdfrac%7BHI%7D%7BIK%7D%3D%5Cdfrac%7B2.5%7D1%3D2.5)
![\left\{\dfrac{GI}{IJ}=\dfrac{HI}{IK}\quad\ \wedge\quad m\angle HIG=m\angle JIK\right\}\implies \triangle HIG\sim\triangle JIK\ \ by\ SAS](https://tex.z-dn.net/?f=%5Cleft%5C%7B%5Cdfrac%7BGI%7D%7BIJ%7D%3D%5Cdfrac%7BHI%7D%7BIK%7D%5Cquad%5C%20%5Cwedge%5Cquad%20m%5Cangle%20HIG%3Dm%5Cangle%20JIK%5Cright%5C%7D%5Cimplies%20%5Ctriangle%20HIG%5Csim%5Ctriangle%20JIK%5C%20%5C%20by%5C%20SAS)