Jenna is making necklaces (n) and bracelets (b) to sell at a craft fair. The price of each necklace is $12 and the price of each bracelet is $7. Jenna has enough beads and wire to make no more than 30 pieces of jewelry. She would like to make at least $240 at the fair. Which system of inequalities models this situation?

12n+7b ≥240

n+b ≤ 30

Step-by-step explanation:

Hi, to answer this question we have to write 2 equations:

First one:

The number of necklaces (n) plus the number of bracelets (b) must be less or equal to the amount of pieces of jewelry that she can make (30).

n+b ≤ 30

Second one:

The product of the number of necklaces (n) and the price per necklace (12) ; plus The product of the number of bracelets (b) and the price per bracelet (7) ; must be greater or equal to the amount of money that she wants to make (240).

12n+7b ≥240

The system of equations is:

12n+7b ≥240

n+b ≤ 30

$18 was the price of the t-shirt

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