The quadratic formula, has a part we call the "discriminant" defined by the variables that are inside the square root, and is denotated by "delta":
<span>Δ=<span>b2</span>−4ac</span>
Whenever we solve a quadratic equation that is complete and we analyze the discriminant, we can get 3 scenarios:
<span>if→Δ>0<span>=></span>∃<span>x1</span>,<span>x2</span>/a<span>x2</span>+bx+c=0</span>
This just means: "if the discriminant is greater than zero, there will exist two x-intercepts"
And for the second scenario:
<span>if→Δ=0→∃<span>xo</span>/a<span>x2</span>+bx+c=0</span>
This means: "if the discriminant is equal to zero, there will be one and only one x-intercept"
And for the last scenario:
<span>if→Δ<0→∃x∉R/a<span>x2</span>+bx+c=0</span>
This means that :"if the discriminant is less than zero, there will be no x-intercepts"
So, if we take your excercise and analyze the the discriminant:
<span>3<span>x2</span>+7x+m=y</span>
we will find the values that satisfy y=0 :
<span>3<span>x2</span>+7x+m=0</span>
And we'll analyze the discriminant:
<span>Δ=<span>72</span>−4(3)(m)</span>
And we are only interested in the values that make the discriminant equal zero:
<span><span>72</span>−4(3)(m)=0</span>
All you have to do is solve for "m".
Total Volume would be 6 + 4 = 10 pints
Let's calculate the volume of alcohol in final solution:
20% * 6 = 1.2 pints
10% * 4 = .4 pints
Total = 1.6 pints of alcohol in 10
Percentage = (1.6/10) * 100 = 16 per cent.
answer is A
F(x) = {(8, 3), (4, 1), (0, -1), (-4, -3)}
f(x) = ¹/₂x - 1
f(x) = ¹/₂x - 1
y = ¹/₂x - 1
x = ¹/₂y - 1
+ 1 + 1
x + 1 = ¹/₂y
2(x + 1) = 2(¹/₂y)
2(x) + 2(1) = y
2x + 2 = y
2x + 2 = f⁻¹(x)
2x + 2 = g(x)
g(x) = {(3, 8), (1, 4), (-1, 0), (-3, -4)}
g(x) = 2x + 2
It is given here that there is 1/3 probability of professional baseball player will get a hit. Hence if at least three hits are gained out of 5 attempts, the calculation goes: 5C3* (1/3)^3*(2/3)^2 + 5C4* (1/3)^4*(2/3)^1 +5C5 *<span>(1/3)^5*(2/3)^0 equal to 0.21. </span>
