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AnnZ [28]
3 years ago
10

how many 7th grade students are expected to move by the end of the year? if 12 students actually moved, did more or fewer 7th gr

ade students move than expected? justify your answer.
Mathematics
1 answer:
igomit [66]3 years ago
5 0
Less because is 12-7 equals 5 it’s less
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The opposite of - |9| is
aleksklad [387]

Hello from MrBillDoesMath!

Answer:   +9

Discussion:

The opposite of a number is that number multiplied by -1. In our case the opposite number is  (-1) *  (- (abs(9))) = -1 * (-9) = +9

Thank you,

MrB


3 0
2 years ago
Read 2 more answers
Triangle ABC was transformed to create triangle A'B'C'.
makkiz [27]

Answer:

The answer is F(x, y-7).

4 0
2 years ago
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<img src="https://tex.z-dn.net/?f=%5Cfrac%7Bd%7D%7Bdx%7D%20%5Cint%20t%5E2%2B1%20%5C%20dt" id="TexFormula1" title="\frac{d}{dx} \
Kisachek [45]

Answer:

\displaystyle{\frac{d}{dx} \int \limits_{2x}^{x^2}  t^2+1 \ \text{dt} \ = \ 2x^5-8x^2+2x-2

Step-by-step explanation:

\displaystyle{\frac{d}{dx} \int \limits_{2x}^{x^2}  t^2+1 \ \text{dt} = \ ?

We can use Part I of the Fundamental Theorem of Calculus:

  • \displaystyle\frac{d}{dx} \int\limits^x_a \text{f(t) dt = f(x)}

Since we have two functions as the limits of integration, we can use one of the properties of integrals; the additivity rule.

The Additivity Rule for Integrals states that:

  • \displaystyle\int\limits^b_a \text{f(t) dt} + \int\limits^c_b \text{f(t) dt} = \int\limits^c_a \text{f(t) dt}

We can use this backward and break the integral into two parts. We can use any number for "b", but I will use 0 since it tends to make calculations simpler.

  • \displaystyle \frac{d}{dx} \int\limits^0_{2x} t^2+1 \text{ dt} \ + \ \frac{d}{dx} \int\limits^{x^2}_0 t^2+1 \text{ dt}

We want the variable to be the top limit of integration, so we can use the Order of Integration Rule to rewrite this.

The Order of Integration Rule states that:

  • \displaystyle\int\limits^b_a \text{f(t) dt}\  = -\int\limits^a_b \text{f(t) dt}

We can use this rule to our advantage by flipping the limits of integration on the first integral and adding a negative sign.

  • \displaystyle \frac{d}{dx} -\int\limits^{2x}_{0} t^2+1 \text{ dt} \ + \ \frac{d}{dx}  \int\limits^{x^2}_0 t^2+1 \text{ dt}  

Now we can take the derivative of the integrals by using the Fundamental Theorem of Calculus.

When taking the derivative of an integral, we can follow this notation:

  • \displaystyle \frac{d}{dx} \int\limits^u_a \text{f(t) dt} = \text{f(u)} \cdot \frac{d}{dx} [u]
  • where u represents any function other than a variable

For the first term, replace \text{t} with 2x, and apply the chain rule to the function. Do the same for the second term; replace

  • \displaystyle-[(2x)^2+1] \cdot (2) \ + \ [(x^2)^2 + 1] \cdot (2x)  

Simplify the expression by distributing 2 and 2x inside their respective parentheses.

  • [-(8x^2 +2)] + (2x^5 + 2x)
  • -8x^2 -2 + 2x^5 + 2x

Rearrange the terms to be in order from the highest degree to the lowest degree.

  • \displaystyle2x^5-8x^2+2x-2

This is the derivative of the given integral, and thus the solution to the problem.

6 0
2 years ago
We theater is giving away a souvenir poster to any customer with a concession stand receive that exceeds $60 the theater sells a
meriva

Answer:  6x + 3.5y > 60

<u>Step-by-step explanation:</u>

Popcorn: cost is $6.00, variable is x

Soda: cost is $3.50, variable is y

Total: GREATER than $60

Popcorn + Soda    >    Total

 6x        +   3.5y    >      60

4 0
3 years ago
In your job at a restaurant, you made a 12-cup pot of coffee at 7:20 a.m. By 7:40 a.m., you had served it all and had to make an
Anarel [89]

Answer:

36 cups

Step-by-step explanation:

every 20 minutes you make 12 cups. 20×3=60, which is 1 hour. You will meed to make 3 pots of coffee that are 12 cups each, 3×12=36

3 0
3 years ago
Read 2 more answers
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