Answer:
See explanation!
Step-by-step explanation:
We know that the maximum miles allowed before oil change is 5,000miles (<u>thus Kaci can drive less or up to 5,000 miles but not more</u>).
Kaci has already driven 3,450miles since last oil change.
Inequalities are typically employed to show a relating or comparative relationship between expressions and can be identified by the sybolism of less, more or/and equal to (i.e. 
, 
, 
, 
).
Let us denote the miles Kaci can drive before oil changing again by 
, then we can write the following inequality:
solving for the remaining miles allowed
Thus Kaci can drive up to and including 1550 miles before chaging car oil again.
There are 2 options to solve that.
1. The first one is by derivatives.
f(x)=x^2+12x+36
f'(x)=2x+12
then you solve that for f'(x)=0
0=2x+12
x=(-6)
you have x so for (-6) solve the first equation, then you find y
y=(-6)^2+12*(-6)+36=(-72)
so the vertex is (-6, -72)
2. The second option is to solve that by equations:
for x we have:
x=(-b)/2a
for that task we have
b=12
a=1
x=(-12)/2=(-6)
you have x so put x into the main equation
y=(-6)^2+12*(-6)+36=(-72)
and we have the same solution: vertex is (-6, -72)
For next task, I will use the second option:
y=x^2-6x
x=(-b)/2a
for that task we have
b=(-6)
a=1
x=(6)/2=3
you have x so put x into the main equation
y=3^2+(-6)*3=(--9)
and we have the same solution: vertex is (3, -9)
Hello!
Given the two points, 
and 
, and to find the distance between these two points is found by using the formula:
is assigned to one the points, in this case, is (4, 1).
is assigned to other point, which is (9, 1).
Then, plug in these values into the formula and solve.
Therefore, the distance between the two points is 5.
Answer:
The exact value of its surface area = 144π m²
The exact value of its volume = 288π m³
Step-by-step explanation:
∵ The diameter of the sphere is 12m
∴ The radius of the sphere = 12 ÷ 2 = 6m
∵ The surface area of the sphere = 4πr²
∴ The surface area = 4 × π × 6² = 144π m²
∵ The volume of the sphere = 4/3 πr³
∴ The volume = 
= 288π m³
