Answer:
<h2>C) x = 22</h2><h2 />
Step-by-step explanation:
3x + 3x + 48 = 180
6x = 180 - 48
x = 132 / 6
x = 22
The answer is 113.1. Hope this helps
Circled numbers are prime factors comment if you need me to clarify anything
In both cases,
![AB^2=AD^2](https://tex.z-dn.net/?f=AB%5E2%3DAD%5E2)
(as a consequence of the interesecting secant-tangent theorem)
So we have
10.
![(4x+7)^2=(6x-3)^2](https://tex.z-dn.net/?f=%284x%2B7%29%5E2%3D%286x-3%29%5E2)
![16x^2+56x+49=36x^2-36x+9](https://tex.z-dn.net/?f=16x%5E2%2B56x%2B49%3D36x%5E2-36x%2B9)
![20x^2-92x-40=0](https://tex.z-dn.net/?f=20x%5E2-92x-40%3D0)
![5x^2-23x-10=0](https://tex.z-dn.net/?f=5x%5E2-23x-10%3D0)
![(5x+2)(x-5)=0\implies\boxed{x=5}](https://tex.z-dn.net/?f=%285x%2B2%29%28x-5%29%3D0%5Cimplies%5Cboxed%7Bx%3D5%7D)
(omit the negative solution because that would make at least one of AB or AD have negative length)
11.
![(4x^2-18x-10)^2=(x^2+x+4)^2](https://tex.z-dn.net/?f=%284x%5E2-18x-10%29%5E2%3D%28x%5E2%2Bx%2B4%29%5E2)
![16x^4-144x^3+244x^2+360x+100=x^4+2x^3+9x^2+8x+16](https://tex.z-dn.net/?f=16x%5E4-144x%5E3%2B244x%5E2%2B360x%2B100%3Dx%5E4%2B2x%5E3%2B9x%5E2%2B8x%2B16)
![15x^4-146x^3+235x^2+352x+84=0](https://tex.z-dn.net/?f=15x%5E4-146x%5E3%2B235x%5E2%2B352x%2B84%3D0)
![(x-7)(3x+2)(5x^2-17x-6)=0\implies\boxed{x=-\dfrac23\text{ or }x=7}](https://tex.z-dn.net/?f=%28x-7%29%283x%2B2%29%285x%5E2-17x-6%29%3D0%5Cimplies%5Cboxed%7Bx%3D-%5Cdfrac23%5Ctext%7B%20or%20%7Dx%3D7%7D)
(again, omit the solutions that would give a negative length for either AB or AD)
Answer:
option a)
0.286
Step-by-step explanation:
Given that,
number of red pens in cup = 5
number of black pens in cup = 10
number of pen randomly selected = 3
There are 5 red pens and 10 black pens. So there are 5 + 10 = 15 pens in all.
probability of having all red pens = (5/15 x 4/14 x 3/13)
= 2/91
probability of having all black pens = (10/15 x 9/14 x 8/13)
= 24/91
probability that all pen are of same colour = 24/91 + 2/91
= 2/7
≈ 0.286