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Ugo [173]
3 years ago
11

Please show your work!!!!

Mathematics
1 answer:
viva [34]3 years ago
6 0

Answer:

4√34

Step-by-step explanation:

Let the unknown side be y

y^2 = 20^2 + 12^2

y^2 = 400 + 144

y^2 = 544

Take the square root of both side

y = √544

y = √(16x34)

y = √16 x √34

y = 4√34

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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
Nookie1986 [14]

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.

3 0
3 years ago
The complement of an angle is 25°. What is the measure of the angle?
Jlenok [28]

Answer:

If the complement of an angle is 25 degrees, then the measurement of the angle will be 65 degrees.

4 0
3 years ago
Adam went on a shopping trip to Somerville. He purchased a set of dishes originally priced at
RUDIKE [14]

Answer:187.2

Step-by-step explanation:

Actual price $390

After 60% discount price will be 156

And Sales tax is 8% . Then the price of sales tax is $31.2.

156+31.2= $187.2

5 0
3 years ago
Can someone explain how to convert 70kg to lbs? i need to show work on my test.
Jlenok [28]

Answer:

70 kg is 154.3 lbs.

Step-by-step explanation:

There is 0.453592 kilograms per pound. That is just the conversion rate.

To find how many lbs 70 kg is, we do 70/0.453592 which is 154.3236.

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3 years ago
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The answer to the question

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