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3 years ago

Solve the system: -5x+6y=55 4x+3y=34 Write down your solution.

Mathematics

1 answer:

svetlana [45]3 years ago

4 0

Answer:

(1, 10)

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Equality Properties

Algebra I

Solving systems of equations using substitution/elimination

Step-by-step explanation:

Step 1: Define Systems

-5x + 6y = 55

4x + 3y = 34

Step 2: Rewrite Systems

4x + 3y = 34

Multiply everything by -2: -8x - 6y = -68

Step 3: Redefine Systems

-5x + 6y = 55

-8x - 6y = -68

Step 4: Solve for x

Elimination

Combine equations: -13x = -13
Divide -13 on both sides: x = 1

Step 5: Solve for y

Define equation: 4x + 3y = 34
Substitute in x: 4(1) + 3y = 34
Multiply: 4 + 3y = 34
Isolate y term: 3y = 30
Isolate y: y = 10

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3 years ago

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At 2 PM, a thermometer reading 80°F is taken outside where the air temperature is 20°F. At 2:03 PM, the temperature reading yiel

Alexeev081 [22]

Use Law of Cooling:
$T(t) = (T_0 - T_A)e^{-kt} +T_A$
T0 = initial temperature, TA = ambient or final temperature

First solve for k using given info, T(3) = 42
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Substituting k back into cooling equation gives:
$T(t) = 60(\frac{11}{30})^{t/3} + 20$

At some time "t", it is brought back inside at temperature "x".
We know that temperature goes back up to 71 at 2:10 so the time it is inside is 10-t, where t is time that it had been outside.
The new cooling equation for when its back inside is:
$T(t) = (x-80)(\frac{11}{30})^{t/3} + 80 \\ \\ 71 = (x-80)(\frac{11}{30})^{\frac{10-t}{3}} + 80$
Solve for x:
$x = -9(\frac{11}{30})^{\frac{t-10}{3}} + 80$
Sub back into original cooling equation, x = T(t)
$-9(\frac{11}{30})^{\frac{t-10}{3}} + 80 = 60 (\frac{11}{30})^{t/3} +20$
Solve for t:
$60 (\frac{11}{30})^{t/3} +9(\frac{11}{30})^{\frac{-10}{3}}(\frac{11}{30})^{t/3} = 60 \\ \\ (\frac{11}{30})^{t/3} = \frac{60}{60+9(\frac{11}{30})^{\frac{-10}{3}}} \\ \\ \\ t = 3(\frac{ln(\frac{60}{60+9(\frac{11}{30})^{\frac{-10}{3}}})}{ln (\frac{11}{30})}) \\ \\ \\ t = 4.959$

This means the exact time it was brought indoors was about 2.5 seconds before 2:05 PM

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4 years ago

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Murljashka [212]

Answer:

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Step-by-step explanation:

1/8 times 2 is 2/16 and 3/8 times 2 is 6/16 so add all up to get 13/16

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Answer:

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Step-by-step explanation:

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