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.If the n days have passed since Sunday, then the total number of cents in her bank account is \(1+2+\cdots+2^n\). This is a geometric series with first term 1, common ratio 2 and n+1 terms. Hence the sum is: \(1+2+\cdots+2^n = \frac{1-2^{n+1}}{1-2} = 2^{n+1}-1.\) If this is greater than 500  (i.e. if the total amount of money in the account is more than $5 ) then \(2^{n+1}-1\ge 500\) , so \(2^{n+1}\ge 501\). The smallest power of 2 that is greater than 501 is  \(2^9\). Thus the first time there is more than $5  in the bank account occurs after n=8 days. This is 8 days away from Sunday, so the day of the week is \(\boxed{\text{Monday}}\) .

Oh, ok, I get it now! Thanks!

We  are looking for this

.01 [  1  -  2^N[ / [ 1  - 2]   =  5  

1 - 2^N   =  -500

-2^N  =  -501

2^N  =  501    take the log of each side

log 2^N  =  log 501  

N *  log 2  =  log 501

N  =  log501/log2

N = 8.9   ⇒    9 days ⇒  [ Monday ]

9/36    =   1/4

a) Total Students  =  50

b)  Blue  =  12/50      Brown  24/50     Green  8/50      Grey  6/50   

c)   Blue   =  24%      Brown  48%      Green 16%     Grey   12%

d)  

i say the answer is A or D

12x² -7x+1=0  →  (4x - 1)(3x - 1)

Note that the constants must both be +1 or -1, and since the  -7x term is negative they must both be -1.  Also the factors of 12 must sum to 7.  This means only 3 and 4 will do.

The solutions are therefore given by 4x -1 = 0  or x = 1/4  and  3x - 1 = 0 or x = 1/3

Here....I'm assuming that BC  and BD  are at right angles to  AB

From point C you measure the angle between the two towers. Knowing the distance from C to B, which trig function helps you find the distance AB?

We can use the tangent here

Write an equation to find an expression for the distance AB. (Don’t solve it yet.)

tan ACB   =  AB/BC

If the angle at C is 88.2° and the distance CB is 100 feet, what is the distance between the towers to the nearest whole foot? (Solve your equation from B and show all your work.)

tan 88.2  = AB/100   multiply both sides by 100

100tan (88.2)  =  AB  = 3182 ft

You want to check your work to make sure it’s right.You should be able to both measure and compute the angle at D. Knowing the distance between the two towers and the distance BD, what inverse trig function would allow you to compute the angle at D?

Given the distance you found in part C and the distance BD is 300 feet, what is the angle at D to the nearest one-tenth degree?

Unsure about this part.......

2d  =  5       divide both sides by 2

d =  5/2

a) 

French  =  .11 * 5000 =  $550

History  = .21  * 5000 = $1050

Reference  =  .15 * 5000 = $750

Science  =  .15 * 5000 = $750

Biography = .11 * 5000 = $550

Geography = .09 * 5000 = $450

Fiction = .18 * 5000 = $900

b) Check  :  add all the numbers in red.....they should total $5000

7....(9,3)  , m  =  4/9

 y - 3  =  (4/9)(x - 9)

8.....    y  =  l 10x  - 2  l  -  7

The parent function  is    y  = l x  l

And we can write

y  =  l  2 (5x - 1)  l   -  7

y = 2 l  5x  -  1  l   -  7

 ( 1/5 ,  - 7 ), x  = 1/5,  translated to the right by 1/5 unit  amd down 7 units

Here's the graph of the parent and the given function and axis of symmetry : 

https://www.desmos.com/calculator/4boazkf6c5

First one

FB / FS   =  ZR / ZD

55/38  =  x / 15.2        multiply both sides by 15.2

15.2 * 55 /  38  =  x  = 22

Second one

JD / JY   =  [ JD + DF] / [ JY + YS]

50/42  =  [ 50 + x ] / [42 + 63 ]

25/21  = [ 50 + x ] / [ 105]      cross-multiply

105/21 * 25  =  50 + x

5 * 25  =  50  + x

125  = 50  + x       subtract 50 from both sides

75  =  x

Third one

In trangle  ABC, angle C  =  80°

So.....by  AA congruency

ΔABC     similar to   ΔJKL

Last one

HG/HF  =  10/22   =  5/11

And 

HJ /HK  =   15/33   =  5/11

Thus  the ratio  of

GJ/FK  =   5/11

So...... Δ HGJ  is similar to  ΔHFK

The third answer is correct.....

