What would you use to represent the solution in an equation with a variable?
I would use the real line that goes from x belongs (-infinite, infinite).
What would you use to represent the solution in an equation with three variables?
To present the solution of an equation with three variables you need the XYZ coordinate system because you would generate a 3D graph because "because the number of variables is equal to the number of dimensions needed to graph the solution correctly".
Could you graph an equation that contains more than four variables?
It CAN NOT be done since the number of variables is equal to the number of dimensions that are needed to graph the solution correctly. Therefore, we can graph only up to three variables (three dimensions).
If you were given the graph of an equation with two variables in a coordinate plane, what would happen to the graph if all the values of y were increased by 1?
if all the values of y are increased by 1, the graph shifts by 1 unit to the right.
What would happen to the graph if all values of x were increased by 1?
If all values of x are increased by 1, the graph moves 1 unit up.
What would happen to the graph if all the <span> y-</span>values were multiplied by 2 or by 1/2?
If the values of y are multiplied by 1/2 then the slope of the graph is smaller so the graph looks wider.
If the values of y are multiplied by 2 then the slope of the graph is larger so the graph looks narrower.
Note that it said find "a" formula for P(x). We can infer from this as there are multiple possibilities.
In fact, there are many possible P(x) that fits the bill.
You got the most important part correct, namely
(x+5)(x-5)^2.
In general, P(x)=A(x+5)(x-5)^2 will work, but we need to satisfy also y-intercept of P(0)=-75.
If we expand the expression, we get
P(x)=A*x^3A-5A*x^2-25A*x+125A
=>
P(0)=125A.
So setting A=-3/5 => P(0)=-75 as required.
or
P(x)=-3/5(x+5)(x-5)^2
will satisfy all requirements.
It would be nice exercise for you to confirm that it is indeed the polynomial required.
Answer:
A. t < –15
Step-by-step explanation:
The temperature has to be less than -15
t < -15
Answer: 1
Explanation: Each child can have up to 13 balloons each. If all 4 children have 13 balloons, that leaves an extra balloon out. 13*4=52, which leaves the 1 extra balloon.
