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polet [3.4K]
3 years ago
14

Please help me Algebra 1

Mathematics
2 answers:
Oduvanchick [21]3 years ago
8 0

Answer:

a.  \sqrt{x^n} = x^\frac{n}{2}

b. \sqrt{x^n}  = x^\frac{(n-1)}{2}\sqrt{x}

Step-by-step explanation:

a) When <em>n </em>is even, then it is divisible by 2. Because of this, you can write:

  • \sqrt{x^n} = (x^n)^\frac{1}{2}
  • \sqrt{x^n} = x^\frac{n}{2}

b) When <em>n </em>is odd, then <em>n - 1 </em> is even. This would make it divisible by 2, and there would be a remainder of 1, so we can write:

  • \sqrt{x^n} = (x^n^-^1^+^1) ^\frac{1}{2}
  • \sqrt{x^n} = (x^n^-^1 × x)^\frac{1}{2}
  • \sqrt{x^n} = x^\frac{(n-1)}{2} × x^\frac{1}{2}
  • \sqrt{x^n}  = x^\frac{(n-1)}{2}\sqrt{x}
BigorU [14]3 years ago
8 0
I don’t know but I think it is b
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Which transformation of AB will produce a line segment A'B' that is parallel to AB?
lyudmila [28]

<em>Options:</em>

<em>Rotation of 180° about point B </em>

<em>Rotation of 90° about point b </em>

<em>Reflection over the x-axis </em>

<em>Translation down 2 units</em>

<em></em>

Answer:

Rotation of 180° about point B

<em></em>

Step-by-step explanation:

Considering coordinates of point B

Assume the coordinates of the line at point B is (x,y)

i.e. B = (x,y)

First, we need to determine the slope at point B

Taking coordinates about the origin.

The slope of B is:

m = \frac{y_2 - y_1}{x_2 - x_1}

Where

(x_1,y_1) = (0,0) --- origin

(x_2,y_2) = (x,y)

m = \frac{y_2 - y_1}{x_2 - x_1} becomes

m = \frac{y - 0}{x - 0}

m = \frac{y}{x}

Taking the options one after the other:

Option A.

When rotated by 180°, the resulting coordinates of B would be

B' = (-x,-y)

Taking the slope of B'

The slope of B is:

m = \frac{y_2 - y_1}{x_2 - x_1}

Where

(x_1,y_1) = (0,0) --- origin

(x_2,y_2) = (-x,-y)

m = \frac{y_2 - y_1}{x_2 - x_1} becomes

m = \frac{-y - 0}{-x - 0}

m = \frac{-y}{-x}

m = \frac{y}{x}

Notice that the slope of B and B' is the same;

m = \frac{y}{x}

<em>Hence:</em>

<em>Rotation of 180° about point B  answers the question</em>

<em></em>

<em>There's no need to check for other options</em>

8 0
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How to find the least common denominator of 3 fractions?
Lina20 [59]

Answer:

  Find the LCD of the first two, then the LCD of that and the third one.

Step-by-step explanation:

You can do it by finding the LCD of two of the denominators, then the LCD of that and the third denominator.

Or, you can factor each of the denominators and find their LCM by multiplying the unique factors to their highest powers.

___

<u>Example:</u>

  1/21 + 1/35 + 1/45

The LCD of 1/21 and 1/35 is (21·35)/5 = 105. The LCD of 1/105 and 1/45 is ...

  (105·45)/15 = 315

__

Using factoring ...

  • 21 = 3·7
  • 35 = 5·7
  • 45 = 3²·5

LCD = 3²·5·7 = 315

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Answer:

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Step-by-step explanation:

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