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3 years ago

Use the associative property to identify which expression is equal to (32)(8)(5x).

1 answer:

6 0

Associative property groups numbers but the order stays the same.
If the '.' In C mean multiply then this is the answer.
None of the others are.

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A line includes the points (7,4) and (8,6). What is it’s equation in slope- intercept form?

coldgirl [10]

Answer:

Step-by-step explanation:

First you have to find the slope

M= y2-y1/ x2-x1.

6-4 / 8-7 = 2/1 or 2

Then you pick one set of coordinates and plug the information into the formula. It doesn't matter which set you use as long as you plug the information in correctly.

I will choose (6,4)

Slope intercept formula is y-y1 =m(x-x1)

Y-4=2(x-6)

Then you simplify.

Y-4=2x-12

+4. +4

Y=2x-8 is your solution.

3 0

2 years ago

A tank contains 60 kg of salt and 1000 L of water. Pure water enters a tank at the rate 6 L/min. The solution is mixed and drain

MissTica

Answer:

(a) 60 kg; (b) 21.6 kg; (c) 0 kg/L

Step-by-step explanation:

(a) Initial amount of salt in tank

The tank initially contains 60 kg of salt.

(b) Amount of salt after 4.5 h

$\text{Let A = mass of salt after t min}\\\text{and }r_{i} = \text{rate of salt coming into tank}\\\text{and }r_{0} =\text{rate of salt going out of tank}$

(i) Set up an expression for the rate of change of salt concentration.

$\dfrac{\text{d}A}{\text{d}t} = r_{i} - r_{o}\\\\\text{The fresh water is entering with no salt, so}\\ r_{i} = 0\\r_{o} = \dfrac{\text{3 L}}{\text{1 min}} \times \dfrac {A\text{ kg}}{\text{1000 L}} =\dfrac{3A}{1000}\text{ kg/min}\\\\\dfrac{\text{d}A}{\text{d}t} = -0.003A \text{ kg/min}$

(ii) Integrate the expression

$\dfrac{\text{d}A}{\text{d}t} = -0.003A\\\\\dfrac{\text{d}A}{A} = -0.003\text{d}t\\\\\int \dfrac{\text{d}A}{A} = -\int 0.003\text{d}t\\\\\ln A = -0.003t + C$

(iii) Find the constant of integration

$\ln A = -0.003t + C\\\text{At t = 0, A = 60 kg/1000 L = 0.060 kg/L} \\\ln (0.060) = -0.003\times0 + C\\C = \ln(0.060)$

(iv) Solve for A as a function of time.

$\text{The integrated rate expression is}\\\ln A = -0.003t + \ln(0.060)\\\text{Solve for } A\\A = 0.060e^{-0.003t}$

(v) Calculate the amount of salt after 4.5 h

a. Convert hours to minutes

$\text{Time} = \text{4.5 h} \times \dfrac{\text{60 min}}{\text{1h}} = \text{270 min}$

b.Calculate the concentration

$A = 0.060e^{-0.003t} = 0.060e^{-0.003\times270} = 0.060e^{-0.81} = 0.060 \times 0.445 = \text{0.0267 kg/L}$

c. Calculate the volume

The tank has been filling at 6 L/min and draining at 3 L/min, so it is filling at a net rate of 3 L/min.

The volume added in 4.5 h is

$\text{Volume added} = \text{270 min} \times \dfrac{\text{3 L}}{\text{1 min}} = \text{810 L}$

Total volume in tank = 1000 L + 810 L = 1810 L

d. Calculate the mass of salt in the tank

$\text{Mass of salt in tank } = \text{1810 L} \times \dfrac{\text{0.0267 kg}}{\text{1 L}} = \textbf{21.6 kg}$

(c) Concentration at infinite time

$\text{As t $\longrightarrow \, -\infty,\, e^{-\infty} \longrightarrow \, 0$, so A $\longrightarrow \, 0$.}$

This makes sense, because the salt is continuously being flushed out by the fresh water coming in.

The graph below shows how the concentration of salt varies with time.

3 0

2 years ago

Solve 3[-x + (2 x + 1)] = x - 1.

vivado [14]

Answer:

The answer is-2.

Step-by-step explanation:

#Hope it helps uh......

8 0

2 years ago

Determine the point on the hyperbola 3x^2−10y^2=20 closest to the point (0, -7).

stepan [7]

Answer:

Step-by-step explanation:

7 0

3 years ago

You want to buy an item that costs $100. Which of these is the most cost-effective choice for buying the item?. a. using a paid

Paraphin [41]

Answer

c. buying it at a 10 percent discount without sales tax.

Explanation

We are going to compare the 3 choices and then determine the most cost effective.

a. using a paid membership card to buy it at a 10 percent discount.

10% of $100 = 10/100×100 = $10

cost = $100 - $10 = $90

On top of this $90 there is the charges of the membership card.

b. buying it online at a 10 percent discount with a $5 shipping charge.

100%-10% = 90%

90% of 100 = $90

Cost: $90 + $5 = $95

c. buying it at a 10 percent discount without sales tax.

100% - 10% = 90%

90/100 × 100 = $90. This is the must cost effective method since there is no other cost involved.

7 0

3 years ago

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