You only wrote one option, but luckily, those two fractions ARE equivalent!
We know that because if you multiply the denominator AND numerator by 4, you get 16/20.
Look at the beginning of the recursive formula:
It gives us the first value, which is 7. The second part means that for whatever term we want to find, we plug that in for 'n'. Say we want to find the second term, let's plug in 2 for 'n':
We are left with f(1), which is given as 7. So the second term is 7 and then we have the leftover blank. We already know that the second term is 13. 13 - 7 = 6.
Therefore, what must be missing from this recursive formula is + 6.
For the explicit function, we want to know what will give us these same values if we plugged in which term we want for 'n'. So if we plugged in 1 for 'n', we want to get 7, and if we plugged in 2 for 'n' we want to get 13, and so on. I can spot the similarity that all of these are additions of 1 to the multiples of 6. 6 * 1 = 6 + 1 = 7, 6 * 2 = 12 + 1 = 13, and so on. We could just write this as:
If you tried plugging in 1, you'd get 7, if you plugged 2 in, you'd get 13, and so on. So this is our explicit formula, the
2nd blank should be 6, and the
3rd blank should be + 1.
For the fourth blank, f(10) would just be plugging in 10 for 'n' into our formula, let's do this:
Multiply:
Add:
So
the 4th blank should be 61.
I'm assuming you mean students when you write stupids.
Give that x = students, the number of total students is equal to 9 more than 4 times x or:
4x + 9
Set that equal to 101 and solve.
The answer is 23
Answer:
270 seconds
Step-by-step explanation:
Melissa's time = x seconds
Abby's time = (x + 30) seconds
Abby walks at a speed of 8 feet per second, and Melissa walks at a speed of 9 feet per seconds.
But, speed =
For Abby,
8 =
distance = 8(x + 30) ................. 1
for Melissa,
9 =
distance = 9x ............. 2
From equations 1 and 2, for the same distance;
8(x + 30) = 9x
8x + 240 = 9x
x = 240 seconds
Abby's time = (x + 30)
= (240 + 30)
= 270 seconds
So that Abby has been walking for 270 seconds when both students had walked exactly the same distance.
Translating the given problem
into equation form:
Let A = volume of prism A
B = volume of prism B
C = volume of prism C
Eqn 1: A + B+ C = 518
Eqn 2: A = (1/3)B
Eqn 3: B = C
There are 3 equations and 3
unknowns, the system of linear can be solved. Using a calculator (preferably Casio
991-ES), yields:
A = 74 cu.ft
B = 222 cu.ft
C = 222 cu.ft