Answer:
(-4,-7)
(4,7)
(-4,-5)
(1,-1)
Step-by-step explanation:
Look at the left side of the polygon. Since they are both real numbers, we can use those to set up a proportion:
16:12=(x-1):6
Now, we can cross multiply and solve:
96=12(x-1)
96=12x-12
108=12x
9=x
The value of x is 9
Hope this helped!
Answer:
see explanation
Step-by-step explanation:
(1)
The common ratio r of a geometric sequence is
r =
=
, so
=
( cross- multiply )
(x + 1)² = x(x - 1) ← expand both sides
x² + 2x + 1 = x² - x ( subtract x² - x from both sides )
3x + 1 = 0 ( subtract 1 from both sides )
3x = - 1 ( divide both sides by 3 )
x = - ![\frac{1}{3}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B3%7D)
(2)
r =
=
=
= - ![\frac{1}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D)
(3)
If - 1 < r < 1 then the sequence will converge
r = -
meets this criteria , thus the sequence is convergent
Solution to equation
for all real values of x is
.
<u>Step-by-step explanation:</u>
Here we have ,
. Let's solve :
⇒ ![cosxtanx - 2 cos^2 x=-1](https://tex.z-dn.net/?f=cosxtanx%20-%202%20cos%5E2%20x%3D-1)
⇒ ![cosx(\frac{sinx}{cosx}) - 2 cos^2 x=-1](https://tex.z-dn.net/?f=cosx%28%5Cfrac%7Bsinx%7D%7Bcosx%7D%29%20-%202%20cos%5E2%20x%3D-1)
⇒ ![sinx = 2 cos^2 x-1](https://tex.z-dn.net/?f=sinx%20%3D%202%20cos%5E2%20x-1)
⇒ ![sinx = 2 (1-sin^2x)-1](https://tex.z-dn.net/?f=sinx%20%3D%202%20%281-sin%5E2x%29-1)
⇒ ![sinx = 1-2sin^2x](https://tex.z-dn.net/?f=sinx%20%3D%201-2sin%5E2x)
⇒ ![2sin^2x+sinx-1=0](https://tex.z-dn.net/?f=2sin%5E2x%2Bsinx-1%3D0)
By quadratic formula :
⇒ ![sinx = \frac{-b \pm \sqrt{b^2-4ac} }{2a}](https://tex.z-dn.net/?f=sinx%20%3D%20%5Cfrac%7B-b%20%5Cpm%20%5Csqrt%7Bb%5E2-4ac%7D%20%7D%7B2a%7D)
⇒ ![sinx = \frac{-1 \pm \sqrt{1^2-4(2)(-1)} }{2(2)}](https://tex.z-dn.net/?f=sinx%20%3D%20%5Cfrac%7B-1%20%5Cpm%20%5Csqrt%7B1%5E2-4%282%29%28-1%29%7D%20%7D%7B2%282%29%7D)
⇒ ![sinx = \frac{-1 \pm3}{4}](https://tex.z-dn.net/?f=sinx%20%3D%20%5Cfrac%7B-1%20%5Cpm3%7D%7B4%7D)
⇒ ![sinx = \frac{1}{2} , sinx =-1](https://tex.z-dn.net/?f=sinx%20%3D%20%5Cfrac%7B1%7D%7B2%7D%20%2C%20sinx%20%3D-1)
⇒ ![sinx = sin\frac{\pi}{6} , sinx = sin\frac{3\pi}{2}](https://tex.z-dn.net/?f=sinx%20%3D%20sin%5Cfrac%7B%5Cpi%7D%7B6%7D%20%2C%20sinx%20%3D%20sin%5Cfrac%7B3%5Cpi%7D%7B2%7D)
⇒ ![x=\frac{\pi}{6} , x=\frac{3\pi}{2}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B%5Cpi%7D%7B6%7D%20%2C%20x%3D%5Cfrac%7B3%5Cpi%7D%7B2%7D)
But at
we have equation undefined as
. Hence only solution is :
⇒ ![x=\frac{\pi}{6}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B%5Cpi%7D%7B6%7D)
Since , ![sin(\pi -x)=sinx](https://tex.z-dn.net/?f=sin%28%5Cpi%20-x%29%3Dsinx)
⇒ ![x=\pi -\frac{\pi}{6} = \frac{5\pi}{6}](https://tex.z-dn.net/?f=x%3D%5Cpi%20-%5Cfrac%7B%5Cpi%7D%7B6%7D%20%3D%20%5Cfrac%7B5%5Cpi%7D%7B6%7D)
Now , General Solution is given by :
⇒ ![x=2k\pi + \frac{\pi}{6} , x=2k\pi + \frac{5\pi}{6}](https://tex.z-dn.net/?f=x%3D2k%5Cpi%20%2B%20%5Cfrac%7B%5Cpi%7D%7B6%7D%20%20%2C%20x%3D2k%5Cpi%20%2B%20%5Cfrac%7B5%5Cpi%7D%7B6%7D)
Therefore , Solution to equation
for all real values of x is
.
Heya! Princess Kimmie ![\star](https://tex.z-dn.net/?f=%5Cstar)
Let the Direct Variation Equation of Given Ordered pairs be : y = nx
Given : y = 4.8 when x = 4
Substituting the above values in our Equation, we get :
⇒ 4.8 = n × 4
⇒ ![n = \frac{4.8}{4} = 1.2](https://tex.z-dn.net/?f=n%20%3D%20%5Cfrac%7B4.8%7D%7B4%7D%20%3D%201.2)
⇒ The Equation is y = 1.2x
Option 3 is the Answer ![\star](https://tex.z-dn.net/?f=%5Cstar)