Answer:
One possible equation is 
, which is equivalent to 
.
Step-by-step explanation:
The factor theorem states that if 
(where 
is a constant) is a root of a function, 
would be a factor of that function.
The question states that 
and 
are 
-intercepts of this function. In other words, 
and 
would both set the value of this quadratic function to 
. Thus, 
and 
would be two roots of this function.
By the factor theorem, 
and 
would be two factors of this function.
Because the function in this question is quadratic, and would be the only two factors of this function. In other words, for some constant 
(
):
.
Simplify to obtain:
.
Expand this expression to obtain:
.
(Quadratic functions are polynomials of degree two. If this function has any factor other than and , expanding the expression would give a polynomial of degree at least three- not quadratic.)
Every non-zero value of corresponds to a distinct quadratic function with -intercepts and . For example, with 
:
, or equivalently,
.
Answer:
4 minutes
Step-by-step explanation:
2 will cook together for 1 minute. and it will take an additional 2 minutes to cook the 3rd pancake.
To find your constant of variation, you just need to figure out what you multiply the x by in order to get f(x). In other words, what do you multiply the 3 by to get 6? What do you multiply the 7 by to get 14? Another way to think of it is to divide f(x) by the x to get your constant.
Answer:
5 more men
Step-by-step explanation:
10 men do a job in 6 hours.
To do the job in 2 hours, 1/3 of the time, you need 3 times as many men.
30 men do a job in 2 hours.
To do the job in twice the time, 4 hours, you need half the men.
15 men do a job in 4 hours.
15 men - 10 men = 5 men
You need 5 more men.
