Answer:
3.5ft
Step-by-step explanation:
To calculate the volume of something, you need to know the formula. Length x width x height. You already know the width, and the height, so you need to find the length.
4ft x 6ft x 3.5ft = 84ft^3
This one is prime. The sum of two squares doesn't factor.
The more interesting case is q^2-1, which factors into (q-1)(q+1).
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:
r = - 
Step-by-step explanation:
Given that r varies inversely as t , then the equation relating them is
r = 
← k is the constant of variation
To find k use the condition t = - 6 when r = - 2, then
- 2 = 
( multiply both sides by - 6 )
12 = k, thus
r = 
← equation of variation
when t = - 7, then
r = 
= -
