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Only the last one is actually tough....the notation may be giving you trouble......

First one

(f + g)(x)   means  f(x) + g(x)  =  [ 5x^2 - 2x ] + [ 3x^2 + x - 4 ]  =   8x^2 - x - 4

Second

(f * g) (x)   means   f(x) * g(x)  =

 [ 3x^2 + 5 ] * [  x - 2 ]  =

3x^3 - 6x^2 + 5x - 10

Last one   

(f / g)(x)    =   f(x) / g(x) 

[ hint : factor the denominator first....see if you can use one of these factors in the numerator  !!!]

4x^2 + 19x - 5                (4x - 1)(x + 5)              x + 5

____________   =         ____________  =      ______ 

 4x^2 - x                              x(4x - 1)                    x

Note that  either  x = 0  or  x = 1/4    makes the second denominator 0....so...we can't have these values of x

So...... third answer  !!!

Sorry....   4.32 x 10^(-4)   means move the decimal point 4 slots to the LEFT  (I missed the ' - ' sign on my first answer....

= .000432

We can solve this

(x + 3)  = 10 ( x - 1) + 4

x - 1  = 10 (x - 1)

10 (x - 1) - 1(x - 1) = 0

9 ( x - 1) = 0

x = 1  =  the floor

This  means that  any   x  on the interval  [ 1, 2)  will solve this equation

I just enetered in the calculator and resulted   17400

thanks

r + pq = s - tq       rearrange as

pq + tq  = s - r

q ( p + t )  =   s - r        divide both sides by p + t

q =   ( s - r)

       ______

        ( p + t)

Q = -5,200 – 42P + 20Px + 5.2I + 0.20A + 0.25M

Q = -5,200 – 42(500) + 20(600) + 5.2(5,500) + 0.20(10,000) + 0.2(5,000)

Q = -5,200 – 42(500) + 20(600) + 5.2(5,500) + 0.20(10,000) + 0.2(5,000)

Q = -5,200 – 21,000 + 12,000 + 28,600 + 2,000 + 1,000

Q = -5,200 – 21,000 + 12,000 + 28,600 + 2,000 + 1,000

Q = -5,200 – 21,000 + 12,000 + 28,600 + 2,000 + 1,000

Q = -5,200 – 22600

So I would like to teach you how to do these so the numbers next to each other ones in parethasees you multiply those two numbers and after the multiplication is complete you will get your Q tell me how you do it and I will see if your correct.

Second one.....a little tricky to interpret !!!

(p*c)(2)  =  p(2) *c(2)  =

[ 80 - 2(2) ]  * [ 50 + 5(2) ] =

[ 76] * [ 60 ]  =

$4560

The "2"  represents the number of $5 ncreases above $50  = 2*5 + 50 = $60 per customer

So...the company can expect $4560 in revenue when they charge $60 per customer

thanks :)

4.32 x 10^4   means   move the decimal 4 spots to the right

= 43200 

First one

(r - c)(4)  =  r(4) - c(4)  =

[ 4^2 + 6(4) + 10 ] - [ 4^2 - 4(4) + 5 ]  = 

[ 16 + 24 + 10 ] - [ 16 - 16 + 5 [ =

50 - 5  =

45

This means that the store will have a profit of $4500 after 4 months

but how do you know....

Thanks and I don't think your wrong

The ramp  forms the hypotenuse of a right triangle

We are looking fo the side adjacent to the 10°  angle  = distance  

So....the cosine relates the adjacent and the hypotenuse.....so

cos (10°) =  distance / 8       multilpy both sides by 8

8 * cos(10°)  =  distance ≈   7.9 ft

Does anyone know why people cheat like that??

Thanks, CS.....yep....trig not necessary....similar triangles work fine  !!!!

Melody, also look at FiestyGeco. He/she has posted their entire Geometry homework on here... I am in the course he/she was in a couple years ago.

https://web2.0calc.com/questions/pls-help-due-tmrow_9

Wow, 11 questions?

We don't even really need trig... the cosine value is already shown in the diagram.

\(\Delta PQR \sim \Delta TSR\) because of AAA Similarity ... Angle STR is congruent to itself and angles PQR and TSR are both 90 degrees.

\(\frac{PQ}{TS}=\frac{5}{3}\), so this is the ratio for all sides.

Therefore, \(15 \div \frac{5}{3}=15 \times \frac{3}{5}=9\)

You are very welcome!

:P