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FrozenT [24]
3 years ago
15

For f(x)=√(2x+1) , find the following:

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

Part a.

The domain is the set of x values such that x \ge -\frac{1}{2}, basically x can be equal to -1/2 or it can be larger than -1/2. To get this answer, you solve 2x+1 \ge 0 for x (subtract 1 from both sides; then divide both sides by 2). I set 2x+1 larger or equal to 0 because we want to avoid the stuff under the square root to be negative.

If you want the domain in interval notation, then it would be \Big[ -\frac{1}{2} , \infty \Big) which means the interval starts at -1/2 (including -1/2) and then it stops at infinity. So technically it never stops and goes on forever to the right.

-----------------------

Part b.

I'm going to use "sqrt" as shorthand for "square root"

f(x) = sqrt(2x+1)

f(10) = sqrt(2*10+1) ... every x replaced by 10

f(10) = sqrt(20+1)

f(10) = sqrt(21)

f(10) = 4.58257569 which is approximate

-----------------------

Part c.

f(x) = sqrt(2x+1)

f(x) = sqrt(2(x)+1)

f(x+2a) = sqrt(2(x+2a)+1) ... every x replaced by (x+2a)

f(x+2a) = sqrt(2x+4a+1) .... distribute

we can't simplify any further

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This is asking how many ways can we choose 13 songs from a set of 25.
The formula is:
n! / r! * (n -r)!    =

25! / 13! * 12! which equals

25 *24 *23 *22 *21 *20 *19 *18 *17 *16 *15 *14 *13!  divided by
13! * 12! which equals

25 *24 *23 *22 *21 *20 *19 *18 *17 *16 *15 *14 divided by
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which equals

<span> <span> <span> 2,490,952,020,480,000 </span> </span> </span> divided by <span> <span> <span> 479,001,600 </span> </span> </span>

and that equals
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Here's a combination calculator to check your work:
http://www.1728.org/combinat.htm






4 0
2 years ago
Find x the missing side length of the triangle
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Answer:

16.6

Step-by-step explanation:

a = 14

b = 9

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2 years ago
The brackets for a shelf are in the shape of a triangle. Find the angles of the triangle if the
zimovet [89]

Answer:

Step-by-step explanation:

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6 0
3 years ago
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lbvjy [14]

Step-by-step explanation:

Given bi-quadratic equation is:

x^4+95x^2 -500=0

Substituting x^2=a, given bi-quadratic equation reduces in the form of following quadratic equation:

a^2 +95a -500=0\\

Let us factorize the above quadratic equation:

a^2 +95a -500=0\\\therefore\: a^2 +100a -5a-500=0\\\therefore\: a(a +100) -5(a+100)=0\\\therefore\: (a +100)(a -5)=0\\\therefore\: (a +100)=0\:\: or \:\: (a -5)=0\\\therefore\: a = - 100\:\: or \:\: a = 5\\\\CASE\: (1)\:\\When\: a = - 100 \implies x^2 = - 100\\\therefore x=\pm \sqrt{-100}\\

Since square root of a negative number cannot be found, so:

x \neq \pm \sqrt{-100}\\

CASE\: (2)\:\\When\: a =5 \implies x^2 =5\\\therefore x=\pm \sqrt{5}\\

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2 years ago
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