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a -   12 midnight to 12 noon same day = 12 hours

V = 40 x 1/2^(12/36) =31.75 mg left in the bloodstream.

b - 20 = 40 x 1/2^(t/36), solve for t

t = 36 hours - as you might expect because it is the drug's "half-life"

I'm not very good at this but heres what I know: think about the options you have for each digit. The hundreds digit doesn't matter so you have 1-9 which is 10 options, then for the tens digit you can do casework for each number. For instance if it's 1, then the units digit is anything from 2-9. e.t.c

1: Your equation would be ; 35s + 20p= 150.

2: If each sweater is $35, and she wants to buy 3, you will multiply 35 by 3 to get 105, then you'd subtract 105 from 150 to get 45. A pair of pants are $20, and she only has $45 left. Holly would be able to buy 2 pairs of pants.

3: Her overall amount of money is $150. To see the number of sweaters Holly can buy, you could do one of two things:

- Divide 150 by 35

Or

- Multiply 35 by one, then two, then three, and so on. 

The easier of the two is the division. You'd get 4 with multiple numbers after the decimal point, but the most sweaters that Holly could buy with $150 is 4.

Ok, I'll help!

a) 35s+20p=150

b) Because she buys 3 sweaters, her total for sweaters is 35*3=105. [My] equation now is 105+20p=150, where 20p is the total money Holly spends on the sweaters. Subtract 150 from both sides, so 20p=45, and p=2.25. But she can't buy 2.25 pants, so this is the total whole number of pants she can buy without going over her money limit. Therefore it is 2, because the quotient when 45 is divided by 20 is 2.

c) Again, [my] equation is when p=0 35s=150. Holly can buy 1 sweater safely without going over the limit, 2 sweaters, 3, and 4. But when[ I ]reach 5, she can't, as she will spend 15*5=$175 on her sweaters, which is OVER her limit. So the greatest number of sweaters she can buy when she buys no pants is 4.

Absolute values can be written two ways.

They are shown here.

1. 5x-(x-5)

or

2. 5x - -1(x-5)

This translates to:

1. 4x+5

2. 6x-5

where x<5.

Equation of line   y = x - 7

Shaded area   y > x-7

This graph reprsents  everything LESS than the line but not including the line

y < mx + b        m = slope = rise/run = 1/3

y < 1/3 x + b       b = y axis intercept = -1

y < 1/3 x -1

Let the number of nickels = N

The number of dimes        =30 - N

0.05N  +  0.10*[30 - N] = 2.60, solve for N

N =8 nikels

30 - 8 nickels =22 dimes.

(2x - 1) / (2x + 2) = 7 / 10

2x - 1 * 10 = 2x + 2 * 7

20x - 10 = 14x + 14

20x - 14x = 14 + 10

6x = 24

x = 4

1/   Use the law of cosines to find an angle B.

2/    Using the same method, find an angle A. Divide the value of this angle by 2.

3/   Now you have a triangle ABM with one known side and all 3 known angles.

4/   Using the law of sines, you can calculate the length of BM.

a)

I don't know what kind of diagram it wants.....but we can calculate the percenteges like this:

We can replace the  %  sign with  / 100

And we can replace the word "of" with *

So.....

Can you finish those?

After you get the answers for these, you might notice the pattern that they are talking about in part b.

.

What is the constant of proportionality that relates miles, y to time, x?    

Distance = Rate x Time 

Thirty coins, all dimes and nickels, are worth $2.60. How many nickels are there?   

IF all 30 coins were dimes, you'd have $3.00. 

You have only $2.60, therefore you need to reduce the total by 40¢. 

Every time you substitute a nickel in place of a dime, you lose 5¢. 

So, you need to replace 8 dimes with nickels to lose 40¢.  

That makes a final mix of 22 dimes and 8 nickels.  

So the answer to the question is 8 nickels.  

Check:     22 dimes    =  $2.20  

                  8 nickels   =  $0.40  

                                     ––––––

Total                               $2.60  

_.

5 a    

   b^2 cancels out     625 = 125 * 5     then the 5's cancel

Multiply first equation by - 1 1/3 to get

-4p - 16/3 q = - 32/3    now add to second equation to get

-7/3 q = 7/3

q = -1

then  since   3 p + 4q = 8       3p -4 = 8       then p = 4

1000!_4  *  100!_4  *  10!_4 =130 1302221110 0132333201 3122022132 1230301003 2233112303 0023022013 1201210330 1112231131 3211111013 1013222232 1332011100 3000000122 1021202112 0000000000 0000000000 0000000000 0000000000 [Which has 40 trailing zeros]. Now, convert this to base 12:

171886B 38B1954098 7094864863 34AA256B70 879A167705 4B2A283341 A280000000 0000000000 0000000000 0000000000 [Which has 37 trailing zeros]

Solve the following system:
{4 q + 3 p = 8 | (equation 1)
3 q + 4 p = 13 | (equation 2)

Swap equation 1 with equation 2:
{4 p + 3 q = 13 | (equation 1)
3 p + 4 q = 8 | (equation 2)

Subtract 3/4 × (equation 1) from equation 2:
{4 p + 3 q = 13 | (equation 1)
0 p+(7 q)/4 = -7/4 | (equation 2)

Multiply equation 2 by 4/7:
{4 p + 3 q = 13 | (equation 1)
0 p+q = -1 | (equation 2)

Subtract 3 × (equation 2) from equation 1:
{4 p+0 q = 16 | (equation 1)
0 p+q = -1 | (equation 2)

Divide equation 1 by 4:
{p+0 q = 4 | (equation 1)
0 p+q = -1 | (equation 2 

 p = 4          and          q= -1
 

(180 -122)   +   (180 -118)    +  3y = 180, solve for y

     58            +        62             + 3y = 180

3y = 180 - 58 - 62 =60

y =20 degrees

3y + 180-118 + (x - 25) = 180, solve for x

3*20  +  62    + (x - 25) = 180

x - 25 = 180 - 60 - 62

x - 25 = 58

x =58 + 25

x = 83 degrees

1/       25 / 20 = 30 / 4x-4

2/       20 / 25 = 4x-4 / 30

3/       30 / 25 = 4x-4 / 20

4/       25 / 30 = 20 / 4x-4

3y +  (x-25)  = 180  Wrong!!!

3y + 180-118 + (x - 25) = 180  

The two sides of the two triangles PQR and STU are similar, that is, 6 and 4, which means that their 3rd side must also be similar. So, you equate the 3rd sides:

(3y - 2) = (y + 4), solve for y

3y - y =4 + 2

2y = 6

y = 3.  Now, you must substitute this value of y into the 3rd side of PQR:

3y - 2 =3*3 - 2 = 7 ft - which is the 3rd side of PQR.

Then, Perimeter of PQR = 6 + 4 + 7 = 17 feet.

If cosθ=3/5 then tanθ = 4/3

I get 1, too, and that was correct. Thanks guest 

30 is to 25     as    4x-4  is to 20

30/25  =  (4x-4) / 20 

65% of 'x' = 39

.65x = 39

x = 39 / (.65)