A machine produces 264 bolts in 42 minutes. At the same rate, how many minutes would it take to produce 308 bolts?
1 answer:
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Answer:
The graph crosses the x-axis 2 times
The solutions are x = -8 & x = 4
Step-by-step explanation:
Qaudratics are in the form
Where a, b, c are constants
Now, let's arrange this equation in this form:
Where
a = 1
b = 4
c = -32
We need to know the discriminant to know nature of roots. The discriminant is:
If
- D = 0 , we have 2 similar root and there is 2 solutions and that touches the x-axis
- D > 0, we have 2 distinct roots/solutions and both cut the x-axis
- D < 0, we have imaginary roots and it never cuts the x-axis
Let's find value of Discriminant:
Certainly D > 0, so there are 2 distinct roots and cuts the x-axis twice.
We get the roots/solutions by factoring:
Thus,
The graph crosses the x-axis 2 times
The solutions are x = -8 & x = 4
Answer:
C
Step-by-step explanation:
We can use the factored form of the quadratic equation, given by:
Where <em>a</em> is the leading coefficient and <em>p</em> and <em>q</em> are the zeros.
We have zeros <em>x</em> = -2 and <em>x</em> = 3. So, let <em>p</em> = -2 and <em>q</em> = 3:
Next, we are given that our <em>y-</em>intercept is (0, -30).
In other words, when <em>x</em> = 0, <em>y</em> = -30. So:
Solve for <em>a:</em>
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Hence, our factored equation is:
For the standard form, expand:
Simplify:
Distribute:
Our answer is C.
