CPhill

\(Let \[f(x) = \left\{ \begin{array}{cl} 2x + 1 & \text{if } x \le 3, \\ 8 - 4x & \text{if } x > 3. \end{array} \right.\]Find the sum of all values of $x$ such that $f(x) = 0.$\)

2x + 1  = 0                      

2x  = -1                           

x = - 1/2     and this is in the domain  of x ≤ 3

8 - 4x = 0

8 = 4x

2 = x       this is not in the domain of x > 3

So......the sum is just -1/2

Expected value =

Amt spent * (probability of losing)  +  Jackpot * (probability of winning)  =

-3 * (99,999/100000) +   250,000* (1/100000)  ≈  -$0.50

 0.841= A^4.5

Take both sides to the  (1/4.5)  = 2/9  power

(0.841)^(2/9)  = A ≈  0.9622

We need to know something about the relationship between the larger and the smaller

Mass = Density * Volume

So.......divide both sides by Volume 

Density  = Mass / Volume  =  8.76 g / 3.07 cm^3  ≈  2.853 g / cm^3

Corresponding angles are equal

I think you might mean "complementary"  angle

If so.....complementary angles always sum to 90°

So.....  call the angle you're looking for, "x"

So we have that

52 + x  =  90         subtract 52 from both sides

x =  38°

 1+3(4-3n) = 85           distribute the 3 across the terms in the parentheses

1 + 12 - 9n  = 85         simplify

13 - 9n  = 85        subtract  13 from both ides

-9n  =  72             divide both sides by 9

n = -8

log_a14

Given  log_a2=3.01, log_a6=.778 and log_a7 is .845

Note that we only need   log_a 2 = 3.01   and log_a 7  = .845     to solve this

By a log property......log m  + log n  =  log ( m * n)    ....so.....

log_a 2  +   log_a 7  =     log_a  ( 2 * 7 )  =   log_a (14)

3.01    +   .845   =    log_a (14)   =   3.855

BTW -  "a"  couldn't be a "real" base!!!

Yep, -7

OK.....except for the last one

Think about this

(2/5) (5/2) * -7

What is the product of the first two terms ???