Daniel has a collection of stamps worth $6. He has 5 more 8 cent stamps then 30 cent stamps. The number of 6 cent stamps is 2 times the amount of 30 cent stamps. The number of 5 cent stamps is 12. How many of each kind of stamps does Daniel have? Please list the number of 30, 5, 6, 8 cent stamps he has.
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12 of the 5 cents stamps,

20 of the 6 cents stamps

15 of the 8 cents stamps

10 of the 30 cents stamps.

Step-by-step explanation:

Let's name:

x = number of 5 cent stamps,

w = number of 6 cent stamps,

y = number of 8 cent stamps,

z = number of 30 cent stamps,

Create the following system of equations based on the info provided:

z + 5 = y

w = 2 * z

x = 12

600 = 5 (12) + 6 w + 8 y + 30 z

replace everything in terms of "z":

600 = 60 + 6 (2 * z) + 8 (z + 5) + 30 z

540 = 12 z + 8 z + 40 + 30 z

500 = 50 z

z = 10

and now we can find the rest:

y = 5 + 10 = 15

w = 2 * 10 = 20

Therefore there are:

12 of the 5 cents stamps,

20 of the 6 cents stamps

15 of the 8 cents stamps

10 of the 30 cents stamps.

well my understanding of this question is they want you to use the y=14.1x -2.3 and put the coordinates they gave you onto the line segment of   y=14.1x -2.3

step-by-step explanation:

the value of x is 9 ⇒ answer b

step-by-step explanation:

* we can solve this problem using cosine and sine rule

- in δ abc

∵ ab = 36 , bc = 28 , ac = 16

- lets find the measure of angle b using the cosine rule

∵ cos b = [ab² + bc² - ac²]/2(ab)(bc)

∴ cos b = [36² + 28² - 16²]/2(36)(28)

∴ cos b = 19/21

∴ m∠b = cos^-1(19/21) ≅ 25°

- lets find the measure of angle a using the sine rule

∵ sina/bc = sinb/ac = sinc/ab

∴ sina/28 = sin25°/16 ⇒ by using cross multiplication

∴ sina = 28 × sin25°/16

∴ sina = 0.7396

∴ m∠a = sin^-1(0.7396) ≅ 48°

- from the figure m∠abd = m∠dbc

∵ m∠abc = 25°

∴ m∠abd = 25°/2 = 12.5°

- in δabd

∵ m∠a = 48° , m∠abd = 12.5°

∵ the sum of the measures of the interior angles of any δ is 180°

∴ m∠adb = 180° - (48° + 12.5°) = 119.5°

∵ ab = 36

∵ ad = x

- use the sine rule to find x

∵ sin∠adb/ab = sin∠abd/x

∴ sin119.5°/36 = sin12.5°/x ⇒ by using cross multiplication

∴ x = 36 × sin12.5°/sin119.5° = 8.95 ≅ 9

* the value of x is 9