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3 years ago

What is the least common denominator of the rational expressions below? 1/x^2-5x+3/x^2+2x-35

Mathematics

1 answer:

Komok [63]3 years ago

5 0

Here the denominators are quadratics , so we need to factorise them first

1/(x²-5x) +3/(x²+2x-35)

factorising x²-5x ,

here GCF is x, so taking x out we have

x(x-5)

factorising x²+2x-35 using AC method,

we find factors of -35 that add up to give 2

(x-5)(x+7)

Since we have x-5 common in both denominators, so lcd of the rational expression will be product of x(x-5)(x+7)

lcd is x(x-5)(x+7)

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Tatiana [17]

For this case we have that by definition of properties of powers and roots, it is fulfilled that:

\sqrt [n] {a ^ m} = a ^ {\frac {m} {n}}

So:

\sqrt [4] {9 ^ {\frac {1} {2} x}} = 9 ^ {\frac {\frac {1} {2}} {4} x} = 9 ^ {\frac {1} {8} x}

So, we have to:

\sqrt [4] {9 ^ {\frac {1} {2} x}} = 9 ^ {\frac {1} {8} x}

Answer:

9 ^ {\frac {1} {8} x}9

Option B

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7 0

2 years ago

Max makes a scale drawing of the distance between Salt Lake City and Arizona. The distance between Salt lake City and Arizona is

kari74 [83]

21cm / 7cm = 3 x 250 km = 750 km

4 0

3 years ago

Jason and Alison are hiking in the woods when they spot a rare owl in a tree. Jason stops and measures an angle of elevation of

Shalnov [3]

Answer:

$Owl= 67.14ft$

Step-by-step explanation:

<em>See comment for complete question.</em>

The given information is represented in the attached figure.

First convert 22°8'6'' and 30° 40’ 30” to degrees

$22^{\circ} 8'6'' = 22 + \frac{8}{60} + \frac{6}{3600}$

$22^{\circ} 8'6'' = 22.135^{\circ}$

$30^{\circ} 40'30'' = 30 + \frac{40}{60} + \frac{30}{3600}$

$30^{\circ} 40'30'' = 30.675^{\circ}$

Considering Jason's position:

$tan(22.135^{\circ}) = \frac{H}{x + 48}$

Where x = distance between the tree and Alison

Make H the subject

$H = (x + 48)tan(22.135^{\circ})$

Considering Alison's position

$tan(30.675^{\circ}) = \frac{H}{x}$

Make H the subject

$H = xtan(30.675^{\circ})$

$H = H$

$(x + 48)tan(22.135^{\circ}) = xtan(30.675^{\circ})$

$(x + 48) *0.4068 = x* 0.5932$

Open bracket

$x *0.4068 + 48 *0.4068 = 0.5932x$

$0.4068x + 19.5264 = 0.5932x$

Collect Like Terms

$-0.5932x+0.4068x = -19.5264$

$-0.1864x = -19.5264$

$0.1864x = 19.5264$

Make x the subject

$x = \frac{19.5264}{0.1864}$

$x = 104.76$

Substitute 104.76 for x in $H = xtan(30.675^{\circ})$

$H = 104.76 * tan(30.675^{\circ})$

$H = 104.76 * 0.5932$

$H = 62.14$

The above represents the height of the tree.

The height of the owl is:

$Owl= H + 5$

$Owl= 62.14 + 5$

$Owl= 67.14ft$

7 0

3 years ago

Which set includes rational numbers but not natural numbers?

Kryger [21]

Answer:

Answer: Natural Numbers count physical things. They can't be negative.

The third option is correct because its fractions and decimals.

Step-by-step explanation:

Hope this helps!

7 0

3 years ago

Read 2 more answers

Find the solution of given expression <br><br><img src="https://tex.z-dn.net/?f=%20%5Csqrt%7B6%20%5Ctimes%20216%7D%20" id="TexFo

Morgarella [4.7K]

6x216 multiply them and u get 1296 then calculate the square root and your answer is 36

5 0

3 years ago

Read 2 more answers