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frosja888 [35]
3 years ago
15

Solve the Solve the simultaneous equations 2x+3y=20 x+5y=31

Mathematics
1 answer:
zlopas [31]3 years ago
6 0

Answer:

x = 1   and   y = 6

Step-by-step explanation:

Given

2x + 3y = 20

x + 5y = 31

Required

Solve for x and y

Make x the subject in the second equation

x = 31 - 5y

Substitute 31 - 5y for x in 2x + 3y = 20

2(31 - 5y) + 3y = 20

62 - 10y + 3y = 20

62 - 7y  = 20

Collect like terms

-7y = 20 - 62

-7y = - 42

Solve for y

y = \frac{-42}{-7}

y = 6

Substitute 6 for y in x = 31 - 5y

x = 31 - 5 * 6

x = 31 - 30

x = 1

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Given that Angelo spends the same amount everyday from the amount in

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  • The constant rate of change of the function is; <u>-5.25</u>
  • The two ordered pair used to find the constant rate of change are; <u>(1, 44.75) and (2, 39.5)</u>

Reasons:

The amount Angelo's mother put on the lunch card = $50

A possible table of values to the question is presented as follows;

\begin{tabular}{r|c|c|c|c|}Days&0&1&2&3\\Money Remaining&&44.75&39.5&\end{array}\right]

Required:

The constant rate of the function that gives the amount remaining from the

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Solution:

  • Slope \ or \ constant \ rate \ of \ change  = \mathbf{\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}}

The two ordered pair that can be used to find the slope or constant rate of change are;

(x₁, y₁) = (1, 44.75), and (x₂, y₂) = (2, 39.5)

With the above two ordered pairs, we have the constant rate of change of the function given as follows;

Constant \ rate \ of \ change\  (The \ slope) =\dfrac{39.5-44.75}{2-1} = \mathbf{ -5.25}

The constant rate of change for the function that gives the amount remaining in the lunch card is; <u>-5.25</u>

Learn more about the constant rate of change of a function here:

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3 0
2 years ago
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Answer:

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Step-by-step explanation:

4x-2x=-3y

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The factors of a polynomial function are the zeros of the function

It is true that x - 3 is a factor of m(x) = x^3 - x^2 - 5x - 3

<h3>How to show why the x - 3 is a factor</h3>

The function is given as:

m(x) = x^3 - x^2 - 5x - 3

The factor is given as:

x - 3

Set the factor to 0

x - 3 = 0

Solve for x

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Substitute 3 for x in the function

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Evaluate

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Since the value of m(3) is 0, then x - 3 is a factor of m(x) = x^3 - x^2 - 5x - 3

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