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[ 3, 4 ] =   (   [ (4)^2 - 7(4) + 15 ] - [ (3)^2 - 7(3) + 15 ]  ) / [ 4 - 3 ] =  0  m/s

[ 3.5, 4] = (   [ (4)^2 - 7(4) + 15 ] - [ (3.5)^2 - 7(3.5) + 15 ]  ) / [ 4 - 3.5 ]  = 0.5 m/s

[ 4, 5 ] =  (   [ (5)^2 - 7(5) + 15 ] - [ (4.5)^2 - 7(4.5) + 15 ]  ) / [ 5 - 4.5 ]   = 2.5 m/s

[ 4, 4.5 ] =  (   [ (4.5)^2 - 7(4.5) + 15 ] - [ (4)^2 - 7(4) + 15 ]  ) / [ 4.5 - 4 ]  = 1.5 m/s

To approximate the instantaneous velocity at t = 4......use this interval

[ 4, 4.001 ]  =  (   [ (4.001)^2 - 7(4.001) + 15 ] - [ (4)^2 - 7(4) + 15 ]  ) / [ 4.001 - 4 ]  ≈ 1.001 m /s

So....the instantaneous velociy at t = 4 =   1 m/s

[ If you take Calculus....you will see that this is true...!!!!]

1. 5 * 24  =   36 cm

First term =   (1)^3 - 3  =  -2

Second term =  (2)^3 - 3  = 5

Can you take it from here???

y = (1/2)x

The slope is  change in y / change in x  =  1/2  =  rate of change

In the table....note that the rate of change is the same......every time y changes by 1, x changes by 2

Also...if we let x = 0 in the function, then y =  (1/2)(0)  = 0

So.  (0,0) is on the graph of the function...this is the y intercept

Which is the  same point as in the table

So....

The y intercepts and rate of change are the same ⇒   "B"

THANK YOU 

\(\bar{\Delta} = \dfrac{f(-2)-f(-5)}{(-2) - (-5)} = \\ \dfrac{0-21}{3} = -7\\ \text{i.e. choice A}\)

OK....we have

x^2 -4x -32

15.   To find the x intercepts  set the above to 0  and factor

x^2 - 4x - 32 = 0

(x - 8) ( x + 4) = 0

Setting each factor to 0 and solving for  x we have that

x - 8 = 0               and       x + 4 = 0

x = 8                                  x = -4

So...the x intercepts (roots) are x = 8 and x = -8

16.    the discriminant is

(-4)^2 -  4 (1) (-32)

16 + 128

144

When the discriminant is > 0.....we will have two real roots

\(1: \text{ obviously no}\\ 4i: \text{ hopefully obviously no}\\ 3+3i:~Re\left(\dfrac{1}{3+3i}\right) = Re\left(\dfrac{3-3i}{18}\right) = \dfrac 1 6 \text{ so yes}\\ 3-3i: \text{same answer as for }3+3i\\ 1-2i: Re\left(\dfrac{1+2i}{5}\right) = \dfrac 1 5 \neq \dfrac 1 6 \text{ so no}\\ 2+3i: Re\left(\dfrac{2-3i}{13}\right) = \dfrac{2}{13} \neq \dfrac 1 6 \text{ so no}\\ 6: \text{ obviously yes}\)

\(\text{Assuming the wall is plumb, the timber, the wall, and the ground form a right triangle}\\ \text{Using the pythagorean theorem and recognizing that the brace will be the hypotenuse we have}\\ \ell = \sqrt{12^2-8^2} = \sqrt{144-64} = \sqrt{80}=4\sqrt{5}~ft\)

1. a varies jointly as b and c. One set of values is a=86.4 when b=9 and c=12. Find a when b=20 and c=6.5

a = kbc

86.4 = k (9)(12)

86.4 = k (108)

86.4 / 108 = k  =  4/5

So

a = (4/5) (20) (6.5)

a =   16 * 6.5

a = 104

2. m varies jointly as n and p. One set of vales is m=60 when n=4 and p=5. Find m when n=12 and p=2

m =  knp

60 = k (4)(5)

60 = 20k

60/20 = k = 3

So

m = 3 (12) (2) 

m = 72

See here for a detailed explanation :

http://mathforum.org/dr.math/faq/faq.birthdayprob.html

P(2 people out of 23 share the same birthday)   =

1 - P (none of the 23 share the same birthday) =

1 -   365! / [ (365 - 23)! * 365^23 ]   ≈    .5073  =    50.73%

First....calculate the number of feet in 100m  =   100 * 3.28 ft   =  328 ft

Divide the by the number of seconds   =  328/ 9.69  ≈  33.85 ft /sec

Multiply this by the number of seconds in one hour  =   3600 sec * 33.85 ft /sec = 121860 ft

Divide this by the number of feet in a mile     (121860 ft / hr)  / (5280 ft / mile) ≈  23.08 mph

Pick out the answer you like from these 3 links:

https://web2.0calc.com/questions/a-square-defg-varies-inside-equilateral-triangle
https://web2.0calc.com/questions/help_92263
https://web2.0calc.com/questions/help-needed-please-geometry

ohhhh i understand thank you

\(0.\overline{123} = \frac{41}{333} \\ \text{So, } \frac{41}{333} \times 9= \boxed{\frac{41}{37}}\)

Since the x intercepts are (-3, 0) and (5, 0).....this must mean that  (x +3) (x - 5) = 0

Expanding....we have that

x^2 - 2x - 15 =    0

You are making me reallly think here - that is a good thing.   I have a new insight.

Your logic sounds good  but I also think that your red statment is written incorrectly......

Do you mean.

 So that means NO numbers below 31 can factors of   30!+1   

Please don't just give answers itsabot.

It is possible that the asker is just being lazy ans wants to use you as a free cheat tool.

OR

They do not know how to plug the numbers in and so your answer does not help.

Better to show them how to plug in the numbers for one of the incorrect answers and then let them find the correct one on their own.

That is my suggestion :)

"A"  cannot be correct....if we sub -3 into this, it does not output -11

Actually....I think you will find that  "D' is what we need

The constant term will be

C(9, 6) * (√x)^6 * (5/x)^3  =  84 * (x)^3 * (5)^3/x^3  =  84 * 125 =  10500

Nvm...

Look:

1*2*3*...*30 = 30! Right?

Without even calculating you can find the answer...

Any number 30 and below will still be able to divide evenly to 30! because their number is being multiplied with 30!

But when you add the extra one,

You will always have a remainder of 1 when dividing with numbers 30 and below.

So that means numbers above 30 can be divisible to 30!

Don't you love that when you answer a though question you feel so smart. But you feel so dumb having to put it onto the forum. lol

you are given the two roots of the equation    x  =  -3   and   x = 5, so the equation becomes

(x+3)(x-5) = 0        (note the sign change)       Expanded

x^2 -2x-15=0   or 

f(x) = x^2-2x-15   or

y = x^2 -2x-15

Just an FYI:

You should realize that Leap Years only affect the days in Feb    from 28    to 29 in a leap year.    Nothing to do with May.

I would suggest you open an account....it is free.    When 'guests' post questions, responders are less likely to show how the answer was derived....either way...if you do not understand something it is your flippin' responsibility to ask for an explanation.  Most of the time you will get one......

Just plug things in. You'll find that A is your answer.