Answer:
No real roots.
General Formulas and Concepts:
<u>Pre-Algebra</u>
- Order of Operations: BPEMDAS
<u>Algebra I</u>
- Standard Form: ax² + bx + c = 0
- Quadratic Formula:
![x=\frac{-b\pm\sqrt{b^2-4ac} }{2a}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-b%5Cpm%5Csqrt%7Bb%5E2-4ac%7D%20%7D%7B2a%7D)
<u>Algebra II</u>
Step-by-step explanation:
<u>Step 1: Define</u>
-3x² + 2x = 1
<u>Step 2: Rewrite in Standard Form</u>
- Subtract 1 on both sides: -3x² + 2x - 1 = 0
<u>Step 3: Define</u>
a = -3
b = 2
c = -1
<u>Step 4: Find roots</u>
- Substitute in variables:
![x=\frac{-2\pm\sqrt{2^2-4(-3)(-1)} }{2(-3)}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-2%5Cpm%5Csqrt%7B2%5E2-4%28-3%29%28-1%29%7D%20%7D%7B2%28-3%29%7D)
- Exponents:
![x=\frac{-2\pm\sqrt{4-4(-3)(-1)} }{2(-3)}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-2%5Cpm%5Csqrt%7B4-4%28-3%29%28-1%29%7D%20%7D%7B2%28-3%29%7D)
- Multiply:
![x=\frac{-2\pm\sqrt{4-12} }{-6}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-2%5Cpm%5Csqrt%7B4-12%7D%20%7D%7B-6%7D)
- Subtract:
![x=\frac{-2\pm\sqrt{-8} }{-6}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-2%5Cpm%5Csqrt%7B-8%7D%20%7D%7B-6%7D)
Here we see that we cannot take the square root of a negative number. We will get no real roots and only imaginary ones.
Answer: x=6
Step-by-step explanation:
1) add 1/8 to both sides
2) divide both sides by 1/4
3) 1.5/.25= 6
The answer is 144.44 because the circumference of a circle is pi X diameter
Answer:
Speed of the first train = 365 mph
Speed of the second train = 356.2 mph
Step-by-step explanation:
Let speed of First train = a
Let speed of the second train = b
The sum of the speeds of two trains is 721.2 miles per hour.
a + b = 721.2 mph
If the speed of the first train is 8.8mph faster than that of the second train
a = b + 8.8 mph
We substitute b + 8.8 mph for a
a + b = 721.2 mph
b + 8.8 mph + b = 721.2 mph
2b + 8.8 mph = 721.2 mph
2b = 721.2 mph - 8.8 mph
2b = 712.4 mph
b = 712.4 mph/2
b = 356.2 mph
a = b + 8.8 mph
a = 356.2 mph + 8.8 mph
a = 365 mph
Just use the Pythagorean Theorem
(9 +x)^2 = 15^2 + x^2
x^2 + 18x + 81 = 225 + x^2
18x = 144
x = 8
So the three sides of the triangle are
15, 8 and 17