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Anton [14]
3 years ago
13

What are the solutions to the following system of equations? y = x2 + 12x + 30 8x – y = 10

Mathematics
1 answer:
atroni [7]3 years ago
7 0
We are given with two solutions: y = x2 + 12x + 30 and 8x – y = 10 and is asked to determinte the solutions of the system of equations. We get y in the second eqn which is equal to 8x -10. we substitute this to first eqn resulting to 
8x-10 = x^2 + 12 x + 30. this is a second order equation. x is equal to -2 + 6i and -2 - 6i.
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The answer is the letter B
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Find the measurements (the length L and the width W) of an inscribed rectangle under the line with the 1st quadrant of the x &am
Leni [432]

The question is incomplete. Here is the complete question.

Find the measurements (the lenght L and the width W) of an inscribed rectangle under the line y = -\frac{3}{4}x + 3 with the 1st quadrant of the x & y coordinate system such that the area is maximum. Also, find that maximum area. To get full credit, you must draw the picture of the problem and label the length and the width in terms of x and y.

Answer: L = 1; W = 9/4; A = 2.25;

Step-by-step explanation: The rectangle is under a straight line. Area of a rectangle is given by A = L*W. To determine the maximum area:

A = x.y

A = x(-\frac{3}{4}.x + 3)

A = -\frac{3}{4}.x^{2}  + 3x

To maximize, we have to differentiate the equation:

\frac{dA}{dx} = \frac{d}{dx}(-\frac{3}{4}.x^{2}  + 3x)

\frac{dA}{dx} = -3x + 3

The critical point is:

\frac{dA}{dx} = 0

-3x + 3 = 0

x = 1

Substituing:

y = -\frac{3}{4}x + 3

y = -\frac{3}{4}.1 + 3

y = 9/4

So, the measurements are x = L = 1 and y = W = 9/4

The maximum area is:

A = 1 . 9/4

A = 9/4

A = 2.25

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3 years ago
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<h3>What is Z-score?</h3>

The z score indicates how many standard deviations your score is from the mean.

At the mean position, the standard deviation is 0 now the z score is the measure of the data which is how far from the mean. So the given data is at two standard deviations to the right of the mean so the Z-Score will be 2.

Therefore the value of the Z-score will be equal to 2.

To know more about Z-scores follow

brainly.com/question/25638875

#SPJ1

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2 years ago
1 over 8 added 5 times equals​
leonid [27]

Answer:

5/8 or 41/8

Step-by-step explanation:

If you mean 1/8 x 5, then that equals 5/8

If mean 1/8 + 5, then that equals 41/8

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3 years ago
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