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PSYCHO15rus [73]
2 years ago
5

Please help meeeeeeeeeeeeedirections: use substitution to solve the solution

Mathematics
1 answer:
dimaraw [331]2 years ago
3 0

Answer:

(-3, 13)

General Formulas and Concepts:

<u>Pre-Algebra</u>

Order of Operations: BPEMDAS

  1. Brackets
  2. Parenthesis
  3. Exponents
  4. Multiplication
  5. Division
  6. Addition
  7. Subtraction
  • Left to Right  

Equality Properties

  • Multiplication Property of Equality
  • Division Property of Equality
  • Addition Property of Equality
  • Subtraction Property of Equality<u> </u>

<u>Algebra I</u>

  • Terms/Coefficients
  • Coordinates (x, y)
  • Solving systems of equations using substitution/elimination

Step-by-step explanation:

<u>Step 1: Define Systems</u>

y = -4x + 1

11y = x + 146

<u>Step 2: Solve for </u><em><u>x</u></em>

<em>Substitution</em>

  1. Substitute in <em>y</em>:                                                                                                   11(-4x + 1) = x + 146
  2. Distribute 11:                                                                                                     -44x + 11 = x + 146
  3. [Addition Property of Equality] Add 44x on both sides:                              11 = 45x + 146
  4. [Subtraction Property of Equality] Subtract 146 on both sides:                  -135 = 45x
  5. [Division Property of Equality] Divide 45 on both sides:                             -3 = x
  6. Rewrite/Rearrange:                                                                                             x = -3

<u>Step 3: Solve for </u><em><u>y</u></em>

  1. Define original equation:                                                                                  y = -4x + 1
  2. Substitute in <em>x</em>:                                                                                                   y = -4(-3) + 1
  3. Multiply:                                                                                                           y = 12 + 1
  4. Add:                                                                                                                      y = 13
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To find the number of seats, let's do it using multiplication!

First, to see how many seats are in one big section of the theatre, multiply 7 groups of seats by 25 seats:

7 x 25 = 175

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175 x 4 = 700

Therefore, there are 700 seats in the theatre.

Hope this helps!
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Solve for w.<br><br> 5w + 9z = 2z + 3w<br><br> w = z<br> w = z<br> w = –2z<br> w = –7z
Semenov [28]

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Consider a tank used in certain hydrodynamic experiments. After one experiment the tank contains liters of a dye solution with a
Alja [10]

Answer:

t = 460.52 min

Step-by-step explanation:

Here is the complete question

Consider a tank used in certain hydrodynamic experiments. After one experiment the tank contains 200 liters of a dye solution with a concentration of 1 g/liter. To prepare for the next experiment, the tank is to be rinsed with fresh water flowing in at a rate of 2 liters/min, the well-stirred solution flowing out at the same rate.Find the time that will elapse before the concentration of dye in the tank reaches 1% of its original value.

Solution

Let Q(t) represent the amount of dye at any time t. Q' represent the net rate of change of amount of dye in the tank. Q' = inflow - outflow.

inflow = 0 (since the incoming water contains no dye)

outflow = concentration × rate of water inflow

Concentration = Quantity/volume = Q/200

outflow = concentration × rate of water inflow = Q/200 g/liter × 2 liters/min = Q/100 g/min.

So, Q' = inflow - outflow = 0 - Q/100

Q' = -Q/100 This is our differential equation. We solve it as follows

Q'/Q = -1/100

∫Q'/Q = ∫-1/100

㏑Q  = -t/100 + c

Q(t) = e^{(-t/100 + c)} = e^{(-t/100)}e^{c}  = Ae^{(-t/100)}\\Q(t) = Ae^{(-t/100)}

when t = 0, Q = 200 L × 1 g/L = 200 g

Q(0) = 200 = Ae^{(-0/100)} = Ae^{(0)} = A\\A = 200.\\So, Q(t) = 200e^{(-t/100)}

We are to find t when Q = 1% of its original value. 1% of 200 g = 0.01 × 200 = 2

2 = 200e^{(-t/100)}\\\frac{2}{200} =  e^{(-t/100)}

㏑0.01 = -t/100

t = -100㏑0.01

t = 460.52 min

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3 years ago
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