2100|2
1050|2
525|3
175|5
35|5
7|7
1|
2100 = 2 × 2 × 3 × 5 × 5 × 7 = 2² × 3 × 5² × 7
there would be 4 students
5 cookies for each
10 slices of pizza for each
hope this helps
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".
To find the slope,we can use the slope formula:
Where x and y are y coordinates and x coordinates respectively.
To find the answer, put any two points into the formula.
In this case, (1,5) and (0,-1) will be used:
x1 and y1 would be the x and y coordinate in the first point(1,5), while x2 and y2 would be the x and y coordinate in the first point (0,-1)
Therefore the answer is 6.
Hope it helps!
I will be glad to help you in the comments. I do need to know though, what is the class this is presented in? Is this algebra, or calculus? Depending on the class, we have different approaches.
