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2 years ago

What is x=3y-1 x=-2y+9

Mathematics

2 answers:

-Dominant- [34]2 years ago

8 0

Are you to combine the answer or are they 2 separate equations you need to solve for y?

NemiM [27]2 years ago

5 0

Since both equal x, just subsitute them
3y-1=x=-2y+9
3y-1=-2y+9
add 2y to both sides
5y-1=9
add 1 to both sides
5y=10
divide both sides by 5
y=2

sub back into any equation
x=3y-1
x=3(2)-1
x=6-1
x=5

x=5
y=2
(5,2)

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Yuri [45]

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3 years ago

Read 2 more answers

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

3 years ago

Please help me i dont understand

irina [24]

Answer:

3x + 4

Step-by-step explanation:

We have a product of 3 and x. That's rewritten as 3x. We then have 4 more, so we add 4. That gives us the final answer of: 3x+4. (It is 1-4x for the third one). ( The fourth one) The sum of seven and the quotient of a number x and eight

Here, x be the number.

" quotient of a number x and eight" translated to x/8

Sum means '+'

"sum of seven and the quotient of a number x and eight" translated to 7+ x/8 +56+x/8

then; the given statement is 56+x/8

⇒

Therefore, the given statement is 56+x/8

6 0

3 years ago

Solve the equation. Round your answer to the nearest hundredth.<br> 47 +3.81k = -41

Harman [31]

Answer:

i have no idea but if i had to guess it would be around -3.00k or -4.00k

Step-by-step explanation:

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3 years ago

Three boxes of supplies have an average (arithmetic mean) weight of 7 kilograms and a median weight of 9 kilograms. What is the

GuDViN [60]

Answer:

Step-by-step explanation:

A) 1

(B) 2

(D) 4

(E) 5

Mean is a measure of central tendency. It is the average of a set of numbers. It is determined by adding the numbers together and dividing it by the total number

Mean = sum of numbers / number of observation

sum of numbers = 3 x 7 = 21

Median is the number that is at the center or middle of a set of obervations

x + 9+ y = 21

x= lowest number

y = highest number

x + y = 21 - 9

x + y = 12

If x = 1 y = 11

if x = 2 y = 10

if x = 3 y = 9

if x = 4 y = 8

the first 3 are plausible and the median would still be 9 if x = 4, median would be 8

3 0

2 years ago