(03.05 mc) shirley wants to buy a skateboard for $64. she has $98 in her account. she spent $10.85 to buy stationary. she also wants to buy some cookies for $1.65 each. what is the maximum number of cookies, n, that shirley can buy so that she has enough money left to buy the skateboard? n ≥ 14 n ≤ 16 n ≤ 14 n ≥ 16

  n ≤ 14

Step-by-step explanation:

One way to work this problem is to assume that Shirley has already spent her money on the skateboard and stationery, then look at how many cookies she can buy with what's left.

The amount remaining after the desired purchases is ...

  $98 -64 -10.85 = $23.15

Then her n cookies will have to satisfy ...

  1.65n ≤ 23.15

Dividing by the coefficient of n gives ...

  n ≤ 14.0303_03 . . . . a repeating decimal equivalent to 1/33

Since Shirley can only buy whole numbers of cookies, the maximum number she can buy is 14. That is, ...

  n ≤ 14

a.)the line for function b is steeper

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