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scoray [572]
3 years ago
14

After 56 cans of soup were sold, a clerk moved the remaining cans to a display case. The display case had shelves that could eac

h hold 9 cans. How many shelves were needed to fit all the remaining cans?
Mathematics
1 answer:
ad-work [718]3 years ago
7 0
We represent the original number of cans of soup by the variable x. After 56 cans of soup were sold, the remaining number of cans of soup is x - 56. Since we have shelves that can hold 9 cans, the number of shelves needed to fit all the remaining cans is 
                                              (x - 56) / 9
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Urgent!! Will mark brainliest!!
horsena [70]

Answer:

1) x is negative and y is positive ⇒ last answer

2) cotФ = -12/35 ⇒ second answer

3) The right identity is cot²Ф - csc²Ф = -1 ⇒ last answer

Step-by-step explanation:

* For any point (x , y) lies on the terminal side of the angle Ф

 in standard position

* x = cosФ and y = sinФ

- If Ф in the first quadrant, then x , y are positive

∴ All trigonometry functions are positive

- If Ф in the second quadrant, then x is negative , y is positive

∴ sinФ only is positive

- If Ф in the third quadrant, then x is negative , y is negative

∴ tanФ only is positive

- If Ф in the fourth quadrant, then x is positive , y is negative

∴ cosФ only is positive

* Lets solve the problems

∵ Ф = 3π/4 ⇒ (135°)

∴ It lies on the second quadrant

∴ x is negative and y is positive

* Lets revise the reciprocal of sinФ, cosФ and tanФ

- cscФ = 1/sinФ

- secФ = 1/cosФ

- cotФ = 1/tanФ

∵ secФ = -37/12

∴ cosФ = -12/37

∵ π/2 < Ф < π

∴ Ф lies on the second quadrant

∴ cotФ is negative values

∵ tan²Ф = sec²Ф - 1

∵ secФ = -37/12

∴ tan²Ф = (-37/12)² - 1 = 1225/144 ⇒ take√ for both sides

∴ tanФ = ± 35/12

∵ cotФ = ± 12/35

∵ cotФ is negative value

∴ cotФ = -12/35

* In the standard position of the angle Ф the terminal

 of it lies on the unit circle O

- By using Pythagorean theorem

∵ x² + y² = 1

∵ x = cosФ and y = sinФ

∴ cos²Ф + sin²Ф = 1 ⇒ (1)

∴ cos²Ф = 1 - sin²Ф

∴ sin²Ф = 1 - cos²Ф

* Divide (1) by cos²Ф

∴ cos²Ф/cos²Ф + sin²Ф/cos²Ф = 1/cos²Ф

* Remember sin²Ф/cos²Ф = tan²Ф and 1/cos²Ф = sec²Ф

∴ 1 + tan²Ф = sec²Ф ⇒ (2) ⇒ subtract 1 from both sides

∴ tan²Ф = sec²Ф - 1 ⇒ subtract sec²Ф from both sides

∴ tan²Ф - sec²Ф = -1

* Divide (1) by sin²Ф

∴ cos²Ф/sin²Ф + sin²Ф/si²Ф = 1/sin²Ф

* Remember cos²Ф/sin²Ф = cot²Ф and 1/sin²Ф = csc²Ф

∴ cot²Ф + 1 = csc²Ф ⇒ (3) ⇒ subtract 1 from both sides

∴ cot²Ф = csc²Ф - 1 ⇒ subtract csc²Ф from both sides

∴ cot²Ф - csc²Ф = -1

* The right identity is cot²Ф - csc²Ф = -1

3 0
3 years ago
(-4,2) is a solution to the following graph. True or False?
emmasim [6.3K]
Plugging in the values of (-4,2) into the two inequality statements to see whether it is part of the solution to the inequality system:

y ≥ -5x + 3
2 ≥ -5(-4) + 3
2 ≥ 20 + 3
2 ≥ 23 (false statement).

For the other inequality statement, substitute 2 for the y value:

y > -2
2 > -2 (true statement).

Since (-4,2) only satisfies one of the inequality statements, then it means that it is not a solution to the graph.

Therefore, the correct answer is FALSE.

Please mark my answers as the Brainliest if you find my explanation helpful :)
5 0
2 years ago
$550 at 4% compounded daily for 13 years
vichka [17]

Answer:Sydney’s

Step-by-step explanation:

Rhrurjeuejej

5 0
3 years ago
Read 2 more answers
Average winter temperatures in 45 states were recorded and divided by geographic region. Choose True or False for each statement
san4es73 [151]

Answer: SU, TU, ST is the right answer

Step-by-step explanation: In a triangle

The largest side and the largest angle are opposite to each other

The shortest side and the shortest angle are opposite to each other.

So using the above axioms we can observe the triangle.

The largest angle is m∠U = 80° so the side opposite to it is the largest i.e. ST is the largest

The smallest angle is m∠T = 25° so the shortest side is SU

The third side will be the middle side as the angle ∠S is greater than 25° and less than 80°

So the sides in order from least to greatest are: SU, TU, ST

5 0
3 years ago
What number gives a result of -8 when 11 is subtracted from the quotient of the number and 6?
forsale [732]

Answer:

18

Step-by-step explanation:

The formula X/6 - 11 = -8

Add 11 to both sides of the equation X/6 = 3

Multiply by 6 both sides to cancel out the division

X = 18

3 0
3 years ago
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