A)
The discriminant (radicand) is √(b^2-4ac), let us call this "d" for the discriminant.
If:
d<0, there are no real solutions (though there are two imaginary ones)
d=0, there is one real solution
d>0, there are two real solutions.
In this case, d=12^2-4(4)9
d=144-144
d=0
So there is one real solution.
B)
9x^2-30x+25=0
9x^2-15x-15x+25=0
3x(3x-5)-5(3x-5)=0
(3x-5)(3x-5)=0
(3x-5)^2=0
x=5/3
x=1 2/3
Answer:
1 < x < 17
Step-by-step explanation:
9, 8
Third side should be less than 9 + 8 = 17
And it should be greater than 9 - 8 = 1
The coefficient 'a' for the quadratic term is a = 3
The coefficient 'b' for the linear term is b = -2
The coefficient 'c' is 0
Step-by-step explanation :
The given expression is,
To solve this problem we are using quadratic formula.
The general quadratic equation is,
Formula used :
Now we a have to solve the above equation and we get the value of 'x'.
a = 3, b = -2, c = 0
The coefficient 'a' for the quadratic term is a = 3
The coefficient 'b' for the linear term is b = -2
The coefficient 'c' is 0
Answer:
The length of the third side is between 16 inches and 64 inches.
Step-by-step explanation:
The length of a side of a triangle is between the sum and the difference of the lengths of the other two sides.
First, we need both sides in the same units. Let's convert feet to inches.
2 ft * (12 in.)/(ft) = 24 in.
The sides measure 24 inches and 40 inches.
Now we add and subtract the two lengths.
40 in. + 24 in. = 64 in.
40 in. - 24 in. = 16 in.
The length of the third side is between 16 inches and 64 inches.
Answer:
See below
Step-by-step explanation:
Recall that we need to use the equation y=a(x-h)^2+k. This means that h=-2 instead of 2 otherwise it would've been (x-2)^2-6. So Renaldo made the mistake of identifying h as 2 instead of -2. The second mistake Renaldo made is that since k=-6, there should be a vertical shift of 6 units down not 2.
