Answer:
Step-by-step explanation:
What this question is asking of you is what is the greatest common divisor of 12 and 15. Or, what is the biggest number that divides both 12 and 15.
in order to find this we have to split each number into it's prime components.
for 12 they are 2,2 and 3 (
2
⋅
2
⋅
3
=
12
)
and for 15 they are 3 and 5 (
3
⋅
5
=
15
)
Out of those two groups (2,2,3) and (3,5) the only thing in common is 3, so 3 is the greatest common divisor. That tells us that the greatest number of groups that can exist and have the same number of girls and the same number of boys for each group is 3.
Now to find out how many girls and boys there are going to be in each group we divide the totals by 3, so:
12
3
=
4
girls per group, and
15
3
=
5
boys per group.
(just as a thought exercise, if there were 16 boys, the divisors would have been (2,2,3) and (2,2,2,2), leaving us with 4 groups [
2
⋅
2
] of 3 girls [12/4] and 4 boys [16/4] )
Answer:
Step-by-step explanation:
step 1
Find the slope m
The formula to calculate the slope between two points is equal to
we have the ordered pairs
(10,5) and (2,-3)
substitute the values
step 2
Find the equation of the line in slope intercept form
we have
substitute and solve for b
The linear function is equal to
Answer:
The domain of the transformed function is:
[0,∞)
Step-by-step explanation:
We know that the domain of a function is the set of all possible values where the function is defined i.e. the possible x-values.
Now we are given a parent function f(x) as:
Now, it is given that the function f(x) is transformed three units downward.
So, the resulting function g(x) is given as:
Hence, the function g(x) is defined for all x≥0.
( Since, the square root function is not defined for negative real numbers and for rest values it is defined)
Hence, the domain is given as:
[0,∞)
Answer:
Step-by-step explanation:
Answer:
g(x), and the maximum is 5
Step-by-step explanation:
for given function f(x), the maximum can be seen from the shown graph i.e. 2
But for the function g(x), maximum needs to be calculated.
Given function :
g (x) = 3 cos 1/4 (x + x/3) + 2
let x=0 (as cosine is a periodic function and has maximum value of 1 at 0 angle)
g(x)= 3 cos1/4(0 + 0) +2
= 3cos0 +2
= 3(1) +2
= 3 +2
= 5 !
