Answer:
3x - 3
Step-by-step explanation:
(x + 4) + (2x - 7) =
The first step is to drop the parentheses since they are unnecessary.
= x + 4 + 2x - 7
Now group like terms together.
= x + 2x + 4 - 7
Combine like terms.
= 3x - 3
Answers:
- Domain is (-4, 3]
- Range is (-5, 5]
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Explanation:
The domain is the set of allowed x input values, aka the set of all allowed x coordinates of the points. We see that
. It might help to draw vertical lines through the endpoints until you reach the x axis. Note the open hole at x = -4 to indicate we do not include this as part of the domain (hence the lack of "or equal to" for the first inequality sign).
The interval
then can be condensed into the shorthand form (-4, 3] which is the domain in interval notation.
It says: x is between -4 and 3. It can't equal -4 but it can equal 3.
So the use of parenthesis versus square brackets tells the reader which endpoint is included or not.
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The range describes all possible y outputs. We see that y = 5 is the largest it gets and y = -5 is the lower bound. It might help to draw horizontal lines through the endpoints until you reach the y axis. The open hole means -5 is not part of the range.
The range as a compound inequality is
. This condenses into the shorthand of (-5, 5] which is the range in interval notation.
Verbally, the range is the set of y values such that y is between -5 and 5. It can't equal -5 but it can equal 5.
Answer:
$ 1,968
Step-by-step explanation:
Boxes purchased = 246
Cost of 1 box = $ 8
Cost of 246 boxes
= 246 × 8
= $ 1,968
Hope it helps ⚜
The amount of money you have if you invested $15,000 dollars for 11 years at 3% annual interest compounded continuously is $20864.521
<h3><u>Solution:</u></h3>
You invested $15,000 dollars for 11 years at 3% annual interest compounded continuously
To find: total amount of money
<em><u>The compound interest formula for compounded continously is given as:</u></em>
![A = p e^{rt}](https://tex.z-dn.net/?f=A%20%3D%20p%20e%5E%7Brt%7D)
Where "p" is the principal
"r" is the rate of interest
"t" is the number of years
Here in this problem,
p = 15000
r = 3 % =
= 0.03
t = 11 years
<em><u>Substituting the values in formula we get,</u></em>
![A = 15000e^{0.03 \times 11}](https://tex.z-dn.net/?f=A%20%3D%2015000e%5E%7B0.03%20%5Ctimes%2011%7D)
![A = 15000e^{0.33}\\\\A = 15000 \times 1.3909 \\\\A = 20864.521](https://tex.z-dn.net/?f=A%20%3D%2015000e%5E%7B0.33%7D%5C%5C%5C%5CA%20%3D%2015000%20%5Ctimes%201.3909%20%5C%5C%5C%5CA%20%3D%2020864.521)
So the amount of money you have is $ 20864.521