All Answers 358298 Answers

i missed up answers are

6y-8

6y-4

6y+ 2

6y+4

8y-2(y+4)         expand using distributive

8y-  2y -8          simplify by adding the 'y' terms together

6y-8                does not match your answer choices....did you enter everything correctly? 

C   16+P

Note that angle A =angle A

And angle CBA = angle EDA

So...by AA congruency....triangle CBA is similar to triangle EDA

[ Since BE = 10 and AE = 11, then BA = 21  ]

So...this implies that

BA / CA = DA / EA

21 / 35  =  DA  / 11     multiply both sides by 11

11 * 21 / 35 = DA

6.6  =  DA

thanks

If the original price was  p    and you took away275 from the price

D   p - 275

Nevermind there were tips on the top of the page I overlooked

Let's take this a little at a time

a)  x is the number of hours after midnight

b) f(x)  is the temp in Celsius

c) Note that 24 represents the number of hours in a day....we don't need any more that that !!!!

d) Here's the graph : https://www.desmos.com/calculator/foicqsv1oh

e )  Looking at the graph.....the coldest temp occurs at the low point on the graph ....the graph shows that the lowest temp occurs at (14.-10)

This means that the coldest temp of -10C occurs 14 hours after midnight = 2 PM

The warmest temp occurs (strangely) at midnight (t = 0)  !!!...this is the highest point on the graph...the temp at this time is 9.6C

f) The graph  shows that the temp decreases from midnight to 2PM

To find the avg rate of decrease we have

[ temp at midnight - temp at 2PM ] / [ 0 - 14 ] =

[ 9.6 -  (- 10) ] / [ 0 - 14 ]   =   19.6 / -14  = -1.4

This means that the temp is falling 1.4C every hour

g)  The temp increases from 2 PM to the next midnight (where it is 0C )

So...the average rate of increase is

[ temp at next midnight - temp at 2PM ] / [24 - 14 ]   =

[ 0 - (-10) ] / [ 10 ]   =   1

This means that the avg rate of increase = 1C per hour

That’s all it gave me was g(10)

it means the function g() evaluated at the number 10

Someone along the line there must be a function g() you were given.  Otherwise, yes, it doesn't make much sense.

There are two entirely different meanings to the word "tangent"

You were given what I'd call the second one.  A line that touches a curve at exactly one point.

The definition you are probably after is entirely different

Consider the following right triangle

The "tangent" of the angle \(\theta\) is given by

\(\tan(\theta) = \dfrac{\text{length of opposite side}}{\text{length of adjacent side}}\)

yea do that

We have that

6e^(-0.38t) = 3.1       divide both sides by 6

e^(-0.38t)  =  3.1 /  6       take the Ln of both sides

Ln e^(-0.38t) = Ln ( 3.1 / 6 )         

Using a log property, we can write

(-0.38t) Ln e  = Ln ( 3.1 / 6)

Since Ln e = 1, we can ignore this....and we have

-0.38t  = Ln ( 3.1 / 6)      divide both sides by -0.38

t =  Ln (3.1 / 6) / ( -0.38)  ≈  1.73 hrs between injections

A line that touches a curve at only ONE point.    Just barely touches it.   the line is a tangent line and the point is a point of tangency.

Last one...square both sides straight away  and we get that

x^2 - 8x + 16 = 2x     rearrange as

x^2 - 10x + 16  = 0    factor

(x - 8) ( x - 2)  = 0

x = 8      or  x = 2

Note that 8 does not work   because 8 - 4   does not equal     - √ (2 * 8)  =  - √16   =  - 

Note that   x = 2 is good

2 - 4  = - √(2 * 2)

-2  = -√4

-2 = - 2   !!!

b)   Divide both sides by 2   to make the numbers smaller

√ [ 44 - 2x ]  =   x - 10          square both sides

44 - 2x  =    x^2 - 20x + 100     rearrange as

x^2 - 18x + 56 =  0      factor as

(x - 14) ( x - 4) =  0

Set both factors to 0 and solve for x and we get that

x = 14     or  x  = 4

The first solution is good, GM

The second isn't because it makes the right side of the original equation negative.......but we cannot get a negative result from a positive radical....!!!!

The number of original  members =  (n - 2) (n + 8)

The reformed number of members is  n (2n - 3)

When we take away at least 4 drummers, we have this inequaliy

Original members - Reformed members ≥ 4   ....so....

(n - 2)(n + 8) - n(2n - 3) ≥  4      simplify

n^2 + 6n - 16 - 2n^2+ 3n ≥  4

-n^2 + 9n - 20 ≥ 0         multiply through by - 1  and reverse the inequality sign

n^2 - 9n + 20 ≤   0       factor

(n - 5) ( n - 4) ≤ 0

Note that....this will be > 0  when  n < 4    or  n > 5

So... the solution must be that     4 ≤ n ≤ 5

So......since n has to be an integer.....the sum of the solutions for n =  4 + 5 =  9

Thank you! your explaintations really help

1 / [ sin x - 1 ]  +    1 / [ sin x + 1 ]         get a common denominator

[ sin  x + 1 ] +   [ sinx - 1 ]

_____________________

[ sin x - 1 ] [ sin x + 1 ]  

  2sin x

_________        multiply  top/bottom by - 1

sin^2 x - 1

-2 sin x

_________

1 - sin^2 x

-2 sin x                - 2 sin x          1                 -2 tan x

_________  =       _______ *   ____   =       _______

  cos ^2 x                  cos x       cos x              cos x

Note that f(-3)  =  -(-3)^2 + 4  =  -(9) + 4  = -5

This is not equal to g(-3)  = 1

So...it appears that since -5 < 1  then

f(-3) < g(-3)

can you exaplin why just so i can make sure i understand

10

-3 + √[10x + 9 ] = x         the idea is to get the radical on one side and everything else on the other

Also....these problems sometimes produce extraneous solutions....we need to be aware of that

Add 3 to both sides

√[10x + 9 ]  = x + 3       square both sides

10x + 9  =  x^2 + 6x + 9    

10x = x^2 + 6x

x^2 - 4x  = 0

x ( x - 4) = 0

x = 0     or   x = 4

Check that both of these solutions are good !!!

ur correct