college level mathematics test.?

B

bbygirll

New member
please show me your work!!


2^(5/2) - 2^(3/2) =


if a dose not equal to b and (1/x) = (1/a) = (1/b), then x =


if 3x^2 - 2x + 7 = 0, then ( x - (1/3) )^2 =


please show me a short cut to this problem:

An apartment building contains 12 units consisting of one- and two-bedroom apartments that rent for $360 and $450 per month, respectively. When all units are rented, the total monthly rental is $4,950. What is the number of two-bedroom apartments?


there is a one square with an area of 5, and the other square with an area of 125. If two squares have the respective areas indicated in square yards, how many yards of fencing are needed to enclose the two regions?


If log10x=3, then x=
the answer is 1000. please tell me why.



please help me out!
it will be very appreciated. =]
 
2^(5/2) - 2^(3/2)
√2^5 - √2^3
4√2-2√2
=2√2
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(1/x) = (1/a) = (1/b)

I have absolutely no idea how to do this one. I'm sure at one time I could have gotten it, but nothing is coming to me, sorry.
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I'm a little lost with this one, here's my scratch work.

3x² - 2x + 7 = 0

(Quadratic Formula)

-b ± √[ (b² - 4ac)]
-----------------------------
2a

2 ± √[ (4 - 84)]
-----------------------------
6
I don't know if you are allowed to use imaginary numbers or not, if you don't use them then x does not exist for that function. If you do then continue with i.

2 = log{base of}(x-⅓)n

n=?
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x=1 bedroom
y=2 bedroom

x + y = 12

360x+450y=4950

y=?

Use substitution. Solve for x, and plug in.

x=12-y
360(12-y) + 450y = 4950
4320-360y+450y=4950
90y=630
y=630/90
y=7

btw, x=5

There are 7 two bedroom apartments and 5 one bedroom
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If one square has an area of 5, then one side must be equal to √5. Therefore, the perimeter is 4√5.

If the other square has an area of 125, then one side must be equal to √125 = 5√5 (√125=√5*5*5 & the square root of 5*5 is 5). Therefore, the perimeter is 4(5)√5=20√5

Add the two perimeters together, 4√5 + 20√5 = 24√5

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Logs are actually very simple once you know what to do and I wish I could draw you my curve that I create when I solve them but I can't.

log10x=3
the base of the log is 10.

The inverse equation of a logarithmic function is exponential. So, we're going to turn it into the exponential.

Here's how you ALWAYS do it.

Base (10) raised to the logarith (3) = the number (x)

10^3 = x
1000=x
 
Hi,

1. 2^(5/2) - 2^(3/2)
= √(2^5) - √(2^3)
= √{(2^4)•2} - √{(2^2)•2}
= 2²•√2 - 2•√2
= 4•√2 - 2•√2
= 2•√2

2.(1/x) = (1/a) = (1/b), where a â‰* b
x = a = b, where a â‰* b
so x = { } or NULL

3. 3•x² - 2•x + 7 = 0 ... divided by 3
.... x² - (2/3)•x + (7/3) = 0
.... (x - (1/3))² - (1/9) + (7/3) = 0
.... (x - (1/3))² = (1/9) - (7/3)
.... (x - (1/3))² = (1/9) - (21/9)
so (x - (1/3))² = -20/9

4. took example by :
... x = one-bedroom apartment
....y = two-bedroom apartment
so Given Equation :
x unit + y unit = 12 unit .. simplify → x + y = 12 ... (1)
$360•x + $450•y = $4,950 .. simplify → 4•x + 5•y = 55 ...(2)
so x + y = 12 → y = 12 - x ... substitute Eq (2), then :
.... 4•x + 5•(12 - x) = 55
.... 4•x + 60 - 5•x = 55
.... 4•x - 5•x = 55 - 60
.... -x = - 5
.... x = 5 unit → y = 12 - 5 = 7 unit
so There are 7 two bedroom apartments & 5 one bedroom apartments.

5. Given :
.... Area â–¡1 = 5, Area â–¡2 = 125
took example by : side â–¡1 = x & side â–¡2 = y
Solution :
Area â–¡1 = 5
......... x² = 5
......... x = √5

Area â–¡2 = 125
......... y² = 125
......... y = 5√5

perimeter of 2 region □ together = 3•x + 3•y + (y - x) ... simplify
perimeter of 2 region □ together = 2•x + 4•y
perimeter of 2 region □ together = 2•√5 + 4•5√5 = 2√5 + 20√5 = 22√5

fencing are needed to enclose the two regions = 22√5 yard

6. log10 x = 3
... (log x / log 10) = 3
... log x = 3 • log 10
... log x = log (10^3)
........ x = 10^3 = 1000

Hope this helps :)
 
1. question

sqr(2^5)-sqr(2^3)

sqr(2*2^4)-sqr(2*2^2)

2^2sqr(2)-2sqr(2)

4*2^1/2-2*2^1/2

since the root part is same you can subtract them form each other
the result would be

2sqr(2)


are you sure it's not 4.590 but 4.950?
 
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