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Note that  OB  =OA

So triangle BOA is isosceles with angles OAB and OBA  equal

So.....measure  of angle OAB =  (180 - 113) / 2 =  67/2  =  33.5° 

\( \sqrt{7+\sqrt{5-\sqrt{3+x}}}=3\)

Square both sides

7  +  sqrt [ 5 - sqrt (3+ x) ]  =  9

sqrt  [ 5 - sqrt (3 + x) ]  =  2         square both sides again

5 - sqrt (3 + x)  = 4

-sqrt (3 + x)  =  -1    square both sides one last time

3 + x =   1

x =  1  - 3  =    -2

a^2 = k / sqrt (b)   where k is the proportionality constant

So

2^2  = k / sqrt (81)

4  = k / 9

4 * 9  = k =  36

So

If  ab =  48  then  a =  48/ b

Then

(48/b)^2  =  36 / sqrt (b)

2304 / b^2 =  36 / sqrt (b)

2304 / 36  =  b^2 / sqrt (b)

2304/36 = b^2 / b^(1/2)

2304/36  = b^(3/2)      

(2304/36)^(2/3)  = (64)^(2/3)  = (64^(1/3))^2  = 4^2  =   b  =  16 

The expression simplifies to 12m^2.

\(file:///var/mobile/Library/SMS/Attachments/54/04/13C468A2-C92B-4BB2-B492-4FF5B24396DB/IMG_3509.PNG\)Give your answer in the form ax+by+c where a, b   and c are integers with no common factor greater than 1

G =  k / S              where k is the proportionality constant

2  =  k /  9

9 * 2   =  k =   18

So

G =   18 / 6   =   3 gallons

Use the fact that a = sqrt(b)*k for some k.  This leads to b = 8.

Thx!

9:33 AM to  11:18 AM =  1 hr 45 min =  1.75 hrs

12:07 PM to 6:45 PM =  6 hours + 38 min    =  6 + 38/60 hrs =  6 + 19/30 hrs

So

Hrs worked x pay per hr =  

( 1.75  + 6 + 19/30) ( $15)   = $125.75 =  $126  to the nearest dollar

The answer is 90*8/70, which rounds to 10.3.

this made a lot of sense thank you

!

OK....no prob.....this one is a little difficult to see,  at first

The graph of  h ( x - 3)  shifts this parabola to the RIGHT by 3 units

We need to find  the place on the parabola where its width =  3 units

Note that this appears to be along the line y = 3

The parabola  intersects this line  at  (-2, 3)  and  ( 1, 3)    (note that the width is 3 !!! )

So  point  (-2,3)  is shifted to  point (1,3)  by  h(x - 3)  and (1,3)  is the point of intersection of both graphs !!!

{Hope that makes sense !! }

sorry phill the latex didnt go through it meant to say

if the graph of y = h(x-3)

If the graph of _____ is drawn on the same set of axes as the graph above, then the two graphs intersect at one point. What is that point?

If the graph of   (what ) ???

(11111, 11112, 11113, 11121, 11122, 11123, 11131, 11132, 11211, 11212, 11213, 11221, 11222, 11223, 11231, 11232, 11311, 11312, 11313, 11321, 11322, 11323, 12111, 12112, 12113, 12121, 12122, 12123, 12131, 12132, 12211, 12212, 12213, 12221, 12222, 12223, 12231, 12232, 12311, 12312, 12313, 12321, 12322, 12323, 13111, 13112, 13113, 13121, 13122, 13123, 13131, 13132, 13211, 13212, 13213, 13221, 13222, 13223, 13231, 13232, 21111, 21112, 21113, 21121, 21122, 21123, 21131, 21132, 21211, 21212, 21213, 21221, 21222, 21223, 21231, 21232, 21311, 21312, 21313, 21321, 21322, 21323, 22111, 22112, 22113, 22121, 22122, 22123, 22131, 22132, 22211, 22212, 22213, 22221, 22222, 22223, 22231, 22232, 22311, 22312, 22313, 22321, 22322, 22323, 23111, 23112, 23113, 23121, 23122, 23123, 23131, 23132, 23211, 23212, 23213, 23221, 23222, 23223, 23231, 23232, 31111, 31112, 31113, 31121, 31122, 31123, 31131, 31132, 31211, 31212, 31213, 31221, 31222, 31223, 31231, 31232, 31311, 31312, 31313, 31321, 31322, 31323, 32111, 32112, 32113, 32121, 32122, 32123, 32131, 32132, 32211, 32212, 32213, 32221, 32222, 32223, 32231, 32232, 32311, 32312, 32313, 32321, 32322, 32323)>>Total == 164 such permutations.

It is incorrect anyway   !!!!!

2x - 5   ≤ -x + 12     rearrange as

2x + x  ≤  12 + 5

3x ≤  17

x ≤  17/3   

x  =  ( inf, 17/3 ] 

Note that  x (x^2 -1)  = (x)(x + 1) ( x - 1)

Multiply throght by ths  factorization and we have

2x^2  + 3x   - 5 =  A ( x - 1)(x + 1)  + B(x)(x + 1)  + C(x)(x - 1)         simplify

2x^2 + 3x  -5 =  A ( x^2 -1)  + B( x^2 + x)  + C(x^2 - x)

2x^2 +  3x - 5 =  (A + B + C)x^2  + (B - C)x  - A

Equating terms we have this syatem

A + B + C  =  2

B - C  = 3           (1)

A = 5

So

5 + B + C = 2 

B + C  =  -3     (2)

Adding (1) and (2)  we get  that  2B  = 0   so B =  0

So

5 + 0 + C  =2

C = 2 -5   =  -3

(A,B,C)  =  (5, 0 , -3)

A horse 64 feet from the center of a merry-go-round makes 27 revolutions. In order to travel the same distance, how many revolutions would a horse 16 feet from the center have to make? 

The circumference of a circle radius 64 is      2 • π • 64  =  128 π  

The circumference of a circle radius 16 is      2 • π • 16  =    32 π  

128 π / 32 π  =  4 

So the horse travelling the smaller circle has to go 4 times around to go

the same distance as the horse travelling the larger circle 1 time around. 

When the horse travels the distance of 27 times around the outer circle, 

the other horse has to go around 4 times as much for the same distance. 

4 • 27  =  108 revolutions  

_.

Sorry, that's not correct. Maybe it's possible to rewrite $x^x$ in terms of an exponential with base $e$?

I used: 19/t  +  5/t

(1 , 2 , 3 , 4 , 6 , 8 , 12 , 24)>>Total==8 such positive integers.

How did u find that answer?

\(x \in \boxed{(-\infty,7/3]}\)

How did u come up with that?