To encourage john to work harder in math his mother said she would pay him 10
cents for each right answer and subtract 5 cents for each wrong answer. if he earned
20 cents after doing 32 problems, how many problems did john get right? how
many did he get wrong? how many would he have to get right to earn more than a
dollar?

he got 12 questions right

he got 20 questions wrong.

Step-by-step explanation:

Let x represent the number of questions that he got right.

Let y represent the number of questions that he got wrong.

His mother said she would pay him 10 cents for each right answer. This means that if he gets x questions right, he would earn $10x.

His mother said she would subtract 5 cents for each wrong answer. This means that if he gets y questions wrong, he would earn

- $5y.

If he solved 32 problems, it means that

x + y = 32

If he earned 20 cents after doing 32 problems,it means that

10x - 5y = 20 - - - - - - - - -1

Substituting x = 32 - y into equation 1, it becomes

10(32 - y) - 5y = 20

320 - 10y - 5y = 20

- 10y - 5y = 20 - 320

- 15y = - 300

y = - 300/ -15 = 20

Substituting y = 20 into x = 32 - y, it becomes.

x = 32 - 20 = 12

To get more than a dollar, he needs to earn at least 110 cents. He already has 20 cents. He needs to get 9 right to earn over a dollar.

If he gets 9 right, he would earn 90 cents more. 90 + 20 = 110 cents = $1.1

step-by-step explanation:

your answer is a

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