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GarryVolchara [31]
3 years ago
14

In a right triangle, Sin (30 + x) º = Cos (3x) º. What is the value of x?

Mathematics
1 answer:
pogonyaev3 years ago
5 0

Answer:

x=15^\circ

Step-by-step explanation:

In a right triangle:

\sin \theta =cos(90^\circ-\theta) $ (Complementary angles)

Therefore, given:

Sin (30 + x) \º = Cos (3x) \º\\30+x+3x=90^\circ\\30+4x=90^\circ\\4x=90^\circ-30^\circ\\4x=60^\circ\\$Divide both sides by 4\\x=15^\circ

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Solve for the indicated variable. Include all of your work in your answer. Submit your solution. P = 3r + 2s; for s.
madam [21]
<h3>Given</h3>

P = 3r + 2s

<h3>Find</h3>

the corresponding equation for s

<h3>Solution</h3>

First of all, look at how this is evaluated in terms of what happens to a value for s.

  1. s is multiplied by 2
  2. 3r is added to that product

To solve for s, you undo these operations in reverse order. The "undo" for addition is adding the opposite. The "undo" for multiplication is division (or multiplication by the reciprocal).

... P = 3r + 2s . . . . . . starting equation

... P - 3r = 2s . . . . . . -3r is added to both sides to undo addition of 3r

... (P -3r)/2 = s . . . . . both sides are divided by 2 to undo the multiplication

Note that the division is of everything on both sides of the equation. That is why we need to add parentheses around the expression that was on the left—so the whole thing gets divided by 2.

Your solution is ...

... s = (P - 3r)/2

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3 years ago
Sweet T has 2 orange picks for every 5 green. If there are 12 picks in all how many picks are orange
e-lub [12.9K]
There are eight orange picks.
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Stacy is selling tickets for the school play. She has a total of 200 seats available, and there will be two types of tickets off
Ganezh [65]

She sold 74 child tickets and 126 adult tickets

Step-by-step explanation:

Stacy is selling tickets for the school play

  • She has a total of 200 seats available, and there will be two types of tickets offered, child and adult tickets
  • She sold each child ticket for $6 , each adult ticket for $10 , and made a total of $1704

We need to find how many of each ticket  she sold

Assume that x is the number of child tickets and y is the number of the adult tickets

∵ She has a total of 200 seats available

∵ She sold x child tickets

∵ She sold y adult tickets

- Add x and y, then equate the sum by 200

∴ x + y = 200 ⇒ (1)

∵ She sold each child ticket for $6

∵ She sold each adult ticket for $10

∵ She made a total of $1704

- Multiply x by 6 and y by 10, then add the products and

   equate them by 1704

∴ 6x + 10y = 1704 ⇒ (2)

Now we have a system of equation to solve it

Multiply equation (1) by -10 to eliminate y

∵ -10x - 10y = -2000 ⇒ (3)

- Add equations (2) and (3) to find x

∴ -4x = -296

- Divide both sides by -4

∴ x = 74

- Substitute the value of x in equation (1) to find y

∵ 74 + y = 200

- Subtract 74 from both sides

∴ y = 126

She sold 74 child tickets and 126 adult tickets

Learn more:

You can learn more about the system of equations in brainly.com/question/2115716

#LearnwithBrainly

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3 years ago
What is the value of k in the function ƒ(x) = 112 - kx if ƒ(-3) = 121?k = a0
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F(x) = 112 - kx
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How to do complete the number line using the following fractions
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You line them up from smallest to greatest
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