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Nevermind I figured it out myself

We perform the polynomial division:

\[
\begin{array}{c|cc cc}
\multicolumn{2}{r}{5x} & +4 \\
\cline{2-5}
2x^2-3x+1 & 10x^3&-7x^2&+ax&+6 \\
\multicolumn{2}{r}{-10x^3} & +15x^2 & -5x \\
\cline{2-4}
\multicolumn{2}{r}{0} & 8x^2 & (a-5)x & 6 \\
\multicolumn{2}{r}{} & -8x^2 & +12x & -4 \\
\cline{3-5}
\multicolumn{2}{r}{} & 0 & (a-5+12)x & 2 \\
\end{array}
\]

 The remainder will be constant if and only if  So the answer is 7

OK....glad to help    !!!

Let  the  number of  dimes  = x

Let the number of quarters  = 26  -x

And

Number of dimes * Value of each  + Number of quarters * value each  = total value of the coins

So...

x * .10   +  (26 - x) * .25  =  5.45     simplify

.10x  - .25x + 6.50  =  5.45         subtract  6.50  from both sides  and simplify the left side

-.15x  = -1.05    divide  both sides by  -.15

x =  7   =  number of    dimes

26 -  x  = 26  - 7   = 19  = number of quarters

Thank you very much for your help sir :)

Let   the points  be    (F,C)  = (32, 0)   and (212, 100)

Find the slope betwen the points

( 100 - 0 ) / ( 212 -32)  =   100 /180   =  5/9

Using the pont  (32,0)   we have that

C  = (5/9)(F - 32)

Yep....cos(x) is even....

Anyone have a pointer or something? Thanks!

1. $953.40

2.$412

3.$1210

idk 4 and 5

Hi! Thanks! I'm kind of confused though this isn't a fraction right? How does this mean 126?

Very precise strategy to find the inverse. Thank you for your help <3

\(\text{This is the same as the probability you've eaten 2 chocolates in 6 candies, and eat the 3rd chocolate on the 7th}\\ P[\text{eaten 2 chocolates in 6 candies}] = \dfrac{\dbinom{3}{2}\dbinom{5}{4}}{\dbinom{8}{6}} = \dfrac{15}{28}\\ P[\text{7th candy eaten is chocolate |2 chocolates already eaten}] = \dfrac 1 2\\ P = \dfrac{15}{28}\dfrac 1 2 = \dfrac{15}{56}\)

On the first day you save $0.01, on the second day you save $0.02, on the third day you save $0.03, etc.

Thus, on the n^th day, you save 0.01·n.

This is an arithmetic sequence because each number is 0.01 greater than the previous number.

The formula for the sum of an arithmetic sequence is:  Sum  =  N(F + L)/2

where  N = number of terms,  F = value of the first term,  L = value of the last term.

a)  N = 100, F = 0.01, L = 0.01·N = 1.00    --->     Sum  =  100(0.01 + 1.00)/2     --->     Sum  =  $50.50.

b)  N  = n, F = 0.01, L = 0.01n, Sum = 500.00     --->     500.00  =  n(0.01 + 0.01n)/2

     --->     1000.00  =  n(0.01 + 0.01n)   

     --->     1000.00  =  0.01n + 0.01n²

     --->     100,000  =  n + n²

     --->     n² + n - 100,000  =  0

Using the quadratic formula with a = 1, b = 2, and c = -100,000   --->  n = 316 (approximately)

would f(x)=cos x be even?

The cosine  function is  even because it is symmetric with the  y  axis

See the graph here : https://www.desmos.com/calculator/1w8wnljmgc

For  an odd function  we  must have that

f(-x) = -f(x)

So....notice for instance that

csc(-pi/2)  =  -1   =   -csc (pi/2)

So....

csc (x) is odd

These types  are problems are easy to solve  !!!

Lisa  does  (1/2)  the job in one hour  and  Jim does 1/3  of the job in one hour

So...together....they  complete

1/2  + 1/3  = 

[ 2 + 3 ]  / 6  =

5/6  of the  job in one hour

Take the reciprocal of this   =   6/5  hrs  to complete the job working together  !!!

is not one-to-one

[-π/2,π/2]

Let's look at the graph  :   https://www.desmos.com/calculator/amo6qtaser

The first statement is false....on its domain, the range is  (-inf, inf)

The second is also false.....the cotangent  doesn't intersect the y axis

The third is true  ...

And  the last is also true

Sorry! Cannot read your LaTex !!.

This one is a little tricky, DragonLord  !!!

The goal is to get x by itself and then "swap" x  and y

We can write

y  = x^2  + 4x  +  5      subtract  5  from both sides

y - 5 =  x^2  + 4x         complete  the  square  on x

y  -5  + 4  =  x^2  + 4x  +  4    factor the right side.....simplify  the left

y - 1  = (x + 2)^2      take both roots

 ±√[y - 1 ]  = x + 2     subtract 2 from  both sides

x = ±√[y -1 ] - 2   "swap"  x and  y

y  = ±√ [x -1] - 2       and we need to take the negative value  [I'll explain this in a second]

y = - √ [x -1]   -2    this is the inverse

However.....we have a resticted domain

To find  out what the  new  domain is we need to  solve  this : 

(-2)^2  + 4(-2)  +  5  =

4  - 8  + 5

-4 + 5

1

This means that the  new  domain is   x ≥  1

See the graph here  :  https://www.desmos.com/calculator/xeind7czif

Here's why  we need  the   "-"  value on the root  function of the  inverse

Note  that  the  point   (-4, 5)  i on the origimal graph

The inverse  "switches"  these coordinates...so....the  point  ( 5, -4)  must  be  on the inverse

See the graph again to confirm this  : https://www.desmos.com/calculator/kt9chuswm0

5 musicians, all together, 5! ways if each scientist is considered an individual

2 scientists, all together,  2 ways if classed as individuals

1 accountant

2*5!*2 = 4*5! = 480 ways

Note:

If you say it is wrong without giving your reason then your response will be whited the same as your other rude responses have been whited.

\(0.1\overline{23}\) is the same thing as 122/990. Since they have to have a GCD of 1, we must simplify them, where we get 61/495. Now we add the numerator and denominator getting \(61+495 = \boxed{556}\)

I know that this question was asked over half a year ago, but hope it helps!