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Fittoniya [83]
3 years ago
13

How do you solve -2/3x + 5 = 20 - x

Mathematics
1 answer:
Monica [59]3 years ago
8 0

-2/3x + 5 = 20 - x

subtract 5 from each side

-2/3 x = 15 -x

add x to each side

-2/3 x +x = 15

get a common denominator of 3 for the x terms

-2/3x + 3/3 x =15

combine like terms

1/3 x = 15

multiply by 3 on each side

x = 45

Answer: x=45

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Write an equation of a parabola that passes through (3,-30) and has x-intercepts of -2 and 18. Then find the average rate of cha
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Answer:

The equation of the parabola is y = \frac{2}{5}\cdot x^{2}-\frac{32}{5}\cdot x -\frac{72}{5}.  The average rate of change of the parabola is -4.

Step-by-step explanation:

We must remember that a parabola is represented by a quadratic function, which can be formed by knowing three different points. A quadratic function is standard form is represented by:

y = a\cdot x^{2}+b\cdot x + c

Where:

x - Independent variable, dimensionless.

y - Dependent variable, dimensionless.

a, b, c - Coefficients, dimensionless.

If we know that (3, -30), (-2, 0) and (18, 0) are part of the parabola, the following linear system of equations is formed:

9\cdot a +3\cdot b + c = -30

4\cdot a -2\cdot b +c = 0

324\cdot a +18\cdot b + c = 0

This system can be solved both by algebraic means (substitution, elimination, equalization, determinant) and by numerical methods. The solution of the linear system is:

a = \frac{2}{5}, b = -\frac{32}{5}, c = -\frac{72}{5}.

The equation of the parabola is y = \frac{2}{5}\cdot x^{2}-\frac{32}{5}\cdot x -\frac{72}{5}.

Now, we calculate the average rate of change (r), dimensionless, between x = -2 and x = 8 by using the formula of secant line slope:

r = \frac{y(8)-y(-2)}{8-(-2)}

r = \frac{y(8)-y(-2)}{10}

x = -2

y = \frac{2}{5}\cdot (-2)^{2}-\frac{32}{5}\cdot (-2)-\frac{72}{5}

y(-2) = 0

x = 8

y = \frac{2}{5}\cdot (8)^{2}-\frac{32}{5}\cdot (8)-\frac{72}{5}

y(8) = -40

r = \frac{-40-0}{10}

r = -4

The average rate of change of the parabola is -4.

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Answer:

x = -\frac{12}{5}

Step-by-step explanation:

To solve the equation, isolate x. Whatever you do to isolate x one on side, you must do to the other.  

1) Multiply both sides by 9 to get rid of the fractions.  

\frac{21-4x}{9} +\frac{8x+15}{3} = 2 \\21-4x + 3(8x + 15) =18 \\

2) Distribute the 3 to 8x and 15. Then, combine like terms.

21-4x + 24x + 45 = 18 \\66 + 20x = 18

3) Move the 66 to the other side, subtracting 18 by 66, then divide each side by 20 to finally isolate x.

20x = -48\\x = -\frac{48}{20} \\x =- \frac{12}{5}

Thus, x = -\frac{12}{5}.

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3 years ago
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