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".
Answer:
B. 10 1/2 feet
Step-by-step explanation:
We are told that she taped 7 boxes.
We are also told that she uses 1 1/2 feet of tape to close each box.
Therefore, the length of tape she will need to use for the 7 boxes will be the product of 7 boxes and 1 1/2 feet of tape per box:
L = 1 1/2 * 7 = 3/2 * 7 = 21/2 = 10 1/2 feet.
She will need to use 10 1/2 feet of tape.
Answer:
x=8 or x=−8
Step-by-step explanation:
I graphed the 4 points and connected the dots. (Sorry I'm not able to show this)
I then realized it was some type of trapezoid however, I wasn't sure which kind of trapezoid (regular or isosceles) so I googled the properties of both and concluded that it makes a regular trapezoid.
