Answer:
B
Step-by-step explanation:
Yes this is a function only one x assign to only 1 y value not multiple. This is in fact a absolute value function. Also it passes the vertical line test.
• The value of the discriminant ,D= -16
,
• The solution to the quadratic equation is
![x=\frac{1+2i}{5}\text{ or }\frac{1-2i}{5}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B1%2B2i%7D%7B5%7D%5Ctext%7B%20%20%20%20%20or%20%20%20%20%7D%5Cfrac%7B1-2i%7D%7B5%7D)
Step - by - Step Explanation
What to find?
• The discriminant d= b² - 4ac
,
• The solution to the quadratic equation.
Given:
5x² - 2x + 1=0
Comparing the given equation with the general form of the quadratic equation ax² + bx + c=0
a=5 b=-2 and c=1
Uisng the quadratic formula to solve;
![x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-b%5Cpm%5Csqrt%5B%5D%7Bb%5E2-4ac%7D%7D%7B2a%7D)
The discriminant D=b² - 4ac
Substitute the values into the discriminant formula and simplify.
D = (-2)² - 4(5)(1)
D = 4 - 20
D = -16
We can now proceed to find the solution of the quadratic equation by substituting into the quadratic formula;
![x=\frac{-(-2)\pm\sqrt[]{-16}}{2(5)}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-%28-2%29%5Cpm%5Csqrt%5B%5D%7B-16%7D%7D%7B2%285%29%7D)
Note that:
√-1 = i
![x=\frac{2\pm\sqrt[]{16\times-1}}{10}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B2%5Cpm%5Csqrt%5B%5D%7B16%5Ctimes-1%7D%7D%7B10%7D)
![x=\frac{2\pm\sqrt[]{16}\times\sqrt[]{-1}}{10}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B2%5Cpm%5Csqrt%5B%5D%7B16%7D%5Ctimes%5Csqrt%5B%5D%7B-1%7D%7D%7B10%7D)
![x=\frac{2\pm4i}{10}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B2%5Cpm4i%7D%7B10%7D)
![x=\frac{2}{10}\pm\frac{4i}{10}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B2%7D%7B10%7D%5Cpm%5Cfrac%7B4i%7D%7B10%7D)
![x=\frac{1}{5}\pm\frac{2}{5}i](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B1%7D%7B5%7D%5Cpm%5Cfrac%7B2%7D%7B5%7Di)
![x=\frac{1\pm2i}{5}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B1%5Cpm2i%7D%7B5%7D)
That is;
Answer:
between 78 and 102 texts and more than 78 text messages.
Step-by-step explanation:
the range of it is 102-178, so its between there, and its more than 78 as well if the range goes up to 102
Use the point slope formula. then, substitute the values inside the formula.
x1 =3
y1= -2
m = 23
y -y1 = m ( x - x1)
y - (-2) = 23 (x - 3)
y + 2 = 23 ( x - 3)
Answer:
A = 236,000 (1.04)^t
population in 2009 : 335,902 people
Step-by-step explanation:
Hi, to answer this question we have to apply an exponential growth function:
A = P (1 + r) t
Where:
p = original population
r = growing rate (decimal form) = 4/100 = 0.04
t= years passed from 2000
A = population after t years
Replacing with the values given:
A = 236,000 (1+ 0.04)^t
A = 236,000 (1.04)^t
Population in 2009.
t = 2009-2000 = 9
A = 236,000 (1.04)^9
A = 335,902 people
Feel free to ask for more if needed or if you did not understand something.