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zysi [14]
3 years ago
6

Given that the quadratic equation has equal roots (k^2-1)x^2-2kx-3k-1=0

Mathematics
1 answer:
Alik [6]3 years ago
7 0

Answer:

(See explanation for further details)

Step-by-step explanation:

The real expression is:

(k^{2}-1)\cdot x{{2} - 2\cdot k \cdot x - 3\cdot k + 1 = 0

The general equation for the second-order polynomial is:

x = \frac{2\cdot k \pm \sqrt{4\cdot k^{2}-4\cdot (k^{2}-1)\cdot (-3\cdot k + 1)}}{k^{2}-1}

This condition must be observed for the case of a quadratic equation with equal roots:

4\cdot k^{2} - 4\cdot (k^{2}-1)\cdot (-3\cdot k + 1) = 0

k^{2} + (k^{2}-1)\cdot (3\cdot k + 1) = 0

k^{2} + 3\cdot k^{3} - 3\cdot k - k^{2}-1 = 0

3\cdot k^{3} - 3\cdot k - 1 = 0

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Answer:

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Step-by-step explanation:

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2 years ago
7,8,9,7,2,5,3,2, 2<br><br> Mean__<br> Median__<br> Mode__<br> Range__
serious [3.7K]

Answer:

Mean: 5

Median: 5

Mode: 2

Range: 7

Step-by-step explanation:

We find the mean by adding all the numbers together to get 45. Then we divide the 45 by the amount of numbers in the set, for this one it is 9. 45 divided by 9 equals 5.

To find the median we put the numbers in the set in order from least to greatest. Next, we find the middle number. median=5

To find the mode we find the number repeated the most. In this set the number that repeats the most is 2.

Range is found by subtracting the largest number and the smallest number. 9-2=7

4 0
3 years ago
Which equation represents the line that passes through the points (-5,2) and (9,0)
V125BC [204]

Step-by-step explanation:

<em>Given </em><em>points </em>

<em>(</em><em> </em><em>-</em><em>5</em><em> </em><em>,</em><em> </em><em>2</em><em>)</em><em> </em><em>and </em><em>(</em><em>9</em><em> </em><em>,</em><em> </em><em>0</em><em>)</em>

<em>First </em><em>calculating </em><em>slope(</em><em>m</em><em>)</em>

<em>=</em><em> </em><em>(</em><em> </em><em>y2 </em><em>-</em><em> </em><em>y1</em><em>) </em><em> </em><em>/</em><em> </em><em>(</em><em> </em><em>x2 </em><em>-</em><em> </em><em>x1</em><em>) </em>

<em>=</em><em> </em><em>(</em><em> </em><em>0</em><em>-</em><em>2</em><em>)</em><em> </em><em>/</em><em> </em><em>(</em><em> </em><em>9</em><em>+</em><em>5</em><em>)</em>

<em>=</em><em> </em><em>-</em><em>2</em><em> </em><em>/</em><em> </em><em>1</em><em>4</em>

<em>=</em><em> </em><em>-</em><em>1</em><em>/</em><em>7</em>

<em>Now </em><em>The </em><em>equation </em><em>of </em><em>line </em><em>is </em><em>given </em><em>by </em>

<em>y </em><em>-</em><em> </em><em>y1 </em><em>=</em><em> </em><em>m </em><em>(</em><em> </em><em>x </em><em>-</em><em> </em><em>x1) </em>

<em>y </em><em>-</em><em>2</em><em> </em><em>=</em><em> </em><em>-</em><em>1</em><em>/</em><em>7</em><em> </em><em>(</em><em>x </em><em>+</em><em> </em><em>5</em><em>)</em>

<em>7</em><em>(</em><em> </em><em>y </em><em>-</em><em> </em><em>2</em><em>)</em><em> </em><em>=</em><em> </em><em>-</em><em>1</em><em>(</em><em>x</em><em> </em><em>+</em><em> </em><em>5</em><em>)</em>

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<em>x </em><em>+</em><em> </em><em>7y </em><em>-</em><em>1</em><em>4</em><em> </em><em>+</em><em>5</em><em> </em><em>=</em><em> </em><em>0</em>

<em>x </em><em>+</em><em> </em><em>7y </em><em>-</em><em> </em><em>9</em><em> </em><em>=</em><em> </em><em>0</em><em> </em>

<em>Which </em><em>is </em><em>the </em><em>required </em><em>equation </em>

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3 years ago
The graph below shows a company’s profit f(x), in dollars, depending on the price of the erasers x, in dollars, being sold by th
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The x-intercept = (0, 0) and (8, 0), Rate of function is 50 and as the price of erasers increasing the company's profit increasing and when price of the eraser decreasing the price the company's profit decreasing.

<h3>What is a function?</h3>

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

We have a graph of a function:

From the graph:

x-intercept = (0, 0) and (8, 0)

Maximum value of the graph = 270 at x = 4

Increasing in the interval x ∈ (0, 4)

Decreasing in the interval x ∈ (4, 8)

As the price of erasers increasing the company's profit increasing and when price of the eraser decreasing the price the company's profit decreasing.

Rate of function = (270-120)/(4-1) = 50

Thus, the x-intercept = (0, 0) and (8, 0), Rate of function is 50 and as the price of erasers increasing the company's profit increasing and when price of the eraser decreasing the price the company's profit decreasing.

Learn more about the function here:

brainly.com/question/5245372

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2 years ago
What transformation was performed on triangle ABC to create triangle A'B'C'?
Paha777 [63]
Reflection, across the y axis
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3 years ago
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