Answer:
There is a total of 66 different fruit salads.
Step-by-step explanation:
One fruit salad differs from the other only in the amount of pieces of certain fruit put in it. In order to easier denote fruit pieces we introduce these notations:
A-how many apples are put into the salad;
B-how many bananas are put into the salad;
C-how many cranberries are put into the salad.
Since she can freely choose the number of pieces of each fruit, we have these conditions for the variables A, B and C:
-
(she cannot choose a negative number of pieces) 
(because she can get the total of 10 pieces of fruit)
Another condition for forming the salad is that the salad must consist of exactly 10 pieces of fruit, hence we have this equation to solve:
but we must obtain the non-negative integer solutions of this equation.
That is equivalent to calculating the number of r-combinations of the multi-set S with objects of k different types with infinite repetition numbers.
The formula for obtaining the number of such r-combinations is:
We have that 
and that 
and we can observe the repetition number as infinite since she can create a fruit salad with only one piece of fruit and the repetition number in such cases is the maximum 10. Finally, we have that the total number of fruit salads equals:
.
Answer:
y=-4/9x+11/3
Step-by-step explanation:
Reminder: slope intercept form is y=mx+b where m= slope and b=y intercept
Two points are given; (6,1) and (-3,5)
First, find the slope
Reminder: slope is y2-y1/x2-x1
You can plug the numbers given into the equation to get 5-1/-3-6 which equals 4/-9
Now, we can use slope point form which is y-y1=m(x-x1)
Once again, plugging the numbers in (any one of the two points will work) will get
y-1=4/-9(x-6)
Simplifying it will get y=-4/9x+11/3.
t(x)=-5x+3
t(-1)=-5*(-1)+3=5+3=8
s(x)=3x-4
s(t(-1))=s(8)=3*8-4=24-4=20
answer is 20
The order is -1.4, -3/5, 1/4, 0.9, and 9/2. So
D is the correct answer
7sin²x-14sin x+2=-5
7sin²x-14sin x+7=0
Then: sin x=t
7t²-14t+7=0
We have to solve this square equation:
t=[14⁺₋√(196-196)]/14=14/14=1
t=1 ⇒sin x=1
x=sin⁻¹ 1=π/2 + 2kπ (k=...-3,-2,-1,0,1,2,3...)
For example:
if K=0 ⇒ x=π/2
7(sin²π/2)-14sin π/2+2=7(1)²-14(1)+2=7-14+2=-5
Answer: x=π/2 + 2kπ (k is an integer)
