Percent means parts out of 100
23%=23/100=0.23
'of' means mutiply
23% of 75=0.23 times 75=17.25
answer is 17.25
Just differentiate <em>G</em> and <em>H</em> :
• d<em>G</em>/d<em>x</em> = d(<em>x</em> ² <em>eˣ </em>)/d<em>x</em> = 2<em>x</em> <em>eˣ</em> + <em>x</em> ² <em>eˣ</em>
so <em>G</em> is not an antiderivative of <em>f</em>.
• d<em>H</em>/d<em>x</em> = d(2<em>x</em> <em>eˣ</em> - 2<em>eˣ</em> ) = (2<em>eˣ</em> + 2<em>x</em> <em>eˣ</em> ) - 2<em>eˣ</em> = 2<em>x</em> <em>eˣ</em> = <em>f(x)</em>
so <em>H</em> is indeed an antiderivative of <em>f</em>.
Alright, we're dealing with a few values here, so let's give them some labels to save us some trouble down the road. We'll call the number of messages sent by Maria <em>m</em>, the number sent by Bill <em>b</em> and the number sent by Change (is that a real name?) <em>c</em>. We don't know exactly what each number is, but let's take a look at what information they do give us.
Change sent 2 times as many messages as Bill, or, using our variable for Change and Bill:

We're also given that Maria sent 7 messages more than Bill, which we can represent with:

Notice that <em>m</em> and <em>c</em> are both in terms of <em>b</em>. We can use this for our next step. We're given at the beginning that together, Maria, Bill, and Change sent 71 messages over the weekend. As an equation using all of our variables, this translates to:

Since <em>m </em>and <em>c </em>are both in terms of <em>b</em>, we can substitute those expressions in and solve for <em>b</em>:

Now that know that Bill sent 16 texts, we can find the numbers for Change and Maria:

So,
Bill sent 16 texts, Maria sent 23, and Change sent 32.
X + 3x + 4x = 56
8x = 56
x = 7
The shortest piece is 7 inches
The middle piece is 7*3 = 21 inches.
The longest piece is 4*7 = 28 inches
Check
7 + 21 + 28 = 56 It does check and the lengths are correct.
Okay, so the pattern is multiplying by 4. so to find the next two numbers: 128 times 4=512 times 4=2048. so all six numbers are 2, 8, 32, 128, 512, and 2048. Add all six together and you get D-2730.