He should have added 1 to both sides to make the -1 on the right go to 0.
Then it would be 0 + m = -16 + 1 = -15
You can check your work by adding -1 and -15, which does in fact equal -16.
Hope this helped :)
Let <em>a</em> be the first term in the sequence. If <em>r</em> is the ratio between consecutive terms, then the second term is <em>ar</em>, the third term is <em>ar </em>^2, the fourth is <em>ar</em> ^3, and so on, up to the <em>n</em>-th term <em>ar</em> ^(<em>n</em> - 1).
So the third, fourth, and fifth terms are such that
<em>ar</em> ^2 = 18
<em>ar</em> ^3 = 27
<em>ar</em> ^4 = 81/2
Solve for <em>a</em> and <em>r</em> :
(<em>ar</em> ^3) / (<em>ar</em> ^2) = 27/18 => <em>r</em> = 3/2
<em>ar</em> ^2 = <em>a</em> (3/2)^2 = 9/4 <em>a</em> = 18 => <em>a</em> = 8
Then the <em>n</em>-th term in the sequence is
<em>ar</em> ^(<em>n</em> - 1) = 9 (3/2)^(<em>n</em> - 1)
You can rewrite this by first rewriting 9 = 3^2, then
9 (3/2)^(<em>n</em> - 1) = 3^2 * 3^(<em>n</em> - 1) / 2^(<em>n</em> - 1) = 3^(<em>n</em> + 1)/2^(<em>n</em> - 1)
Answer:
y = 200·1.15^t
Step-by-step explanation:
The ratio from one year to the next is 1.15, so the balance is a geometric sequence. Since t starts at zero, we can write the balance (y) after t years as ...
y = initial value · (common ratio)^t
y = 200·1.15^t
Answer:
If you choose any value for k other than 6, that will be give you the one solution.
If k=6, you have no solutions because the lines will be parallel.
Step-by-step explanation:
We are going to put each of this in y=mx+b where m is the slope and b is the y-intercept.
kx+2y=5
Subtract kx on both sides:
2y=-kx+5
Divide both sides by 2:
y=(-k/2)x+(5/2)
The slope is -k/2 and the y-intercept is 5/2
3x+y=1
Subtract 3x on both sides:
y=-3x+1
The slope is -3 and the y-intercept is 1.
We want the system to have one solution so we want the slopes to be difference.
So we don't want (-k/2)=(-3).
Multiply both sides by -2: k=6.
We won't want k to be 6.
Answer:
1033.33
Step-by-step explanation:
If you take 30 percent of a number and get 310, then what is that number? In other words, you know that 30 percent of a number is 310 and you want to know what that initial number is.
To solve this problem you multiply 310 by 100 and then divide the total by 30 as follows: (310 x 100) / 30
When we put that into our calculator, we get the following answer: 1033.33
You're welcome :)
