Answer:
-2
Step-by-step explanation:
go back 3 into the negatives
Answer:
f(n) = 2 + 5n. This is an arithmetic sequence.
Step-by-step explanation:
f(1) = 7
f(2) = 7 + 5
f(3) = 7 + 5 + 5 = 7 +10
f(4) = 7 + 5 + 5 + 5 = 7 + 15
In general,
f(n) = 7 + 5(n -1 )
= 7 + 5n - 5
= 2 + 5n
We have the sequence 7, 12, 17, 22, 27 …
This is an arithmetic sequence, because it is a sequence of numbers in which the <em>common difference</em> between consecutive terms is 5.
Step-by-step explanation:
Let the two-digit number is ![xy](https://tex.z-dn.net/?f=xy)
<u>This can be written as:</u>
- 10x + y, where 1 ≤ x ≤ 9 and 0 ≤ y ≤ 9
<u>The difference between the number and product of its digits is:</u>
<u>Rewrite this as below:</u>
d = 10x - xy + y - 10 + 10 =
x(10 - y) - (10 - y) + 10 =
(x - 1)(10 - y) + 10
<u>We see that:</u>
- 0 ≤ x - 1 ≤ 8 according to the condition given above
- 1 ≤ 10 - y ≤ 10 again according to the condition given above
<u>The value of d is then:</u>
- 0 + 10 ≤ d ≤ 8*10 + 10
- 10 ≤ d ≤ 90
<h3>Proved</h3>
Ella has to add 32.833 lbs of water to get 33.333 lbs of syrup.
<u>Solution:</u>
Ella has 0.5 lbs of sugar. Let x lbs be the amount of water Ella should add to get the 1.5% of syrup,
![\Rightarrow0.5\text{ lbs }- 1.5\%](https://tex.z-dn.net/?f=%5CRightarrow0.5%5Ctext%7B%20lbs%20%7D-%201.5%5C%25)
![\Rightarrow x+0.5\text{ lbs }- 100\%](https://tex.z-dn.net/?f=%5CRightarrow%20x%2B0.5%5Ctext%7B%20lbs%20%7D-%20100%5C%25)
On writing the proportion,
![\Rightarrow\dfrac{0.5}{x+0.5}=\dfrac{1.5}{100}\\ \\\Rightarrow0.5\cdot 100=(x+0.5)\cdot 1.5\\ \\\Rightarrow50=1.5x+0.75\\ \\\Rightarrow1.5x=50-0.75\\ \\\Rightarrow1.5x=49.25\\ \\\Rightarrow x=\dfrac{49.25}{1.5}\approx 32.833\ lbs](https://tex.z-dn.net/?f=%5CRightarrow%5Cdfrac%7B0.5%7D%7Bx%2B0.5%7D%3D%5Cdfrac%7B1.5%7D%7B100%7D%5C%5C%20%5C%5C%5CRightarrow0.5%5Ccdot%20100%3D%28x%2B0.5%29%5Ccdot%201.5%5C%5C%20%5C%5C%5CRightarrow50%3D1.5x%2B0.75%5C%5C%20%5C%5C%5CRightarrow1.5x%3D50-0.75%5C%5C%20%5C%5C%5CRightarrow1.5x%3D49.25%5C%5C%20%5C%5C%5CRightarrow%20x%3D%5Cdfrac%7B49.25%7D%7B1.5%7D%5Capprox%2032.833%5C%20lbs)
To get 1.5% syrup Ella should add 32.833 lbs of water. The total weight of syrup is 33.333 lbs.