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1. There are two squares. The perimeter of the larger square is 24 cm longer than the perimeter of the smaller one, and the area of the larger square is 96 cm^2 more than the area of the smaller one. What is the perimeter of the smaller square in cm?

Call the side  of the smaller square , x......the perimeter is  4x

Since the perimeter  of the larger is 24 more....its perimeter   = 4x + 24.....and its side is 1/4 of this = x + 6

Area of smaller square  + 96  = Area of larger square

x^2 + 96  = (x + 6)^2       simplify

x^2 + 96 = x^2 + 12x + 36       subtract x^2 from both sides

96  =  12x + 36

96 - 36  = 12x

60  =  12x      divide both sides by 12

5 = x  =side of the  smaller square

Perimeter of smaller square  = 5 * 4   =  20 cm

The bike store marks up the wholesale cost of all of the bikes they sell by 30%. Andre wants to buy a bike that has a price tag of $125. What was the wholesale cost of this bike?

Hello Guest!

\(x\cdot 130\%=$\ 125\\ x=\frac{$\ 125}{1.3}\)

\(x=$\ 96.15\)

The wholesale cost of this bike was $ 96.15.

  1

NOW our answers almost match.

Actually, they match exactly:

\(\text {Odds against } \mathbf {64:35} = \dfrac{35}{99} \; \mathbf \approx \; 35.356\%\)

It's very cool  when numbers meet on a high hill 

GA

g(x)  shits the parent graph two unts to the right  and up 4 units

This is why parents should never feed harsh laxatives to their children. 

 ...Kicking the shits out of them is a much better alternative.

GA

You deserved it!

Thanks, SMM....good to see you....I took a sabbatical  (LOL!!!)

This one  isn't too bad

Let   L = 2W + 3

So   we have

L * W   = 20

(2W + 3) (W)  = 20    simplify

2W^2  + 3W  = 20

2W^2  +  3W  - 20   =   0       factor  as

(2W  - 5) ( W + 4)  =  0

Only the first factor  helps us

Set to 0 and solve for  W

2W - 5  = 0

2W = 5

W  = 5/2  = 2.5 ft

CPhill!!!! I haven't seen you in such a long time! I just noticed you were answering my question. Thank you!

0.333333333333333 / 0.83333333333333333 =2 / 5

first die: any number
second die: prob 5/6 that it is different from first
third die: prob 4/6 that it is different from first two
fourth die: prob 3/6 that it is different from first three
fifth die: prob 2/6 that it is different from first four.

Hence; q = 5*4*3*2/6^4
Porbability, p, that at least two show the same number is p = 1 - q
p = 1 - 5*4*3*2/6^4  = 1 - (120 / 6^4) =0.9074 x 100 =90.74%

Here's a frequency table  for each possible outcome

2   3   4   5   6  7   8   9   10     11   12    13   14   15   16   17    18    19   20    21  22    23    24

1    2  3   4   5  6   7   8    9      10   11    12   11    10    9     8      7      6     5      4    3     2      1    =   144

P(>15)  =   45  / 144  =     5 / 16

We have a "zero"   at x  = 4

This means that , in the numerator,   4  + A    =   0

So A =  -4

Also....we have a horizontal asymptote  at   y =  -1

Looking at the  coefficients on the  x variables in the numerator and denominato, taking their ratio  and setting it equal to this asymptote, we have that

1 / B =  -1

So   B   = -1

And we have a vertical asymprore at  x  = 3

This means  that, in the denominator,  -1 (3)  + C  = 0  →   C = 3

A + B + C =   

-4 -  1  +  3   =

-2

See the graph here to  confirm this  : https://www.desmos.com/calculator/tx6zbax7ra

RB  + LB  +  RG  +  LG  =   38

RB  = 4LB

LG  = 3LB

If half of the girls are left-handed, then the other half are right - handed

So LG = RG

I don't believe  that there is an answer to this

The number of LG  must be divisible by 3  so that the number of LB is an integer

   LG    RG     LB      RB              Total

     3       3        1        4                 11

     6       6        2        8                 22

     9       9        3      12                 33

   12      12       4      16                 44       too many !!!!   

g(x)  shifts the parent graph two unts to the right  and up 4 units

Question: If the area of triangle ABC is 27, what is the value of p?