Answered here :

http://web2.0calc.com/questions/please-help_40553

13.....

y  =  - 16x^2 +  95x + 10 

The x value that maximizes the height is given by   -95/ 2(-16)   =  -95/-32  =  95/32

So....subbing this back into the function, we can find the max height  =

-16 (95/32)^2  + 95(95/32)  + 10  =  151.02 ft

It will hit the ground when

-16x^2  + 95x  +  10  =  0

-95 ±√ [ 95^2  -  4(-16)(10) ]

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

               2(-16)

-95 ±√ 9665

__________       =    [ take the negative root]

       -32

-95  -  98.3

__________         =    6.04 sec

     -32

14.....this parabola turns upward so we can eliminate the first two answers

Using   (2, 15)   ....the  last  equation  gives

4(2)^2  - 3(2)  +  5

16  -  6  +  5

10 +  5  =   15

So.....the last answer is correct

(1  +   √2)^8  evaluates to  577 + 408√2

So.....this is a root....and so is the conjugate, 577 - 408√2

And the sum of the roots  = -b

So

577  +  577  =  - b  ⇒  1154  ⇒  b  =  -1154

And the product of the roots  = c

So

(  577 + 408√2)  (  577 - 408√2)   =  c   =   ( 332929  - 332928)  =   1

So

b  +  c  =   -1154  +   1   =   -1153

-x^2  + 5x  =  3       rearrange as

x^2  - 5x  +  3   =  0

a  = 1    b  = -5    c  = 3

So....the solutions are

-(-5) ± √  [  (-5)^2  -  4(1)(3)  ]

_______________________

           2(1)

5  ± √[ 25  -  12  ]

______________

           2

5/2   ± √13/2

(-5i)(-3i)  =

15i^2  =

15(-1)  =

-15

17

x  +  y   =  4  ⇒   y  =  4 - x     (1)

x^2  + y^2  =  16       (2)

Sub   (1)  into (2)  and we have that

x^2  + (4 - x)^2   =  16

x^2  +  (x - 4)^2  = 16

x^2  + x^2  - 8x  +  16  =  16      subtract 16 from both sides

2x^2  - 8x  = 0     factor

2x ( x   - 4)  = 0

Setting each factor to 0  we have that x  = 0   and x  = 4

And when x  = 0   , y  = 4 - 0  = 4

And when x = 4, y  = 4 - 4  = 0

So.....the solutions are    (0,4)  and (4,0)

18.....easy,  NSS

Just change the signs  on the constants in the parentheses and we get

3, -2 , 2

If   5 + √3   is a root then so is  5 - √3

There is no x^2 term......and the sum of the roots  = 0/a  =  0

So

 (5 + √3)  + (5 - √3)  + R  = 0   where R is the remaining root

10  + R  =  0    ⇒  R   = -10

And  ....let  R1, R2  and R3   represent the roots...and we have that

R1*R2   +  R1*R3  + R2*R3   =   b  / a   =  b   .....so.....

-10(5 + √3) + -10(  5 - √3)  +   (5 + √3) ( 5 - √3)  =  b

-50 + -50  + 22   =  b   ⇒   -78

And the product of the roots  =  -c   ....so....

-10(22)  =  -c

220  =  c

So   ...b +  c  =  -78   +  220   =  142

#17 {(4,0), (0,4)}

#18 3,-2,2

those are the answers

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y = (x - 2)^2  + 3

If this is rotated 180° about its vertex, the vertex does not change..........the new function is

y  =  - (x- 2)^2  + 3

Shifting this to the left 3 units left and 2 units down  results in the function

y  =  - (x + 1)^2   +  1

To find the zeroes, we have

-(x + 1)^2  +  1  =  0

-(x +1)^2  =  -1

(x + 1)^2  =  1

x + 1  =  ±1

So

x +  1  =  1 ⇒  x  = 0

x + 1  =  - 1  ⇒  x  = -2

So    a  +  b  =    0   +   -2    =    - 2

Here's the graph :  https://www.desmos.com/calculator/zbkwtqadyr