Answer:
(x-8)(x+7)
Step-by-step explanation:
using quadratic formula we have
x= ![\frac{-b+-\sqrt{b^{2}-4*a*c}}{2*a}](https://tex.z-dn.net/?f=%5Cfrac%7B-b%2B-%5Csqrt%7Bb%5E%7B2%7D-4%2Aa%2Ac%7D%7D%7B2%2Aa%7D)
we have:
x^2-x-56=0
a= 1 b=-1 c=-56
so we have:
x=(-(-1)+-sqrt(1^1-4*(1)*(-56)))/(2*1)
x=1+-sqrt(1-4*(-56))/(2)
x=(1+-sqrt(225))/2
x=(1+-15)/2
so we have the roots:
x1=(1+15)/2 =8
x2=(1-15)/2=-7
so the answer is (x-8)(x+7)
Answer
The missing length is 10
Step-by-step explanation:
Represent the missing length with x
The sides of the given shape are directly proportional.
Mathematically:
(15 + x) to (12 + 8) and x to 7
Represent as a ratio:
![(15 + x) : (12 + 8) = x : 8](https://tex.z-dn.net/?f=%2815%20%2B%20x%29%20%3A%20%2812%20%2B%208%29%20%3D%20x%20%3A%208)
![15 + x : 20= x : 8](https://tex.z-dn.net/?f=15%20%2B%20x%20%3A%2020%3D%20x%20%3A%208)
Convert to fraction
![\frac{15 + x}{20} = \frac{x}{8}](https://tex.z-dn.net/?f=%5Cfrac%7B15%20%2B%20x%7D%7B20%7D%20%3D%20%5Cfrac%7Bx%7D%7B8%7D)
Cross Multiply:
![(15 + x)*8 = 20 * x](https://tex.z-dn.net/?f=%2815%20%2B%20x%29%2A8%20%3D%2020%20%2A%20x)
![120 + 8x = 20x](https://tex.z-dn.net/?f=120%20%2B%208x%20%3D%2020x)
Collect Like Terms
![20x - 8x = 120](https://tex.z-dn.net/?f=20x%20-%208x%20%3D%20120)
![12x = 120](https://tex.z-dn.net/?f=12x%20%3D%20120)
Solve for x
![x = \frac{120}{10}](https://tex.z-dn.net/?f=x%20%3D%20%5Cfrac%7B120%7D%7B10%7D)
![x = 10](https://tex.z-dn.net/?f=x%20%3D%2010)
<em>The length of the missing side is 10</em>
Answer:
1024
Step-by-step explanation:
The discriminant of y=ax^2+bx+c is b^2-4ac
given
9x^2+10x+0
a=9
b=10
c=0
discriminant=10^2-4(9)(0)=100-0=100
the discriminant is 100