The two solutions are:
![\boxed{a_{1}=\frac{3}{2} \ and \ a_{2}=-\frac{6}{5}}](https://tex.z-dn.net/?f=%5Cboxed%7Ba_%7B1%7D%3D%5Cfrac%7B3%7D%7B2%7D%20%5C%20and%20%5C%20a_%7B2%7D%3D-%5Cfrac%7B6%7D%7B5%7D%7D)
<h2>
Explanation:</h2>
Here we have the following equation:
![10a^2-3a=18](https://tex.z-dn.net/?f=10a%5E2-3a%3D18)
To write this quadratic equation in Standard form, let's subtract 18 from both sides, so:
![10a^2-3a-18=18-18 \\ \\ 10a^2-3a-18=0](https://tex.z-dn.net/?f=10a%5E2-3a-18%3D18-18%20%5C%5C%20%5C%5C%2010a%5E2-3a-18%3D0)
The problem states:
<em>Solve for a using the quadratic formula </em><em>or</em><em> completing the square.</em>
So, let's choose the quadratic formula:
![For: \\ \\ ax^2+bx+c=0 \\ \\ \\ The \ quadratic \ formula \ is: \\ \\ x_{12}=\frac{-b \pm \sqrt{b^2-4ac}}{2a}](https://tex.z-dn.net/?f=For%3A%20%5C%5C%20%5C%5C%20ax%5E2%2Bbx%2Bc%3D0%20%5C%5C%20%5C%5C%20%5C%5C%20The%20%5C%20quadratic%20%5C%20formula%20%5C%20is%3A%20%5C%5C%20%5C%5C%20x_%7B12%7D%3D%5Cfrac%7B-b%20%5Cpm%20%5Csqrt%7Bb%5E2-4ac%7D%7D%7B2a%7D)
So:
![a_{12}=\frac{-(-3) \pm \sqrt{(-3)^2-4(10)(-18)}}{2(10)} \\ \\ a_{12}=\frac{3 \pm \sqrt{9+720}}{20} \\ \\ a_{12}=\frac{3 \pm \sqrt{729}}{20} \\ \\ a_{12}=\frac{3 \pm 27}{20} \\ \\ \\ Two \ solutions: \\ \\ a_{1}=\frac{3 + 27}{20} =\frac{30}{20} \therefore \boxed{a_{1}=\frac{3}{2}} \\ \\ \\ a_{2}=\frac{3 - 27}{20} =\frac{-24}{20} \therefore \boxed{a_{2}=-\frac{6}{5}}](https://tex.z-dn.net/?f=a_%7B12%7D%3D%5Cfrac%7B-%28-3%29%20%5Cpm%20%5Csqrt%7B%28-3%29%5E2-4%2810%29%28-18%29%7D%7D%7B2%2810%29%7D%20%5C%5C%20%5C%5C%20a_%7B12%7D%3D%5Cfrac%7B3%20%5Cpm%20%5Csqrt%7B9%2B720%7D%7D%7B20%7D%20%5C%5C%20%5C%5C%20a_%7B12%7D%3D%5Cfrac%7B3%20%5Cpm%20%5Csqrt%7B729%7D%7D%7B20%7D%20%5C%5C%20%5C%5C%20a_%7B12%7D%3D%5Cfrac%7B3%20%5Cpm%2027%7D%7B20%7D%20%5C%5C%20%5C%5C%20%5C%5C%20Two%20%5C%20solutions%3A%20%5C%5C%20%5C%5C%20a_%7B1%7D%3D%5Cfrac%7B3%20%2B%2027%7D%7B20%7D%20%3D%5Cfrac%7B30%7D%7B20%7D%20%5Ctherefore%20%5Cboxed%7Ba_%7B1%7D%3D%5Cfrac%7B3%7D%7B2%7D%7D%20%5C%5C%20%5C%5C%20%5C%5C%20a_%7B2%7D%3D%5Cfrac%7B3%20-%2027%7D%7B20%7D%20%3D%5Cfrac%7B-24%7D%7B20%7D%20%5Ctherefore%20%5Cboxed%7Ba_%7B2%7D%3D-%5Cfrac%7B6%7D%7B5%7D%7D)
<h2>Learn more:</h2>
Solving for a variable: brainly.com/question/14198414#
#LearnWithBrainly
Answer:
A≈12.57
Step-by-step explanation:
Using the formulas
A=πr2
d=2r
Solving for A
A=1
4πd2=1
4·π·42≈12.56637
X=1, because they both have the same height (y), so they'll cross each other!
We can form two ratios to help us solve this:
(2x+6):10 = (x+6):8
(2x+6) (x+6)
--------- = --------
10 8
Cross multiply:
8(2x+6) = 10(x+6)
Foil:
16x + 48 = 10x + 60
Move like variables to the same side:
16x - 10x = 60 - 48
6x = 12
x = 2
Line AE = 2x+6
Plug 2 for x into the equation: 2(2) + 6 = 10
Hope this helps, and May the Force Be With You!
-Jabba
Answer:
0
Step-by-step explanation
The company started off with $10 in the first section(quarter). They lost (subtract)$15 in the second section, In the third section they lost (subtract)$20. In the final section they gained (plus) a profit of $25.
10-15-20+25=0