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Arlecino [84]
2 years ago
14

Select all the correct answers.

Mathematics
1 answer:
Wittaler [7]2 years ago
6 0

If the measure of angle θ is 3π/4, the true statements are:

  1. sin(θ) = √2/2.
  2. The measure of the reference angle is 45°.

<h3>How to determine the true statements?</h3>

In Trigonometry, an angle with a magnitude of 3π/4 (radians) is equivalent to 135° (degrees) and it's found in the second quarter. Thus, we would calculate the reference angle for θ in second quarter as follows:

Reference angle = 180 - θ

Reference angle = 180 - 135

Reference angle = 45°.

Also, a terminal point for this angle θ is given by (-√2/2, √2/2) which corresponds to cosine and sine respectively. This ultimately implies that sin(θ) = √2/2.

tan(θ) = cos(θ)/sin(θ)

tan(θ) = [(-√2/2)/(√2/2)]

tan(θ) = -1

In conclusion, we can logically deduce that only options A and B are true statements.

Read more on terminal point here: brainly.com/question/4256586

#SPJ1

Complete Question:

If the measure of angle θ is 3π/4, which statements are true. Select all the correct answers.

A. sin(θ)=sqrt2/2

B. The measure of the reference angle is 45

C. The measure of the reference angle is 30

D. The measure of the reference angle is 60

E. cos(θ)=sqrt2/2

F. tan(θ)=1

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Please help me w this an explain how you got it!.
pishuonlain [190]

Answer:

Vertex → (2, 4)

Step-by-step explanation:

Quadratic equation has been given as,

y = -x² + 4x

We rewrite this equation in the form of a function as,

f(x) = - x² + 4x

By comparing this equation with the standard quadratic equation,

y = ax² + bx + c

a = -1 and b = 4

Vertex of the parabola represented by this equation is given by [-\frac{b}{2a}, f(\frac{-b}{2a})]

x coordinate = -\frac{4}{2(-1)}

                     = 2

y-coordinate = f(2)

                     = - (2)² + 4(2)

                     = -4 + 8

                     = 4

Therefore, vertex of the given function is (2, 4)

6 0
2 years ago
Describe the transformation of the parent function f(x)=x^2 to 1/2 (x+1)^2-5
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3 years ago
Distances in space are measured in light-years. The distance from Earth to a star is 6.8 × 1013 kilometers. What is the distance
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I light year = 9.46 x 10¹² km

-------------------------------------------------------------------------------------
Find the number of light years
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\text {Number of light years = } \dfrac{6.8 \times 10^{13}}{9.46 \times 10^{12}}

\text {Number of light years = } 7.18

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Answer: The distance from Earth to the star is 7.18 light-years.
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8 0
3 years ago
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Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used. Match each equation with the operation yo
Tanzania [10]

The quadratic equations and their solutions are;

9 ± √33 /4 = 2x² - 9x + 6.

4 ± √6 /2 = 2x² - 8x + 5.

9 ± √89 /4 = 2x² - 9x - 1.

4 ± √22 /2 = 2x² - 8x - 3.

Explanation:

Any quadratic equation of the form, ax² + bx + c = 0 can be solved using the formula x = -b ± √b² - 4ac / 2a. Here a, b, and c are the coefficients of the x², x, and the numeric term respectively.

We have to solve all of the five equations to be able to match the equations with their solutions.

2x² - 8x + 5, here a = 2, b = -8, c = 5.                                                  x = -b ± √b² - 4ac / 2a = -(-8) ± √(-8)² - 4(2)(5) / 2(2) = 8 ± √64 - 40/4.     24 can also be written as 4 × 6 and √4 = 2. So                                                                                     x = 8 ± 2√6 / 2×2= 4±√6/2.

2x² - 10x + 3, here a = 2, b = -10, c = 3.                                                   x =-b ± √b² - 4ac / 2a =-(-10) ± √(-10)² - 4(2)(3) / 2(4) = 10 ± √100 + 24/4. 124 can also be written as 4 × 31 and √4 = 2. So                                                                              x = 10 ± 2√31 / 2×2 = 5 ± √31 /2.

2x² - 8x - 3, here a = 2, b = -8, c = -3.                                                    x = -b ± √b² - 4ac / 2a = -(-8) ± √(-8)² - 4(2)(-3) / 2(2) = 8 ± √64 + 24/4.     88 can also be written as 4 × 22 and √4 = 2. So                                                                             x = 8 ± 2√22 / 2×2 = 4± √22/2.

2x² - 9x - 1, here a = 2, b = -9, c = -1.                                                     x = -b ± √b² - 4ac / 2a = -(-9) ± √(-9)² - 4(2)(-1) / 2(2) = 9 ± √81 + 8/4.                                          x = 9 ± √89 / 4.

2x² - 9x + 6, here a = 2, b = -9, c = 6.                                                    x = -b ± √b² - 4ac / 2a = -(-9) ± √(-9)² - 4(2)(6) / 2(2) = 9 ± √81 - 48/4.                                                                             x = 9 ± √33 / 4

To match we solve the monomials.

1. -15u^3 + 5u^3

Adding

-15u^3 + 5u^3=-10u^3

2.  10u^3 +(-5u^3)

Adding

10u^3-5u^3=5u^3

3. 10u^3 + 5u^3

Adding

10u^3 + 5u^3=15u^3

4.  5u^3+ (-10u^3)

Adding

5u^3-10u^3 =-5u^3

Two separate ways to find the answers.

7 0
3 years ago
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Dvinal [7]

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Answer:

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Step-by-step explanation:

The scale tells you that ...

  17 cm on the scale drawing represent 1 mm on the actual object.

17 cm is larger than 1 mm, so the scale drawing is larger.

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3 years ago
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