Use the steps to determine the exact value of sin(−135)°.

Identify the reference angle, θ.

θ =
°

Answers

Answer 1
Answer: To solve for sin(-135), the reference angle will be obtained as follow:
sin(-135)
=-sin(135)
=-sin(180-135)
=-sin 45
hence
the reference angle θ=45°
Answer 2
Answer:

Answer:

The reference angle will be {\theta}=45^(\circ)

Step-by-step explanation:

To solve for sin(-135), the reference angle can be obtained as follows:

= sin(-135)

=- sin(135) (Because sin(-{\theta})=-sin{\theta})

Thus, the above equation can be written as:

=-sin(180-135)

=-sin45

Hence, the reference angle will be {\theta}=45^(\circ)


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Explain how you can use the Triangle Sum Theorem to find the measures of the angles in an equilateral triangle.The angles of an equilateral triangle are . Let the measure of each angle be x. Then, by the Triangle Sum Theorem, x + x + x = 3x = °_____________. Solving for x gives x = °____________.

Answers

Answers:

The first blank is 180

The second blank is 60

======================================

The triangle sum theorem basically says that adding up all three angles of any triangle always leads to 180 degrees. So that's why

(angle1)+(angle2)+(angle3) = 180

x+x+x = 180

3x = 180

Divide both sides of that last equation by 3. This is to undo the multiplication of 3 done to x.

3x = 180

3x/3 = 180/3 ... divide both sides by 3

x = 60

Each angle of this equilateral triangle is 60 degrees. In an equilateral triangle, all three sides are the same length. Also in an equilateral triangle, all three angles are the same measure and always 60 degrees.

Final answer:

The Triangle Sum Theorem says that all angles in a triangle add up to 180 degrees. In an equilateral triangle, all angles are equal. Hence, each angle is 60 degrees.

Explanation:

The Triangle Sum Theorem states that the sum of the measures of the angles in a triangle is always 180 degrees. Now, in an equilateral triangle, all angles are equal. Let's denote the measure of each angle with x. According to the theorem, the sum of these measures is x + x + x = 180. Simplifying this gives 3x = 180. Hence, solving for x, which refers to the measure of each angle in the equilateral triangle, we get x = 180 / 3 = 60 degrees. Thus, each angle in an equilateral triangle measures 60 degrees.

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11
What is the independent variable of the following statement?
Luke
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The amount of candy he buys
The amount of money he has
The store he goes to
The type of money he has

Answers

10.Yes
11.Number 3

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Answers

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Answers

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Step-by-step explanation:

Ok, we know that:

For the first 4km, we have a fixed price of 9 pesos.

For any km after the 4km mark, we have an extra of 0.75 pesos.

Then if x is the number of kilometers, we can write this as:

f(x) = 9 pesos if  0km ≤ x ≤ 4km

f(x) = 9 pesos + (x - 4km)*0.75 pesos if  4km ≤ x

Where we use (x  - 4km) because we start counting after the 4km mark.

If 60% of a given number is 18.0 what is 25% of the given number​

Answers

Answer:

7.5

Step-by-step explanation:

60% = 0.6

18 / 0.6 = 30 (given number)

25% = 0.25

30 * 0.25 = 7.5

Best of Luck!

Answer:

2.7

Step-by-step explanation:

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