CPhill

Equi   =  "Equal"

Lateral  =  "Side"

so.....

"Equal- Side"  =  "Equil-Lateral "

4)If f(x)=2x^3 −5x^2 −7,find f(h−1).

So we have

2 (h - 1)^3  - 5(h - 1)^2  -  7   =

2( h^3  -  3h^2 +  3h - 1 )  -  5 (h^2 - 2h  + 1)  - 7   =

2h^3  - 6h^2  + 6h  -  2  -  5h^2  + 10h  -  5  -  7   =

2h^3  -  11h^2  +  16h  - 14

5)  Find the average rate of change of f (x) = 2x^2 − 5x −12 over the interval [–2,–2+h], whereh>0.

We have

[   (  2 ( -2 + h)^2  - 5 ( -2 + h) -  12)   -  ( 2(-2)^2 - 5(-2) - 12 )  ]  /  [ (- 2 + h)  - (-2) ]  =

[  (  2 (h^2 - 4h + 4)  + 10 - 5h - 12 )  -  ( 8  + 10 - 12 ) ]  /  h  =

[ 2h^2  -  8h  + 8  +  10  - 5h  - 12   - 8  - 10  + 12 ]  / h  =

[  2h^2   - 13h ] /  h   =

h ( 2h - 13)  /  h  =

2h - 13

6) The value of a boat is $800,000 in year 2006 and it depreciates $30,000 per year, after year 2006. Find a model to represent the boat’s value V(in $1000) as a function of t. Variable t represents the number of years t after year 2006. 

We have that

V(t)   =  800  -  30t

Where  V(t)  is the value in thousands, t years  after 2006

Note that

1/5  =  20/100   =  20%

0.4  =  4/10  =  40%

So....from  least to greatest, we have

15% , 1/5, 25% , 0.4

1.  For the first....just  add  the 4  and 6  and append the radical...so we have...

10 ⁴√ [ 2x ]  ⇒  first answer

2.  A little trickier, NSS

Ratio  3 : 2     means that there are  3 + 2  = 5 equal parts......and the longer piece is  3 of these parts

So......the longer piece  =  

(3 /5) √250   =

(3/5) √ [ 125 * 2 ]    =

(3/5) √ ( 25 * 5 * 2 ]  =

(3/5) √ 25 * √5 * √2  =

(3/5) * 5  * √10  =

3 √ 10  units

Simple interest formula :

Interest earned  =  Principal * Interest Rate * Time (in years)

So......for the first one

Interest earned =  1450 * (.09)  * (5)  =  $652.50

The second one is a little trickier....we have...

10   =  250 *  .04  * Time             simplify

10  =  10  * Time                       divide both sides by 10

1  =  Time   

So  ...   1  year

Notice  that

AB  = AD

DC  = BC

and

AC  = AC

So.....by  SSS congruence,  triangle  ADC  is congruent to triangle ABC

So   angle  ADC  =  angle ABC   =   ( 180  - 32 - 41)°  =  107°    =  "B"

Notice that a 5%  discount is the same thing as selling something for  (100 - 5)% = 95% of its original price

So....the first watch costs   50  x . 95  =  $47.50

And...a 20% discount means the same thing as selling something for (100 - 20) %  = 80% of its original price

So.....the second watch  costs    60 x .80   =  $48

So...the first watch is the better deal

Thanks for that good answer, hectictar.......here's another way to do this......

We can actually  use the same "formula" to figure both of these

% increase / decrease   =    (  l New Value - Old Value l  / Old Value  x 100 ) %

So...for the first one we have

(   l  180 - 120 l  /  120  x 100) %  =

(  l   60  l   /  120   x 100 ) %  =

(  60  / 120  x 100 ) %   =

( 1 / 2  x 100 ) %  =

50%  increase

For the second one, we have

(  l  8  - 10  l  /  10   x 100 ) %    =

(  l -2 l  / 10  x 100 ) %  =

(  2  / 10  x 100 ) %  =

( 1 / 5  x 100 ) %  =

20%  decrease

3)  We have a triangle at the top left with a base of 3 units  and a height of 4 units

So its area  is  (1/2) (3) (4)  =  6 inches^2

And we have a reatangle with dimensions 8 x 7   =  56 inches^2

So  the total area is   6 + 56   =    62 inches^2

Answered here :

https://web2.0calc.com/questions/in-the-figure-ad-cd-and-ab-cb