Call the number of hamburgers 'H' and the number of cheeseburgers 'C'.
We are told that:
and
by back substitution:
or
thus
and so
To check:
CHECKS
Solve your equation step-by-step.
x2+4x+4=0
Factor left side of equation.
(x+2)(x+2)=0
Set factors equal to 0.
x+2=0
or
x+2=0
x=−2
<span> To get an explicit formula, we need to find an expression which gives the n-th term without having to compute earlier terms in the sequence. Looking at the numbers, and from the recursive formula, we see that the sequence is built by subtracting n from the previous term. This is similar to the triangular number sequence 1,3,6,10,15,... which has the explicit formula a_n = n(n+1)/2. In our case we are subtracting n from the previous term, so we multiply by -1/2 instead of 1/2. However, we also need to add a constant term to reproduce the numbers of the sequence. We can write a_1 = -1(2)/2 + c = 8. Therefore, c = 9.
So the explict formula is:
a_n = -n(n+1)/2 + 9</span>
Answer: Answer A 13
Step-by-step explanation: 20% of 65 is 13
Answer: Gonzo runs 0.435 seconds faster than Kermit.
Step-by-step explanation:
This is just a simple subtraction problem.
To make both numbers even in place value, add a 0 (zero) in the back of 12.35 to make it 12.350.
Then you simply subtract using regrouping methods:
12.350
11.915 -
————
0.435
Now let’s check our answer:
11.915
0.435. +
—————
12.35
As a result, Gonzo ran 0.435 seconds faster than Kermit.