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liberstina [14]
2 years ago
14

What are the two possible answers for the equation Ix/5I = 3?

Mathematics
1 answer:
bagirrra123 [75]2 years ago
5 0

Answer:

Either x = -15 or x = 15.

Step-by-step explanation:

|x| = \left\lbrace \begin{aligned} & x && \text{if $x \ge 0$} \\ & -x && \text{if $x < 0$}\end{aligned}\right..

Hence, there are two possibilities to consider:

  • Either (x / 5)  \ge 0,
  • Or (x / 5) < 0.

If (x / 5) \ge 0, then |x / 5| = x / 5.

Substitute into the original equation: x/ 5= 3. Solve for x: x = 15.

Important: verify that the solution x = 15 meet the assumption (x / 5) \ge 0. Indeed, (x / 5) = (15 / 5) = 3 and is indeed non-negative. Hence, the solution x = 15\! is valid.

On the other hand, if (x / 5) < 0, then |x / 5| = - x / 5.

Substitute into the original equation: (-x / 5) = 3. Solve for x: x = -15.

Similarly, verify that the solution x= - 15 satisfies the current assumption that (x / 5) < 0. Indeed, this assumption is met, and x = -15 is also a valid solution.

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Answer:

Rhombus

Step-by-step explanation:

The given points are A(−5, 6), B(−1, 8), C(3, 6), D(−1, 4).

We use the distance formula to find the length of AB.

|AB|=\sqrt{(-1--5)^2+(8-6)^2}

|AB|=\sqrt{16+4}

|AB|=\sqrt{20}

The length of AD is

|AD|=\sqrt{(-1--5)^2+(6-4)^2}

|AD|=\sqrt{16+4}

|AD|=\sqrt{20}

The length of BC is:

|BC|=\sqrt{(-1-3)^2+(8-6)^2}

|BC|=\sqrt{16+4}

|BC|=\sqrt{20}

The length of CD is

|CD|=\sqrt{(-1-3)^2+(6-4)^2}

|CD|=\sqrt{16+4}

|CD|=\sqrt{20}

Since all sides are congruent the quadrilateral could be a rhombus or a square.

Slope of AB=\frac{8-6}{-1--5}=\frac{1}{2}

Slope of BC =\frac{8-6}{-1-3}=-\frac{1}{2}

Since the slopes of the adjacent sides are not negative reciprocals of each other, the quadrilateral cannot be  a square. It is a rhombus

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What is the sum of StartRoot negative 2 EndRoot and StartRoot negative 18 EndRoot? 4 StartRoot 2 EndRoot 4 StartRoot 2 EndRoot i
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Adding  \sqrt{-2}\,\,and\,\,\sqrt{-18} we get 4\sqrt{2i}

Option C 4 StartRoot 2 EndRoot i is correct.

Step-by-step explanation:

We need to find the sum of: \sqrt{-2}\,\,and\,\,\sqrt{-18}

Finding sum:

\sqrt{-2}+\sqrt{-18}

\sqrt{-2} can be written as \sqrt{2}i

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We know 18 = 2x3x3 = 2x3^2 so,

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Adding like terms:

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So, adding  \sqrt{-2}\,\,and\,\,\sqrt{-18} we get 4\sqrt{2i}

Option C 4 StartRoot 2 EndRoot i is correct.

Keywords: Square root expressions

 Learn more about Square root expressions at:

  • brainly.com/question/4034547
  • brainly.com/question/3511750

#learnwithBrainly

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