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In my above post, I was using the wrong diagram. 

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Answer:      A (3, 12)         B (12, 0)           C (0, p)

1/   AB = arctan(12 / 9) = 15

2/   CY = 2*27 / 15 = 3.6

3/    ∠ABO  ≅  ∠YCZ = arctan(12 / 9) = 53.13010235º

4/   OZ = 12 * tan ∠ABO = 16

5/   CZ = CY / cos∠YCZ = 6

6/   p = OZ - CZ = 10

( See above diagram ) 

1 - (1001, 1111, 1221, 1331, 1441, 1551, 1661, 1771, 1881, 1991, 2002, 2112, 2222, 2332, 2442, 2552, 2662, 2772, 2882, 2992, 3003, 3113, 3223, 3333, 3443, 3553, 3663, 3773, 3883, 3993, 4004, 4114, 4224, 4334, 4444, 4554, 4664, 4774, 4884, 4994, 5005, 5115, 5225, 5335, 5445, 5555, 5665, 5775, 5885, 5995, 6006, 6116, 6226, 6336, 6446, 6556, 6666, 6776, 6886, 6996, 7007, 7117, 7227, 7337, 7447, 7557, 7667, 7777, 7887, 7997, 8008, 8118, 8228, 8338, 8448, 8558, 8668, 8778, 8888, 8998, 9009, 9119, 9229, 9339, 9449, 9559, 9669, 9779, 9889, 9999) =90 palindromes

2 - (1001, 1771, 2002, 2772, 3003, 3773, 4004, 4774, 5005, 5775, 6006, 6776, 7007, 7777, 8008, 8778, 9009, 9779) >>Total = 18 such palindromes

How many integers satisfy -4 ≤ 2x+1 ≤ 6?

Hello Guest!

      \(-4 ≤ 2x+1 ≤ 6\)

 \(x\in\{-2,-1,0,1,2\}\)

  !

That is a link to something on your home computer. It is not going to work here.

That is not the graph.

Never mind.

Here is your graph, and the answer graph as well

1. What is the frequency of an orange light that has a wavelength of 620 x 10-9 m?

In your case the V is the speed of light.

https://www.desmos.com/calculator/zzxbryrahc

Please give the link to your graph.

OP  becomes OQ   under a dilation (which means it gets bigger)

It gets bigger by a factor of 4

OQ is 28units.

So now you tell me, what is OP?

I'm using x instead of  theta

sin^2 x  = 6sin x + 7

sin^2x  - 6 sin x - 7   = 0      factor

(sin x  - 7) (sin x + 1)  = 0

set  each factor to 0  and  solve  for x

sin x  - 7  = 0                   sin x + 1   = 0

sin x  = 7                          sin x = -1

impossible                         x =    θ =  -3pi/2  + 2pi*n    where n is an integer

If the area of triangle ABC is 27, what is the value of p?

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Solving this geometry problem in several easy steps:

1)   AB = sqrt(12² + 10²) = 15.62049935

2)   CY = 2*27 / AB = 3.456995759

3)   ∠ABO ≅ ∠ YCZ = arctan(12 / 10) = 50.19442891º

4)   OZ = 12 * tan∠ABO = 14.4

5)   CZ = CY / cos∠YCZ = 5.4

6)   p = OZ - CZ = 9

PV=0; P=1000; R=0.07/12; N=10*12;    P*(((1 + R)^N - 1)*((1 + R)^-N)* R^-1)
PV =$ 86,126.35 Amount deposited.

Interest earned=[1000 x 120] - $86,126.35 =$33,873.65 interest earned on the fund.