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3 years ago

11

Use algebra tiles to model the expression. Then, use the model to help you write an equivalent expression, and complete the stat

ements.
3(x + 1)

2 answers:

Sonja [21]3 years ago

6 0

Answer:

1. 3

2. 3

3. 3

4. 3x + 3

Step-by-step explanation:

OLga [1]3 years ago

3 0

Answer:

1. 3

2. 3

3. 6

4. 3times+6

Step-by-step explanation:

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A large tank is filled to capacity with 700 gallons of pure water. Brine containing 3 pounds of salt per gallon is pumped into t

inn [45]

Answer:

The number A(t) of pounds of salt in the tank at time 't' is;

${A(t)}= -2,100 \times e^{\dfrac{-t}{100} } + 2,100$

Step-by-step explanation:

In the question, we have;

The volume of pure water initially in the tank = 700 gal

The concentration of brine pumped into the tank = 3 pounds per gallon

The rate at which the brine is pumped into the tank, = 7 gal/min

The rate at which the well mixed solution is pumped out = The same 7 gal/min

The number of pounds of salt in the tank at time 't' is found as follows;

The rate of change in A(t) with time = The rate of salt input - The rate of salt output

$The \ rate \ of \ change \ in \ A(t) \ with \ time = \dfrac{dA}{dt}$

The rate of salt input = 7 gal/min × 3 lbs/gal = 21 lbs/min

The rate of salt output = (A(t)/700) lb/gal × 7 gal/min = (A(t)/100) lb/min

Therefore, we have;

$\dfrac{dA}{dt} = 21 - \dfrac{A(t)}{100}$

Therefore;

$\dfrac{dA}{dt} + \dfrac{A(t)}{100}= 21$

The integrating factor is $e^{\int\limits {\frac{1}{100} } \, dx } = e^{\frac{x}{100} }$

$e^{\dfrac{t}{100} } \times \dfrac{dA}{dt} + e^{\dfrac{t}{100} } \times\dfrac{A(t)}{100}= e^{\dfrac{t}{100} } \times21$

$\dfrac{d}{dt} \left[ e^{\dfrac{t}{100} } \times{A(t)}{} \right]= e^{\dfrac{t}{100} } \times21$

Using an online tool, we get;

${A(t)}= c_1 \times e^{\dfrac{-t}{100} } + 2,100$

At time t = 0, A(t) = 0

We get;

$0= c_1 \times e^{\dfrac{-0}{100} } + 2,100$

c₁ = -2,100

Therefore, the number A(t) of pounds of salt in the tank at time 't' is given as follows;

${A(t)}= -2,100 \times e^{\dfrac{-t}{100} } + 2,100$

8 0

3 years ago

A small chain of stores wants to advertise. They are thinking of creating a TV ad for $47,918.00, but they might put up billboar

Nina [5.8K]

It would cost $30,220.00 more to make the Tv Ad.

6 0

3 years ago

8.17 8.073 8.2<br> 8.03 8.063<br> 8.016<br> Least to greatest

Katena32 [7]

Answer:

8.016, 8.03, 8.063, 8.073, 8.17, 8.2

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers

How do you change 0.0112 in to a fraction?

ioda

$\frac{7}{625}$
If there was a number other than 0 before the decimal point, it would serve as the whole number in our final answer.
First count the number of digits after the decimal point. For this problem it's 4.
Then make the denominator 10 raised to the power of your answer in the first step so the denominator for this question is 10⁴=10000
The numerator will be the number after the decimal point.
The fraction will be = 112/10000
Then reduce it to the lowest term
If you divide the numerator and denominator by 16 you get 7/625 which is the lowest possible fractional term.

5 0

3 years ago

Read 2 more answers

Please explain your answer. THX!!!!

Sidana [21]

Answer:

1) $cos(x)sin^{2}x$

2)0

Step-by-step explanation:

for part 1:

Given cos(x) - cos^3(x)

= cos(x) (1- cos^2(x))

Using the identity $cos^{2}x +sin^{2}x=1\\ sin^{2}x=1-cos^{2}x$

= cos(x)sin^2(x)

for part 2:

given

= $cos\frac{5\pi }{8}cos\frac{\pi }{8} + sin\frac{5\pi }{8}sin\frac{\pi }{8}$

Using the identity cos(a)cos(b) + sin(a)sin(b)= cos(a-b)

= $cos(\frac{5\pi }{8} -\frac{\pi }{8})$

= $cos\frac{4\pi }{8}$

= $cos\frac{\pi }{2}$

=0!

5 0

3 years ago