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If you rewrte  x²  =  bx - 1  as  x²​  - bx + 1, then the question can be rewritten as:

For what values of b will the function f(x)  =  x² - bx + 1 have:     two roots?  one root?  no roots?

x²​  - bx + 1  will be a perfect square if  b = -2  or  b = 2, giving either  f(x)  =  x² + 2x + 1  or  f(x)  =  x² + 2x + 1

When the function is a perfect square, the equation has only one root.  One root:  b = -2 or 2.

When b is a value between -2 and 2, the equation has no roots.  No roots if b is in the interval  (-2, 2).

When be is a value that is either larger than 2 or smaller than -2, the equation has no roots.  Two roots if b is either in the interval  (-infinity, -2)  or  (2, infinity).

The "no roots", "two roots" answer can be checked by graphing or proven by completing the square.

Using the rules:  0, 1 = blue; 2, 3, 4, 5, 6, 7, 8, 9 = red

A)  blue - red - red - red - red - red - red - red - red - red 

B)  With success = blue, proportion of success = 1/10  =  0.10  =  10%

C)  With the theoretical probability of drawing 4 blues in a row as 0.16%, and drawing only 4 marbles, iit is highly unlikely that the person drew 4 blues in a row. However, if the marbles weren't thoroughly mixed, the student might have drawn the same marble 4 times in a row. 

Also, note that in this simulation, blue was drawn twice in a row; the last draw of the first 10 and the first draw of the second 10.  If the person drew thousands of times, it becomes highly unlikely that the person does not draw at least 4 blues in a row. (As it is likely that some person will win more than one lottery, so long as you do not specify which person and which lotteries.)

And, if thousands of persons drew marbles, it is likely that at least one person would draw at least 4 blue marbles in a row.

The population is all year 9,10, 11 and 12 grade students - maybe in New York (the location is not made clear)

The sample is the 25 students who were randomly chosen.

The population is everyone or everthing that fits the required description.

 A sample is used if the population is too big to use in its entirity. The sample is a subset of the population.

if A add C is 12 and B add D is 2 and A takeaway B is 9 and C takeaway D is 14, what is A, B, C and D?

A+C=12       C=12-A

B+D=2         B=2-D

A-B=9          B=A-9

C-D=14      C=14+D

12-A=14+D

A+D = -2

A-9 =  2-D

A+D=11

Yep I agree - there are no solutions  :))

You know that 1750 divide 7 is 250.

You're 2nd.

The only real logical guess is that jaoe saved  £102.5 and zyron stole all of filipa and jacks money leaving him with £62.5.

Yes you are right, the question was open to interpretation.  The wording is inprecise!!

If I know that sinx = 3/4 and that 90<x<180 how can i find cosx and tanx

Think of the acute angle first.

Draw a right angled triangle and label on of the acute angles x

sinx=3/4 so label the opposite side 3 and the hypotenuse 4

Find the other side using the pythagorean theorem.

It will be   sqrt(16-9)=sqrt7

BUT x is really in the second quadrant so cos and tan will both be negative

\(cos x =\frac{- \sqrt7}{4}\\ and\\ tan x = \frac{-3}{\sqrt7}\\ \)

if the population of a country 324,597, the growth rate is .085 what is the projection is 10 years?  Now add 1% to the growth rate what is the new projection for 10 years.

I believe your question is worded incorrectly. It looks to me that the growth rate of 8.50% is for the entire 10-year period. Similarly, the 9.5%. Or, your first growth rate of .085 should read 0.0085 or .85% per year. I don't know of any "country" or even an "Island" that grows at 8.5% or 9.5% per year!. Ckeck your book carefully.

Thanks for the help

The fourth line in my answer above should say: Use S and M in the first equation.

Fair enough!

Hi Alan,

Yes it can be very annoying BUT not this time.  

There was an error in the question last time and it could not be answered.  :))

I didn't notice it had been asked a little earlier.  Annoying when this happens!

thanks guest :)

so for example

10⁶ = 1 with 6 zeros = 1000000

J + S + M = 165

J = 3S. So S = J/3

M = S + 40. So M = J/3 + 40

Use S and J in the first equation

J + J/3 + J/3 + 40 = 165

5J/3 = 125

J = 125*3/5

J = 75

John had saved $75

Hi Misaki,

I guess you are the guest that asked this earlier today - or maybe the other was a classmate //

Anyway it makes more sense now and I see that Alan is answering for you ;)

Add up all three equations and you get

2x + 2y + 2z = 54

So. x + y + z = 27

.

what is 180.33423432x99.11110

180.33423432 x 99.11110 = 17873.1243311

If you are referring to Laplace transforms, the transform is usually considered to be from the time domain.

If you have a function of time, say f(t), its Laplace transform L(s) is given by:

\(L(s)=\int_0^\infty e^{-st}f(t)dt\)

The Laplace transform of the derivative f'(t) is given by s*L(s) - f(0)

.

1. A model car is a 1/40 scale model.          

a) Express this in a ratio

I'm guessing it's 1:40                 Sounds good to me :)

The way ratios and the related fractions are expressed is quite confusing.  ://

b) If the length of the real car is 5.5m, what is the length of the model car?

Divide the real car length by 40

plz help

2. A piece of wood is cut in the ratio 3:7.

a) What fraction of the whole is the longer piece?  

Ths whole is 10 units long.    The longer peice is  7/10 

plz help

b) If the wood is 1.5m long, how long is the shorter piece?

I think it's; 3+7=10

3/10*1.5=0.45m    =45cm     Yes that is definitely correct

The question is ambiguous.

It depends on whether the right-angle is at A or B.

Start by dividing both sides by 3

Do that and post what you get and if you need more help I am here :)